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How to Play a Pair of 4s in Blackjack

When you are dealt a pair of 4s in blackjack you have three viable playing options:
・Split or
・Double down

Which blackjack strategy you should invoke depends upon what the dealer’s upcard is, the number of decks of cards being used, and whether double down after pair splitting is allowed.

The basic playing strategy for a double- or multi-deck game where doubling down after pair splitting is not allowed (NDAS) is to

・Always hit regardless of the dealer’s upcard

If the blackjack rules allow doubling down after pair splitting (DAS)

・You should split against a dealer’s upcard of 5 and 6

In a single-deck game, the basic playing strategy is

・If NDAS, double down your total of 8 against a dealer’s upcard of 5 and 6; otherwise hit
・If DAS, split against dealer’s upcard of 4, 5, or 6; otherwise hit

The following color-coded blackjack charts summarize the basic strategy for a pair of 4s.
(Note: P = Split; H = Hit; Dh = Double Down if allowed otherwise hit.)

Dealer’s Upcard

Dealer’s Upcard

Dealer’s Upcard

Dealer’s Upcard

Whether you should hit, split, or double down is based on one of these three criteria:

・You will win more money on average
・You will lose less money on average
・You will turn a losing hand into a winning hand on average

For example, suppose you are dealt a pair of 4s in a six-deck game with DAS and the dealer’s upcard is a 6. The basic playing strategy (shown in the above chart) states to split. The reason is because splitting has a greater positive expectation of winning than either hitting or doubling down. In other words, you will win more money in the long run by playing two hands, each starting with a 4, than by either hitting or doubling an 8 (i.e, a pair of 4s).

Here’s another example: suppose you are dealt a pair of 4s in a six-deck game with NDAS and the dealer’s upcard is a 3. Doubling and splitting have negative expectations whereas hitting has a positive expectation, making it the best play.

A final example is being dealt a pair of 4s in a single-deck game against a dealer’s 6 upcard. If the rules specify NDAS, all three viable playing options (hitting, splitting, and doubling) have positive expectations but doubling is more positive making it the better play.

If the playing rules allow you to resplit, then it is advantageous for you to do so. For example, if you were dealt a pair of 4s against a dealer’s 5 upcard with DAS, you should split. Suppose on the first 4, you are dealt another 4 on the draw. You should resplit to form a third hand. If the casino allows resplits up to a total of four hands, then you should resplit again if you are dealt another 4. Resplitting pairs is a player-favorable option that you should always take advantage of.

If the playing rules don’t allow you to double down on an 8, then you should hit (see single-deck chart above with NDAS).

You will always win more or lose less if you follow the above basic playing strategy for splitting, hitting, or doubling down on a pair of 4s.

For a complete basic playing strategy for any set of playing rules, consult Chapter 3 in the Ultimate Blackjack Strategy Guide.


1.Roulette starts with players making bets.
2.The croupier (or dealer) throws a ball into the spinning roulette wheel. Players can still makes bets within the process.
3.While the ball is rolling at the roulette wheel, the croupier/dealer announces: “No more bets.”
4.At that point players are not allowed making bets
5.The ball lands on a number in the roulette wheel. If there are winners who bet the number, section or color, they will be rewarded according of their betting odds.

Okay, getting on with it: The players buy in for chips (or bring chips to the table), then place their bets on any number or propositions:

・Inside bets are placed directly on one or more numbers
・Outside bets are placed on certain propositions such as high-low, odd-even, red-black, first, second and third dozen, etc.
・There are other combinations of bets that can also be made

Here are the bets at roulette and their edges (Do Not Fall Asleep!):



(French: En Plein)
You bet one or more numbers by placing your bet on that or those numbers on the layout. If your number or one of your numbers should hit you win 35 to 1 on that number. The house edges: American double-zero wheel, 5.26 percent; the European single-zero wheel, 2.70 percent.


(French: A Cheval)
This bet is placed on more than one number by placing your chip(s) on the line between two numbers. The payoff if either number hits is 17 to 1. The house edges are 5.26 for the American double-zero wheel and 2.70 for the single-zero European wheel.


(French: Transversal)
You’d think with all these titles for the bet that it would pay off at thousands to one. Nope. It is merely a bet on three numbers. You make the bet by placing your chips on the outside border of the three numbers. A winning bet pays off at 11 to1. The house edge on the American double-zero wheel is 5.26 percent and it is 2.70 percent on the single-zero European wheel.


(French: Carre)
The bet is that one of four selected numbers will win. The bet can only be accepted if the four numbers form a square and, of course, being clever someone named the bet the Square. The bet is placed on the intersection where all four numbers meet. A winning bet pays 8 to 1. The house edge on the American double-zero wheels is 5.26 percent and it is 2.70 percent on the single-zero European wheels.


Also known as “The Monster” or “The Beast”
This bet is only found on the American double-zero wheels. It incorporates five numbers: the 0, 00, 1, 2 and 3. A winning wager is paid at 6 to 1. The house edge (hold onto your heart) 7.89 percent! If you want to bet those five numbers you are better off just placing a chip or chips on each number and that will bring the house edge back down to 5.26 percent.


(French: Sixain)
You place this bet on the outside borders of the six numbers you wish to bet on. The bet pays off at 5 to 1. The house edge on the American double-zero wheels is 5.26 percent and it is 2.70 percent on the single-zero European wheels.



(French: Colonne)
You are wagering that one of the columns of numbers on the layout will have the winning number. You place this number at the bottom of the column that you think will win. A winning bet is paid 2 to 1. The 0 or 00 are not a part of either column so if these two show the wager is lost. The house edge on the American double-zero wheels is 5.26 percent and 2.70 percent on the single-zero European wheels.


(French: Douzaine)
The bet is whether one of a dozen numbers on the layout will hit. These are not a dozen consecutive numbers on the wheel; they are strictly layout numbers. You place this bet on First Dozen, Second Dozen or Third Dozen. You can bet two of the dozens. The payout is 2 to 1. Again the 0 and 00 will cause your bet to lose. The house edge on the American double-zero wheels is 5.26 percent and 2.70 percent on the single-zero European wheels.


(French: Impair et Pair)
To be placed on either the Odd or Even section of the layout. There are 18 odd numbers and 18 even numbers. Neither the 0 or 00 count for either bet and if one of them hits the house wins. The winning bet is paid even money which means one to one. The house edge on the American double-zero wheels is 5.26 percent and 2.70 percent on the single-zero European wheels.


(French: Passe et Manque)
This bet is placed on either the 1 to 18 or the 19 to 36 section of the layout. Once again if the 0 or 00 shows, the bet loses. Payoff is even money (one to one). The house edge on the American double-zero wheels is 5.26 percent and 2.70 percent on the single-zero European wheels.


(French: Rouge et Noir)
This is another even-money bet that you can pick the color of the number that will hit. The house edge on the American double-zero wheels is 5.26 percent and 2.70 percent on the single-zero European wheel.

Playing roulette looks easy; pick a number or some proposition such as red/black, bet it and then wait to see what happens. That is, of course, the essence of the game. But it is not actually how the game is played.

Roulette has rules about the following:

– how to get chips
– how to determine value of the chips
– when to bet
– how to bet that bet or those bets
– when you must stop betting
– how to handle other players at your table
– what happens if you win
– what happens if you lose
– when to start betting all over again

In many casinos the roulette chips are not the same as the chips used at the other table games (although those regular chips can be used at roulette). The roulette chips can be quite colorful.

In some European casinos the roulette chips are indeed the same as chips at other games and (boy! oh! boy!) the dealers better be sharp not to mix up the various players’ bets.

So you arrive at the table, take out your money and put it on the table when the game is between decisions. You tell the dealer how much each of your roulette chips will be worth, she indicates that amount on her “wheel” of chips, and then she parcels your chips out to you.
They now have the value you want them to have.


After you cash in you will notice that there is a “buck” or “puck” or small symbolled object sitting on the table. That object indicates which number was hit on the last decision. When the dealer removes it the betting begins.

Usually players make their own bets but the dealers will help players who can’t reach far enough to place the bet they want.


If you are betting straight up on the number(s) you just put your chip(s) on the number(s). If you are betting any of the proposition bets on the outside of the layout such as the even-money bets of red/black (French: Rouge et Noir), odd/even (French: Impair et Pair), high/low (French: Passe et Manque) you place these right on the proposition. These all pay 1-to-1.

The first, second or third dozen (French: Douzaine); the first, second or third column (French: Colonne), you will again place your wager exactly on the proposition. These bets pay 2-to-1.

Now here are some other bets and where you place them and how much they pay on a win:

Split Bet (French: A Cheval): If you want to bet two numbers next to each other place your chip(s) on the line between the two numbers. The win is 17 units per 1 unit wagered.

The Street Bet, or Three Number Bet or “Side Bet” or The Trio (French: Transversal): If you wish to bet on three numbers, place your wager on the outside border of the three numbers. A win pays off at 11 to1.

The Corner, the Square, the Four Number Bet (French: Carre): After three numbers comes? Yes, of course, four numbers! The numbers much form a square. Place the bet where at the intersection where all four numbers meet. A win pays 8 to 1.

The Five Number Bet: This bet (the worst of all roulette bets because it has the highest house edge of 7.89 percent) is place on the 0, 00, 1, 2 and 3. A win pays 6 to 1. This bet is also known as the “beast” or the “monster” or the “mother-in-law.”

The Line Bet, or Six Number Bet, or Sixline Bet (French: Sixain): Split Bet

(French: A Cheval): This wager is placed on the outside borders of six numbers. A win pays 5 to 1.


The dealer will spin the wheel, even as bets are being made, but at a certain point he will wave his hand over the layout and say, “No more bets.” From that point on (okay, guess) no more bets are to be placed.

Now some players, known as PITA’s (for pain-in-the as*es) will keep betting. At that point the dealer can disqualify those bets.

Most roulette players are nice people, as are no doubt you. But some of them are somewhat (how can I say this gently?) apelike. Since everyone places their own bets, and since multiple bets can be places on the same number or proposition, the apes have a tendency to push and shove other players to get their bets down. They will even knock over piles of chips – other players’ chips.

There is, of course, no need for such aggressive activities as dealers give roulette players plenty of time to make their bets.

You have three choices:

1. Ask the ape-man or ape-woman to please place his/her bets somewhat less aggressively because he/she has been knocking over chips and sometimes people. Chances are the ape-thing will just growl and continue on its way.

2. Tell the dealer to stop them. “Dealer, dealer, this creature over here is a beast and keeps bumping other players and knocking over chips.” The dealer might say something to them and maybe it will work.

3. Or, get up and go to another table.


When a number hits, the dealer will call out the number, (perhaps also the color, and whether it is odd or even, etc.). She will put the “puck” on the number and sweep the board of all the losing bets.

She will then pay the winning bets.


While the “puck” is in place on the winning wager, no betting can take place. When the winners are paid, the dealer will remove the puck and he’ll say something such as “You may now place your bets.” At this time you take your next shot at corralling Lady Luck.

If you follow these general rules you should enjoy your roulette experience. it’s fun to play roulette and people have played it for centuries. If you have never played roulette before why not give it a try? I think you’ll find it an exciting game. But again, follow the rules!

・The organization of numbers on the American and European wheels is different.
・There are 37 numbers on the single-zero wheel and 38 numbers on the double-zero wheel.
・The house edges on the single-zero wheel are smaller than the house edges on the double-zero wheel.
・On the American double-zero wheels, the house edge can go from 2.63 percent to 7.89 percent. The usual house edge on the American game is 5.26 percent.
・On the European single-zero wheels the house edge can go from 1.35 percent to 2.70 percent. The usual house edge on the European game is 2.70 percent.
・You can easily see that the European game is quite superior to the American game.

Like craps, roulette has a multitude of bets which I’ll discuss shortly. However the range of the house edges on roulette bets is not as great or as varied as the range in craps. On the American double-zero wheels, the house edge can go from 2.63 percent to 7.89 percent. The usual house edge on the American game is 5.26 percent.

On the European single-zero wheels the house edge can go from 1.35 percent to 2.70 percent. The usual house edge on the European game is 2.70 percent. You can easily see that the European game is quite superior to the American game.

The American wheel has 38 numbers and the payment for a winning bet is 35 to 1. In a fair game, one where the casino does not have the edge, the payout for the winning bet should be 37 to 1. In short, you bet 1 and you win 37. So you will lose 37 times but win once and the game is even; there is no edge for either the player or the casino. That is zero percent.

Casinos cannot make a profit on such a game, so they pay back less than the bet is worth, 35 units instead of 37 units. It keeps two units for itself. Just divide 2 into 38 and then multiplay the result by 100 and the house edge is 5.26 percent. (I will discuss the other house edges when I deal with the specific bets that come in with more or less than a 5.26 percent edge.) This 5.26 percent is the house edge on the inside numbers and the outside propositions such as red-black, odd-even and so forth.

The European roulette game as stated is better than the American roulette game, because of that single 0. There are 37 numbers and the casino pays back 35 to 1 for a winning bet. The casino is keeping “1” as opposed to the American casinos keeping “2.” Just divide 1into 37 and the house edge is 2.70 percent. (I will later explain the other bets that come in with a lower house edge than 2.70 percent.)

[Please note: The ball is spun one way around the ball track but the wheel is spinning the opposite way. These directions can be changed intermittently or after every spin.]

The house edges on roulette, especially the American double-zero wheels, are quite high. Going up against a 5.26 percent edge makes the game difficult to beat for an aggressive bettor even in the short run. That’s bad for the player.

On the other hand, the game is rather leisurely so that there are not hosts of decisions in a given hour. That’s good for the player.

Yes, the edge is high but the opportunity for that edge to wipe you out early is (somewhat) limited – assuming you have some discipline in your betting. If you are a wild gambler roulette can still be a dangerous game for you.

So what does a 5.26 percent house edge mean in terms of money? I realize this web site is international so I am going to use the word unit(s) as the unit of measure for money. For example, if I say this bet has a 2 to 1 chance against winning that means 2 units to 1 unit. You can change such units into your own particular currency.

A 5.26 percent house edge means that out of 100 units, the player’s expectation is to lose 5.26 units. In American dollars that means for every $100 wagered, the player stands to lose on average $5.26.

So here is a handy dandy chart of the units concerning the various bets in roulette:

Keep in mind that “even-money bets” merely pay even money, meaning one unit for one unit but the actual edge is 20 to 18 on the American wheel and 19-18 on the European wheel. Why? Because those zeros count against you.

Take notice of those two bottom bets in the chart? Consider that the good news and in one case, the very last line, the very good news.

Here’s why:

Some casinos give players who bet the outside even-money bets of red-black, odd-even, and high-low an added benefit: if the 0 or 00 hit, the bet only loses half its money. You will see in a moment what an amazing bargain that is.

This return is done in two ways: Surrender or En Prison.

For decades now, casinos in some parts of the United States have offered surrender on the even-money bets. If the 0 or 00 hits, the dealer takes half your bet and returns the other half.

Instead of facing a house edge of 5.26 percent, the even-money wagers now come in with a 2.63 percent edge. That reduces in half the casino’s hit on your bankroll. That’s good thing as it cuts your losing expectation in half as well.

You will find that some casinos outside the United States offer surrender. Now a word of warning: You don’t usually see a sign signifying this fact and it is best to ask the croupier, “Do you return half the even-money bets if the 0 (or 00) hits?”

On the European wheel a casino that offers surrender reduces the house edge to 1.35 percent – one of the best wagers in the casino!

When the 0 hits on European single-zero wheels, the even-money bet is locked up, neither won nor lost. It is, in a sense, put in prison.

Here’s an example: You bet black and the 0 hits. The black bet stays on the table for the next round. If black hits, you get your bet back; if red hits you lose your bet; if the 0 hits again, your bet continues to remain in prison.

En prison reduces the house edge to 1.35 percent on the European game, again making this wager one of the very best in the casino.


If you are an outside even-money bettor you will not find a better roulette game than one that utilizes either surrender or en prison. I recommend for straight-up players (pure punters) to seriously consider forgoing betting on individual numbers and move their bets to odd-even, red-black or high-low.

Why not take advantage of a good rule that reduces the house edge in half? If the casinos are giving you something good why be ungrateful for it? That makes sense to me. So there’s my not-too-subtle hint: bet the lowest house edge bets.

Many American casinos have special roulette chips of various colors for denominations that you don’t usually see in the rest of the casino. The player determines what his colored chips are worth and each player must have a distinct color.

In Europe this is usually not so and the typical casino chips will be the same at the roulette game. This can, at times, cause some confusion for the croupiers which might make players call them “horse’s asses.”

Now the croupier will indicate that players can make their bets and the bets are placed on the layout. At a certain point the croupier says, “No more bets” and all players must stop betting – except for the annoying players who just keep on betting.

Should someone place a bet after the dealer says, “No more bets,” the player’s hand is chopped off, leaving a bloody mess on the layout. (Sorry, no, the bet just doesn’t count.) The croupier usually calls “no more bets” after he has started the ball spinning in the groove that goes around and around the top of the wheel.


Many players love to watch the ball spin around the wheel and then land and bounce from pocket to pocket until it meets its final resting place. It is reminiscent of primitives anticipating that the wheel will tell them their futures, which it certainly will. Some modern tables have a video screen above the wheel so players who are too far away to see the actual wheel can watch it on a monitor.

It is now common to see a scoreboard that highlights which numbers have just been selected, usually the last 16 or 20. This allows trend bettors to figure out what trends they want to bet.

There are now also scoreboards that can tell you which numbers have come up on all the roulette tables being used in the casino!

The layout of the roulette wheel has nothing to do with the organization of the numbers on the wheels. Check out the previously pictured roulette wheels and you will see that the numbers are well spread out and not in numerical order. The players are generally interested in placing their bets on the layout (check layout design) without regard to how the numbers appear on the wheel, something of a mistake on their part as you shall see later on.

The casinos of the past knew that some wheels through age and use could form a bias, meaning certain pockets would tend to latch onto a ball more than other pockets (these were usually deeper pockets), or that the wheel could become slightly unbalanced allowing a certain section to hit more than other sections.

If players concentrated on the layout as opposed to the wheel’s design then all would be well with the world and the casino would continue to win – except that some players caught on and discovered they could read the wheels. Such players were able to “break the banks” of casinos!

Let’s take a look at the spacing of numbers first on the American double-zero wheels, and then on the European single-zero wheels.


・There are 38 numbered pockets for the ball to land in, 1-36 and 0, 00.
・Half the numbers are red; half are black and the 0 and 00 are usually green, although on some wheels these might be blue.
・You can see that directly (or almost directly) across from each even number is an odd number. Check out 34 and you will see that it is almost directly across from 33. Then look at 36 and it is across from 35.
・This is not, however, a perfect design since the numbers 18 and 19 are only separated by the number 33.
・Pairs of odd numbers alternate with pairs of even numbers except in the areas of the 0, which splits 2 and 28, and 00 which splits 27 and 1.
・The colors of the numbers match the color of the numbers on the layout. The colors only deal with one bet, the black or red.


・There are 37 numbered pockets for the ball to land in, 1-36 and 0.
・Half the numbers are red; half are black and the 0 is either green or blue.
・Some of the positions of the numbers are similar to the American wheel with an odd number being directly across from an even number such as 27 across from 28 but this does not prevail throughout the wheel.
・The colors of the numbers match the colors on the layout; again this is used for one bet, the red and black.

・The layout where players make their wagers is not the same as the distribution of the numbers on the actual wheels.
・The layout is done in numerical order; the wheel is done by splitting up the numerical order.
・Inside bets are placed directly on one or more numbers.
・Outside bets are placed on certain propositions such as high-low, odd-even, red-black, first, second and third dozen, etc.


Question 1: What is the house edge on roulette?
On a 37 to 1 wager the payback for a winning bet will not be 37 units for 1 unit wagered but 35 units to 1 unit. The house edge on that is 5.26%. On the European wheel the payout will be 35 units to 1 unit instead of 36 units to 1 unit for a house edge of 2.70%.

Question 2: What is the difference between the arrangement of numbers on the wheel and on the betting layout?
The numbers on the layout are done in numerical order, 1 through 36 with the 0 or 00 being at the top of the layout. The numbers are not laid out that way on the wheel. Instead they are staggered, usually on opposite or near opposite sides.

Question 3: Why is the five number bet also called “the beast”?
The five number bet is called “the beast” on the American wheel because the house edge is 7.89% – the highest edge at the game

Question 4: What happens when a casino allows surrender?
If a 0 or 00 hits, half of the even-money bets of red/black, high/low and odd/even are returned to the player. This reduces the house edge in half at the game.

Question 5: What happens when the casino allows en prison?
En prison also reduces the house edge in half. If the 0 hits, the even-money bet is locked up for the next round. If it hits on the next spin the bet is returned to the player; if the opposite proposition happens, the bet is lost. Another 0 and this procedure occurs again.

Question 6: Translated into money what does a 2.70% and a 5.26% house edge actually mean?
The house edge of 2.70% means a player is expected to lose on average 2.7 units of every 100 units he bets.A 5.26% means the player will lose 5.26 units of every 100 units he bets.

Question 7: What is an “inside” bet?
An “inside bet” is any bet directly on the numbers.

Question 8: What is an “outside proposition” bet?
An “outside proposition bet” is any bet on the various propositions that ring the layout including the even-money bets.

Question 9: On even-money bets what is the likelihood of your proposition hitting on the American wheel?
An even-money bet on the American wheel will win 18 times and lose 20 times.

Question 10: On even-money bets what is the likelihood of your proposition hitting on the European wheel?
An even-money bet on the European wheel will win 18 times and lose 19 times.

How To Win at Slots | The Ultimate Slot Machine Guide

Slot machines are games with odds based in math, just like all other casino games. But few players understand just how those odds work, and whether they can do anything to improve their odds.

The objective of this chapter is to introduce you to how slot machine odds work and what that means to your chance to win at slots.

・Slots machine results are as random as humans can program a computer to be.
・Odds of the game are set so the house will have an edge
・Except in rare cases, slot machines are not games of strategy

Casino games make money for the house by paying less than the true odds of winning the bet. On table games, that can be relatively simple. At double zero roulette, for example with numbers 1 through 36 plus 0 and 00, the true Roulette odds against any specific number are 37-1, but the house pays single-number winners only 35-1.

Slot machine odds work in a similar fashion to the roulette example, except there are many more possibilities on the slots. There are thousands, and sometimes millions, of reel combinations. There also is an open field for game designers to assign how much each winning combination pays. The number of winning combinations and the payoffs per winner work together to determine a game’s odds.

The sheer number of possibilities makes the math that goes into slot machine odds more complicated than on table games.

・On early three-reel slots with 10 symbols per reel, there were 1,000 possible combinations (10 x 10 x 10).
・If blank spaces between lines are used as stops, the number of combinations increases to 20x20x20, or 8,000.
・With bigger reels holding 20 symbols and 20 spaces, combinations increase to 40x40x40, or 64,000.

The change to virtual reels enabled programmers to make the reels to behave as if they had any number of stops. With 100 stops on each of three reels, there are 1 million combinations. The Megabucks three-reel slot that paid the world record jackpot of more than $39 million has about 50 million combinations. Most modern video slots have five video reels can be as long as the gamemaker needs them to be. With 100 symbols on each of five reels, there are 10 billion combinations.

To see how slots pay less than true odds to give the house an edge, let’s set up an example that’s as streamlined as slot odds can get, a game of the type used in the early decades after Charles Fey invented the three-reel slot machine in 1895. A hypothetical three-reel slot game with one 7, two bars, three cherries and four watermelons per reel would have 1,000 possible combinations and return 83.2 percent to players with this pay table.

・Each of three reels has 10 symbols. Each reel has one 7 – that’s the top jackpot symbol.
・Each reel also has two bars, three cherries and four watermelons.
・There are 1,000 possible three-reel combinations – 10 symbols times 10 symbols times 10 symbols.
・Only one combination – or 1 x 1 x 1 – will be three 7s.
・Eight combinations will be three bars, 27 will be three cherries and 64 will be three watermelons.
・900 of the 1,000 combinations mix different symbols.

If the game paid at true odds, then the payoffs would be set up so that each 1,000 coins wagered would bring 1,000 coins in payoffs. One way to do that would be to have payoffs of 170 coins on three 7s, 30 on three bars, 10 on three cherries and 5 on three watermelons. But the casino must have an edge, or it couldn’t pay the bills and offer the game. So instead it pays 160 on three 7s, 25 on three bars, 8 on three cherries and 4 on three watermelons. Multiplied by the frequency of wins, those payoffs total 832 coins. By paying less than the true odds of the game, the machine has a payback percentage of 83.2 percent, or a little less than today’s 1- cent games.

Modern slot machine or online slots odds work in much the same way, except that the math is more complex for several reasons:

・Random number generators work from much larger number sets, leading to exponentially greater possibilities.
・Many more than four reel symbols are actually used.
・Most modern slots have more paylines than the one line in the sample slot above.
・Game programmers have to account for the effect of bonus events.

In the classic WMS Gaming video slot Super Jackpot Party, there are eight reel symbols that form winning combinations, plus the noisemaker and party guy symbols that launch a bonus event. All of the symbols need to be assigned sets of random numbers, and payoff values assigned to three-, four- and five of a kind winners. That makes calculations much more complex than in our example game above.

The number of paylines also complicates the math. Even if there’s only one jackpot symbol on each reel, a 30-line game means there are 30 chances to line up those symbols in a winning combination, instead of just one. So it goes for every possible combination – programmers have to account for each combination 30 times.

As for bonus events, nearly all modern slot machines have events in which regular play stops, and with no further wagers, you get a spin of a bonus wheel, a pick’em event, free spins or some other extra. Bonus event payoffs have to be included in the calculation of the game’s overall return.

We can’t see the random numbers being generated, and it’s those numbers that really determine whether we win. In fact, there’s a list of things we can and can’t see that are important to our chance of winning.

・We can’t see the odds of the game.
・We can’t tell if one machine is higher paying than another.
・We can see a machine’s pay table, and that gives us a clue to volatility.
・We can see what kinds of bonuses are offered, and that also is a volatility clue.

Casinos don’t post payback percentages on individual games, and there’s no way for a player to calculate the odds since all the random number details are regarded as proprietary and not revealed. Even on different machines with the same game, we don’t know if the paybacks are the same. Game manufacturers make several versions of the same game available to casino operators, and each version has its own payback percentage. Two machines can look identical, but have different payback percentages.

However, a machine with a large top jackpot gives back less on smaller wins than a game with a smaller top prize, and that means the big jackpot games usually are more volatile. That’s not always the case – the big jackpot can be rare enough that the game still has a normal percentage of lower payoffs, but it’s a starting point.

In addition, games with free spin bonuses are more volatile than games with pick’em bonuses. Volatility matters in choosing what you want out of a game. Are you the type of player who wants to maximize chances at a really big win and are willing to accept that fast, bankroll-eating losses are part o f the game? Then you want a high-volatility game.

Would you rather have a game that gives frequent small wins and extends your playing time, but rarely pays big? Then you want a low-volatility game. But regardless of whether the game you choose has high volatility, low volatility or something in between, you can be sure the house has taken an edge with payouts that are less than the true odds of winning your bet.

・Casinos have an edge on slot machines because winners are paid less than true odds.
・Slot odds are mathematically complex because of the number of possible outcomes and the different paybacks per winner.
・You can’t look at a slot game and tell the odds. In fact, two identical-looking games can have different odds.
・Looking at a machine can give you a clue as it its volatility, and that can help in choosing a game.

When a casino buys a slot machine from a manufacturer, it can choose from a variety of targeted payback percentages. The manufacturer might make the same game available in 87-, 89-, 91- and 93-percent versions, and it’s up to the operator to choose which works best in game mix and for its competitive position.

That the games have targeted payback percentages in their programming leads to misconceptions from players. A common theme in my email over the last 20 years has been, “How can games be both programmed and random? The programming must keep them on track for the percentage.”

The short answer is that slots are programmed for a target percentage in the same way table games are: Odds of the game are set so they will naturally lead to an expected payback percentage.

Let’s use roulette as an example, because the math is uncomplicated.
・A double-zero roulette wheel has 38 numbers – 0, 00 and 1 through 36.
・The odds against any specific number coming up on any spin are 37-1.
・The casino pays only 35-1 on any winning single number.
・The two-unit difference between 37-1 odds and 35-1 payoffs is kept by the house.
・Divide that two-unit difference by 38 possibilities and you get 0.0526, for a 5.26- percent house edge.

In that way, roulette is “programmed” so that in the course of thousands of wagers, the house will keep 5.26 percent. Results can be random. The same number can turn up three or four or five times in a row. But over time, the odds of the game lead to that percent-edge.

What if instead of reels with symbols and results driven by a random number generator, we set up a slot-like game with slot-like payoffs by using a series of roulette-like wheels?
・Let’s say we line up three roulette-type wheels, each marked into 100 segments.
・We mark each segment with a slot symbol. Each wheel gets one 7, five bars, 10 cherries and so on.
・We have a dealer spin and drop a ball on each wheel.
・The total number of three-wheel combinations is 100x100x100, or 1 million.

That’s the same number of possible combinations you’d get on a slot machine if the random number generator was working with sets 100 numbers for each reel.

From there, it’s easy to calculate the number of possible combinations that have the ball landing in the same symbol on each wheel. For the 7, since there is only one on each wheel, it’s 1x1x1 – there is only one three-7s combination. For bars, it’s 5x5x5, or 125 out of the million total combinations. For cherries, it’s 10x10x10, or 1,000 three-cherry combos.

Note that we’re not using computer software here. We’re using physical equipment, but it’s giving us the equivalent of “programmed” combinations and odds. That’s just how the odds work on modernized computerized slot machines. They don’t force a game to pay an exact percentage, they just let the normal odds of the game drive long-term results to an expected percentage, the same way table games do.

The notion that slots are both programmed and random can be difficult to fathom. Confusion over slot programming has jammed my email box for years. Here are some of the questions readers ask most often.

A. “Random results” is not the same as saying “equal results.” A game doesn’t have to be programmed so that a jackpot symbol shows up as often as a blank space, or a bonus symbol as often as a cherry.

The odds of the game are set so that blank spaces will show up more often than winning symbols and small winners will show up more often than big winners. On three-reel slots, that will lead to there being more losing spins than winners, and on five-reel video games it will lead to more “wins” for amounts less than the size of your bet than bigger winners. The programmer sets the odds of the game, and then lets random chance take its course.

A. Streaks are a normal part of the probability of the game. Let’s take a three-reel game with a 12% hit frequency — you’ll have a winner an average of once per 8.333 spins. On your first spin, there’s an 88% chance it’ll be a loser. There’s a 77% chance you’ll lose two in a row, 68% chance you’ll lose three in a row, and so on.

At 20 in a row, there’s still a 7.8% chance of every spin being a loser. That’s easily within normal probability. Anyone playing a machine with a 12% hit frequency for very long will have streaks of 20 or more losses.

A. Your choices do make a difference in pick’em-style bonus events, but not in any way you can predict or control. The programmer knows that over a very long time, the bonus even will yield an average payback.

Let’s make up a simple slots bonus event, in which you pick one of three symbols to reveal a bonus award. If you touch one symbol, you get 25 credits, if you touch a different one, you get 50, and if you touch the other you get 75. You don’t know which symbol hides each award, so your results are random. However, over a very long time, you’ll get each award about a third of the time, so will average 50 credits.

The programmer can build that average into calculations for the payback percentage. You have a random result contributing to odds that drive paybacks into a long- term average – the same as on the reel-spinning part of the slot game, and the same way table games work.

・Slot machines have targeted payback percentages built into their programming, but results are random.
・Programmed percentages on the slots work in the same way as percentages on the tables – the odds of the game lead to expected returns.
・Random results are not the same as equal results. Odds are set so big winners turn up less often than other combinations.

With some rare exceptions, Las Vegas-style slot machines with random number generators are not designed to be tests of skill. There is no strategy that can overcome the house edge.

Games are not beatable in the long run. There could be a change coming as both brick-and-mortar casinos and online operators try to reach out to the Millennial generation. The State of Nevada legalized fully skill-based electronic games in 2015, and it’s expected some games will make their way onto casino floors in 2016. In some international markets, skill already is part of the mix. Japanese pachinko parlors offer games known as pachisuro, a blend of slot game play and traditional pachinko, and skillful play may improve your results. Still, Las Vegas is the trend-setter in slot development, and its random number generator slots are designed to so the house can count on its edge. Even so, a few beatable games have made it to casino floors.

In the mid-to-late 1990s there were a flurry of games where you could collect coins or symbols on a video screen until you reached a trigger point for a bonus award. Players in the know could look for machines that were already part way toward slots free bonus territory, and play only when enough of the trigger was completed to give the player an edge. Such games are rare today.

In a casino with older equipment, you still might spot such games occasionally.

Here’s how they worked:

Piggy Bankin:

This WMS Gaming three-reel slot was the banked bonus trend-setter. Piggy Bankin’ had a Dotmation screen in the top box, above the mechanical reels. Every time the reels showed three blank spaces, a coin was added to a piggy bank animated in orange dots. When the Break the Bank symbol landed on the payline, an animated hammer broke the bank, and the player collected the amount displayed. It was soon discovered that if you played only with enough coins in then bank, you had an edge.

Racing 7s:

Before taking a full plunge into video, IGT had its “Vision Series” with a color LCD panel in the top box. Racing 7s featured red, white and blue 7s on a track. Each time a corresponding 7 would land on the payline in the main game, that color 7 would move a notch closer the finish line. To get an edge, you looked for a screen with 7s already close to the finish and a bonus payout.

Fort Knox and Buccaneer Gold:

Silicon Gaming, no longer in business, offered several games with banked bonuses.

On Fort Knox, if five numbers in a 10-digit code had already been solved through reel spins, you had an edge. Once the full code was solved, the vault would open for your bonus. In Buccaneer Gold, the object was to collect five daggers sticking in the ship’s rail. If there already were three or four daggers when you started, you had an edge.

S&H Green Stamps:
This was Bally Technologies’ entry into the banked bonus field. During play, you’d collect Green Stamps as they landed on the video reels. If you filled a book of 1,200 stamps, you’d go to a slots bonus event. The trick was to look for machines with 600 stamps or more already in the book. At that level, the player had an edge. In casinos with all new equipment, you won’t find these games. In casinos with older equipment, it’s possible. More important than the specific games is that you understand that if you ever see such a build-a-bonus, banked game, starting close to the finish improves your odds.

A number of players over the years have told me they beat the slots by looking for larger than usual progressive jackpots. It’s a method that works better on video poker where the house edge on the base game is smaller than on the slots. Slot payback percentages are low enough that even what looks like an oversized jackpot may not be enough to overcome the full house edge. Still, if you always wait to play a game until its jackpot is a certain size, you will be playing a game with a lower house edge than if you played for lesser amounts.

Here’s the method a jackpot-hunting player relayed to me:
・She starts by making daily rounds and charting jackpot amounts on different machines.
・Of the machines she tracks, she notes the payoff amount when someone wins the jackpot.
・Over many readings, she gets an idea of the average size of the jackpot when it hits.
・She then plays only when the jackpot reaches that average. For example, if the jackpot starts building from a $1,000 base and her chart of dozens of jackpots or more shows it hits at an average of about $2,500, then she starts playing the game only when the jackpot is $2,500 or more.

If you’re going to play such games anyway, there’s no harm and some gain in delaying your play until the jackpot exceeds a targeted amount. However, profits are not guaranteed.

・Knowing the average size of the jackpot does not tell you the break-even point.
・There is no guarantee that you’ll be the one to hit the jackpot.
・Waiting for the jackpot to be a certain size does not increase your chances of winning the jackpot.

Let’s expand on that a little. Imagine a game where the jackpot usually hits at about $2.500. Unbeknown to you, the jackpot has to reach $5,000 before the game’s return reaches 100 percent. That means even if you start playing only when the jackpot is $2,500 or more, you still are playing a game on which the house has an edge. Waiting does ensure that when you do hit the jackpot, your average payout will be higher than if you started playing at the base level.

So if you’re jackpot hunting, good luck, but be aware there are pitfalls as well as big rewards.

Chapter 5, BONUS EVENTS, will deal more extensively with skill-based events. For now, understand that even though fully skill-based gaming has not yet launched in Nevada, there are games with skill-based bonuses. Among those marketed in recent years are IGT’s Centipede, where you play a version of the old arcade game in your bonus event, and GTECH’s Zuma, based on the popular online game.

Though your skill makes a difference in these games, they are not beatable slots. Even if you’re a Centipede grand master, the house still has an edge. With some variation by jurisdiction, a maximum of 4 percent of a game’s overall payout can be based on skill, and the house edge is high enough that getting the full 4 percent will not take you into profitable territory.

・As games that are not strategy-driven, most slot machines are not beatable in the long run.
・Banked bonus games offer an opportunity to get an edge, if you see that you’re already part way toward triggering a bonus.
・There might be profit opportunity in games with progressive jackpots, but there’s no certainty.
・Your skill matters in skill-based bonuses, but expertise doesn’t give you an edge on the games.

Question 1: Does the house gets an edge on slots by blocking winning combinations?
No. The house gets an edge by paying less than the true odds of winning on slots.

Question 2: On a mechanical slot with three reels and 10 symbols on each reel, how many possible three-reel combinations are there?
1,000 possible combinations.

Question 3: How many reel combinations are possible on modern slots with video reels or virtual reels?
Slots can be programmed with any number of slots on a virtual reel or video reel, so there can be as many reel combinations as the game designer needs.

Question 4: Do identical-looking machines always have the same payback percentages?
No, identical-looking machines don’t always have the same payback percentage. You can’t tell a game’s odds by looking from the outside.

Question 5: Do the slot payback percentages are “programmed” only in that the odds of the game are set to lead to a desired payback percentage?
Yes. Slot payback percentages are “programmed” only in that the odds of the game are set to lead to a desired payback percentage.

Question 6: Does randomness mean all symbols must turn up on an equal portion of spins?
No. Results can be random while still setting the odds so some symbols occur more often than others.

Question 7: Do long winning or losing streaks defy the odds of the games?
No. Long winning or losing streaks are part of normal probability.

Question 8: On most slots, is there an opportunity to overcome the house edge and be consistently profitable?
No. Most slots do not offer an opportunity to overcome the house edge and be consistently profitable.

Question 9: What is a “banked bonus”?
A banked bonus is an event in which you collect representations of coins or symbols until you have enough to trigger a bonus event.

Question 10: Does waiting until a progressive jackpot reaches a certain size increase your chances of winning the jackpot?
No, until a progressive jackpot reaches a certain size does not increase your chances of winning the jackpot, but it increases your average payout when you win the jackpot.


1.After all bets are made at the Baccarat table, two hands are dealt consisting of two cards to each hand (known as the player hand and the Bank Hand)
2.The objective is to guess which hand will have a total closest to 9
3.Players can wager on the Bank Hand, player hand, or on the tie bet
4.Face cards and tens have a count of zero, and aces count as one. All other cards count their face value
5.If the count of a hand exceeds 9, the total is adjusted by subtracting 10.
6.There are house rules that determine whether the bank or player hand receives a third draw card. (there is a maximum of three cards per hand.)
7.Players who wager on a winning player hand receive a 1 to1 payoff
8.Players who wager on a winning Bank Hand also receive a 1 to 1 payoff but must pay a 5% commission (including the 5% commission, the payoff odds are 19 to 20.)
9.The payoff odds for a winning tie bet are 8 to1

Most everyone remembers the famous image of secret agent James Bond playing the casino game of Baccarat (pronounced bah-cah-rah) in the popular James Bond novels and movies. Although the game appears serious and elegant (and intimidating to average players), it’s actually as simple to play as betting on a flip of a coin; and, get this, the house edge is one of the lowest in the casino.

The casino game of Baccarat is based on the Italian game of baccara. The Italian word “baccara” simply means zero, and the latter refers to the fact that in baccarat, all the picture cards and tens have a value of zero.

Baccarat was first played in the 1400s in Italy and France. During the reign of King Louis XIV (1643-1715), Baccarat was one of the most popular games played by French royalty. Even though public gambling became illegal in France (in 1837), Baccarat continued to be played in the homes by the elite and common folks. This kept the game thriving for many years until it appeared again in casinos that sprang up on the Riviera (circa. 19th century). It eventually became the premier game in European casinos.

Over the years, there have been several versions of the game:
・American Baccarat (also known as punto banco)
・Chemin de fer (also known as Chemmy)
・Baccarat Banque

The above versions of Baccarat have virtually the same rules; the major difference is how the cards are dealt. (I’ll explain the details of each game in Chapter 2.)

Punto Banco made its debut in Las Vegas on November 20, 1959, thanks to professional gambler Tommy Renzoni, who convinced the management at the Sands casino to try it. Renzoni had previously introduced the game at the Capri casino in Cuba, saw how popular it was, and after he made a few modifications to the game, knew it would be a big hit in Las Vegas. He was right; after the Sands started offering Punto Banco, more casinos began offering it on the Strip and downtown casinos, more players were playing it, and the game’s popularity took off.

Many American players feel intimidated by Baccarat, mistakenly believing it’s a game played by high rollers wearing formal attire in a separate part of a casino (known as the high-limit pit). That’s unfortunate because there is a low-stakes version of the game (Mini-Baccarat) that is usually played in the main casino on a blackjack-sized table. (See below for details on mini- and Midi-Baccarat tables.)

Why play Baccarat? The game has these advantages:

・Playing rules are easy to learn
・Game offers even an inexperienced player one of the best odds in a casino
・No matter your betting level, you can usually find high- and low-stakes versions of the game in a casino
・Baccarat is also available in online casinos

Regardless of the number of players, only two hands are dealt in Baccarat: the Bank Hand and the Player Hand. Before the cards are dealt, you place a wager with chips (also called checks) on which hand will come closest to a total of nine. You can wager either on:

・The Bank Hand
・The Player Hand
・A tie (meaning, both hands will have the same total)

(Note: You could wager on any combination of the above if you wanted to, such as a bet on the Bank Hand and another bet on the Tie.)


A winning bet on the Player Hand is paid at 1 to 1. For example, if you bet $10 on the Player Hand and it wins, you would receive $10 in winnings.

A winning bet on the Bank Hand is paid at 1 to 1 minus a 5% commission on the winning bet. This is equivalent to a 19 to 20 payoff, meaning if you wager $10, you would win $9.50. (The reason you pay a commission on only the Bank Hand will be discussed shortly.)

A winning bet on the Tie is usually paid at 8 to1, meaning if you win, you receive 8 winning chips and you get to retain the original 1 chip wagered on the Tie. For example, if you wager $10 on the Tie and it wins, you would receive $80 in winnings and retain the original $10 wager. If there is a tie, a bet on the Bank or Player Hand is a push, meaning neither hand wins or loses. After a tie, you can remove or add chips to either wager, switch wagers, or just remove your chips and not bet.

(Note: Some casinos state a 9 for 1 payoff for a winning bet on the Tie. This means they pay you 9 chips but keep the original 1 chip you wagered. A 9 for 1 payoff is equivalent to an 8 to1 payoff.).

Baccarat is usually played with mostly eight decks of cards (and sometimes six decks) that are dealt from a dealing shoe. Every card has a numerical value (see table on the right), and card suits have no relevance in Baccarat.

The values of the cards are as follows:
・Tens and picture cards (Jack, Queen, and King) have a numerical value of 0
・Aces have a numerical value of 1
・2s through 9s have a numerical value equal to their face value.

The highest total a hand can have in Baccarat is 9. (A hand can’t “bust” if it totals greater than nine.) If the numerical value of the cards in a hand exceeds a total of 9, then you can do either of the following to arrive at the adjusted total of the hand:
・Drop the first digit of the sum
・Subtract 10 from the total

Here are some hands and their adjusted totals:

In the first hand, the sum of the value of the cards is 15. Since a hand in Baccarat can’t exceed a total of 9, either drop the first digit (the 1 in 15) or subtract 10 (15 minus 10) to get the adjusted total of 5. (Either way you do it is up to you; just be consistent.)

The second hand above totals 14 (8 + 6 = 14). If you drop the first digit, or subtract 10, you arrive at the adjusted total of 4.

There are three sizes of Baccarat tables:

1.Full-size Punto Banco Baccarat

The rules for playing are the same; the differences are the number of players, how the cards are dealt, and the minimum and maximum betting limits.


Also known as Big Baccarat, the full-size Baccarat table is located in a high-limit pit (or sometimes in a Baccarat room). The tables can accommodate up to 14 players, and the betting limits are often the highest in the casino (e.g., in casinos on the Las Vegas Strip, the betting range is usually $100 minimum bets up to $100,000 maximum bets). Players traditionally handle the cards; the biggest bettor on the Bank Hand gets to turn over the Bank cards, and the biggest bettor on the Player Hand turns up the Player cards. Three dealers staff the table. Big Baccarat caters to high-end players (i.e., high rollers or whales), who sometimes wager thousands of dollars on each hand. Casinos also tolerate these players when they occasionally bend, crumble, crush, and even tear in half the cards in the process of peeking at them before turning them up. (Because of this, fresh decks of cards are introduced into play before each shuffle.)


Mini-Baccarat is a low-stakes version of the big Baccarat game. Mini-Baccarat tables are located in the main casino next to the blackjack tables, and they can accommodate up to 6 or 7 players. Minimum betting limits are usually $5 to $15, with a maximum betting limit of up to $5,000. The table has only one dealer, and unlike the big Baccarat table, players are not allowed to handle the cards (the dealer deals the cards). Because of the latter rule, the game is much faster than the big Baccarat version (over 200 hands dealt per hour vs 40-70 for big Baccarat).


Midi-Baccarat tables have seats for up to 9 players and are staffed by one dealer. Since players like to handle the cards, Midi-Baccarat was designed to allow this. (However, casinos don’t tolerate players bending or crushing the cards.) The game can be found in either the high-limit room or in the main casino. Midi-Baccarat isn’t as fast as Mini-Baccarat but casinos can usually deal more hands per hour than the big Baccarat game. The betting limits are lower than the latter but higher than Mini-Baccarat tables (e.g., $25 up to $10,000).

By way of an example, I’ve summarized below how the cards are dealt on the Big Baccarat table (also known as the full-size table).

After the dealer shuffles a fresh pack of eight decks of cards, she will ask one of the seated players to insert the cut card somewhere into the stack of eight decks. (By doing this, the casino is allowing the customer to establish the starting point for the dealing of the cards.) The dealer will cut the cards so that the card following the placement of the cut card by the customer is at the top of the stack of cards (and will be the first card dealt from the shoe). The dealer then counts 15 cards, beginning with the last card in the stack of cards, and inserts a cut card. (When this cut card appears in play, the round in progress is completed and then the game is paused while a fresh set of eight decks is put into play and shuffled.) The eight shuffled decks are then placed into the dealing shoe and the dealer will remove the first card and turn it over. The face value of the card determines how many additional cards are “burned” or removed from the shoe. For example, if the first card was a six, then the next six cards are removed from the shoe and burned. If the first card was a ten, then ten cards are burned. All the burned cards (and subsequent discards) are dropped by the dealer into a discard bowl located under the table through a slot located in the middle of the table.

A full-size Baccarat table has room for up to 14 players. The table layout (see below) has each seat numbered from #1 through #15. (Usually, the unlucky number 13 is not displayed on a Baccarat layout; likewise, the number 4 is often not displayed because in some Asian cultures, the number 4 represents death.) In front of each player there is an area (or box) on the layout for placing your chips on the Player Hand, Bank Hand, or the Tie. (See diagram below.)

Three casino dealers direct the game. One dealer (the Caller) is positioned in the middle of the table (where the cards for the Player and Bank Hands will be placed). The Caller’s job is to direct the flow of the game and call the winning hand. The other two dealers are positioned next to each other and located opposite the Caller. Their task is to collect the losing bets and pay off winning bets from players seated on their half of the table, and they also keep track of all the commissions owed by players on winning Bank Hand bets.

Traditionally, players had the chance to deal the cards on the full-size Baccarat table; however, nowadays the Caller will deal the cards from a shoe and then give the cards to the player using a device known as a paddle. The initial two Player Hand cards are given to the player who made the largest wager on the Player Hand. This player looks at the two cards and then tosses them to the Caller, who places the cards on the layout labeled PLAYERS and then announces the total of the hand (e.g., Player shows 6). This procedure is repeated with the Bank Hand, with the player with the largest wager on the Bank Hand getting to look at the two cards before tossing them to the Caller, who announces the total of the Bank Hand (e.g., Bank has 3). If one or both hands require a third card, the Caller will give the draw card to the same player (via the paddle) to look at and then toss back to the Caller. The Caller will announce the winner (e.g., Bank Hand wins 7 over 5). The dealers will then collect the losing bets, pay off the winning bets at even money (except the Tie bet, which wins 8 to1), and in the case of a winning Bank Hand, place a marker indicating the 5% commission owed into the players’ commission boxes (located in front of the two dealers … see diagram). For example, if the player in seat #3 wagered $20 on Bank Hand and it won, the players wins $20 and the dealer places a $1 marker in the #3 commission box.

Note: In casinos where the rules still allow players to deal the cards, the procedure is as follows. After the shuffle, the player in seat #1 is given the shoe. When directed by the Caller, this player will deal the first card to the Caller, the second card is placed under the front corner of the shoe, the third card is dealt to the Caller, and the fourth card is placed under the front corner of the shoe. The two cards dealt to the Caller represent the Player Hand; the two cards under the corner of the shoe is the Bank Hand. The rest of the procedure follows the rules above. (The player with biggest wager on Player Hand gets to look at the two cards comprising the Player Hand and same for player with largest wager on Bank Hand. The Caller will tell the player holding the shoe when to deal a third draw card to one or both hands.) As long as the Bank Hand keeps winning, the same player retains the shoe. When a Player Hand wins, the shoe is passed to the next player. (Any player can refuse the shoe so you don’t have to deal the cards if you don’t want to.)

At Midi-Baccarat tables, the dealing procedure is the same as the above, with the dealer dealing the cards from the shoe and the players given the cards to look at and then face. At Mini-Baccarat tables, the dealer deals the cards and faces them (players are not allowed to handle the cards). Regardless of which size table you play, the playing rules and payoffs are the same.

Four things to keep in mind when you play Baccarat:
1.If you want, you could play at any Baccarat table alone; it’s not necessary to have more than one player to play the game
2.You are expected to pay off your markers in the commission box, either at the completion of the shoe, or when you are ready to leave the table. You could pay off your commission markers at any time, but since this transaction slows down the action, it’s frowned upon. It’s best to wait until the end of a shoe (or when you quit playing) to pay what you owe, rather than pay off the markers every time you win a Bank Hand, or several times during the playing out of a shoe.
3.It’s important not to lose all your money when playing Baccarat; otherwise, you won’t be able to pay off your commission markers. (that could be embarrassing.)
4.If the bank and Player Hands have the same total, any player wagering on the tie receives an 8 to 1 payoff and all bank and Player Hand wagers push (meaning, the wagers don’t win or lose)


As I mentioned above, sometimes one or the other hand will require a third card. The third card draw rules often confuse players, which is another reason they shy away from playing Baccarat. Listen up:Baccarat is not like blackjack where you have to memorize a bunch of rules to know when to stand or hit. Nope, because when you play Baccarat, players have no playing options. There are standard house rules that determine when the Player Hand needs a third card and ditto for the Bank Hand. Moreover, it’s up to the Caller to determine which hand requires a third card. However, you will enjoy the game better if you have some familiarity of the third card draw rules, which I’m about to cover.


The criterion that determines if the Player Hand receives a third card is the total of the initial two cards.

・Player hand draws a third card if the initial two cards total 0 to 5.
・Stands on a total of 6 through 9.

Notice that it makes no difference what the initial two-card Bank Hand totals or whether the Player hand is “beating” the Bank Hand as far as the third card draw rule. The rule is quite simple:

・If the sum of the two cards is 0 to 5, it draws a third card
・If the sum is 6, 7, 8, or 9, it automatically stands.

Now is a good time for me to explain what happens when the Player or Bank Hands initial two cards total 8 or 9. A total of 8 and 9 in Baccarat is known as a “natural” and when this occurs, neither hand can draw a third card. (A total of 9 is the highest total you can get in Baccarat, much like 21 in blackjack; the 8 is the second highest hand.)

Here are a few examples of Player Hands and whether they stand or draw:

The third card rule for the Bank Hand is slightly more complicated than the Player Hand. But keep this in mind … it’s not necessary to memorize the following rules if you don’t want to because the Caller is paid to know them and he will determine when it’s necessary that one or both hands should receive a third card.

The rule for the Bank Hand drawing a third card depends on three criteria:
・Total of the initial two card Bank Hand
・Whether the Player Hand stood or drew a third card
・What the value is of the Player Hand’s third card

Here is a summary of the Bank Hand Third Card Rules:
Rule #1: Bank Hand draws if the initial two cards total is 0, 1 or 2.
Rule #2; Bank Hand stands if the initial two cards to either the bank or Player Hand total 8 or 9 (natural).
Rule #3. Bank Hand stands if the initial two cards total 7.
Rule #4. Bank Hand stands if the initial two cards total 6 and the Player Handdid not draw a third card. (if the Player Hand drew a third card, see rule 5.)
Rule #5: When the Bank Hand’s initial two cards total 3, 4, 5, and 6 and Player Hand draws a third card, the Bank Hand stands or draws as follows:

I’ve summarized the above Bank Hand draw rules in the following table (similar to a blackjack strategy table).

Let’s try a few sample hands so you get the hang of the rules for standing and drawing. The first column below is the Player Hand; the second column is the Bank Hand. The third column is the correct action based on the house rules.

Note: Keep in mind that even though it is not necessary to memorize the above third card rules, if a dealer makes a mistake you won’t know it. My suggestion is you should become familiar with the third card rules. The Player Hand is simple to remember; the Bank Hand is more complicated but you can always jot down the above Third Card Rules on paper and refer to them when you play. After playing awhile, you will quickly become familiar with the rules.

BTW: In the event, a dealer makes a mistake, be sure to bring it to her attention immediately before the cards are discarded, and ask for a casino supervisor to review the hand.

The math of Baccarat has been determined by numerous gambling mathematicians. Below is the bottom line. (Assumes an 8-deck game; 1 to 1 payoff for a winning bet, and in the case of the Bank Hand, a 5% commission; and an 8 to 1 payoff for the Tie bet).

・Bank Hand wins 45.87% of the hands, loses 44.63% of the hands, and ties 9.51%
・Player Hand wins 44.63% of the hands, loses 45.87%, and ties 9.51%

If you ignore, the hands that tie, then:
・Bank Hand wins 50.68% of the hands and loses 49.32% of the hands.
・Player Hand wins 49.32% of the hands and loses 50.68% of the hands.

Notice that when you exclude tied hands, the Bank Hand wins more often than it loses. To compensate for this, the casino charges a 5% commission on a winning Bank Hand. (With the 5% commission, the house advantage on the Bank Hand is close to the house advantage on the Player Hand. See below for house advantages.)

The House Edge for the Bank, Player and the Tie bet can be calculated by multiplying the probability that the hand will win by the amount wagered plus the probability of the hand losing times the amount lost (expressed as a negative value). The result is the player’s expected value per hand, which is the opposite of the house advantage.

(+1 unit) x (.4463 probability of winning) plus (–1 unit) x (.4587 probability of losing) plus (0 units) x (0.0951 probability of tie) = –0.01235.
(This means a player would have a –1.24% expected value, or the house advantage is 1.24%.)

(+0.95) x (.4585) plus (–1) x (.4462) plus (0) x (.0951) = –0.01058 or a house advantage of 1.06%.

(+8 units) x (0.09516) plus (–1) x (.4585) plus (-1) x (.4462) = –0.14356 or house edge of 14.36%.

If you ignore the 9.51% of the hands that result in a tie, the house advantage for the Player and Bank Hand per resolved bet can be expressed as follows:
BANK HAND: 1.17%


Note: A house advantage of 1.36% on the Player Hand (excluding hands that tie) means that for every $100 worth of resolved bets that you make on the Player Hand, your expected loss is $1.36. You could get lucky and win money or lose more than $1.36, but over time you can expect to lose $1.36 for every $100 worth of resolved bets on the Player Hand. Betting on the Bank Hand will cost you slightly less money: ($1.17 per $100 wagered). (See Chapter 3 for further discussion on betting strategies for Baccarat.)

Whether you express the house edge per hand (including ties) or per resolved bet (excluding ties), the expected player losses will be the same.

The following is true about Baccarat:
・Bank hand has a slightly lower house edge than the Player Hand
・The tie bet has an outrageous 14.36% house edge and should be avoided


In the past, some casinos have reduced the commission on the Bank Hand to less than 5%. I once took advantage of a 4% commission on winning Bank Hand bets at Binion’s Horseshoe casino in downtown Las Vegas. There have been other casinos (land-based and online) that have offered a lower commission. This is a good deal for players. The following table shows how much you can lower the house edge on the Bank Hand based on the commission charged. (From the book Gambling 102 by Michael Shackleford). (Note: A negative house advantage indicates a player advantage. A player gains the advantage when the commission is reduced to 2% or lower.

Bottom Line: If you ever learn of a land-based or online casino that has a lower than 5% commission on a winning Bank Hand, take advantage of it before it becomes history.

・Baccarat is based on the Italian game of baccara, which means zero
・There are only three bets that you can make when you play baccarat. A bet on the Bank Hand, the Player Hand, or the Tie
・Objective of the game is to guess which hand (Bank or Player) is closest to 9.
・There are three different sized baccarat tables: mini-baccarat, midi-baccarat, and the full size (or big) Baccarat table.
・Mini-Baccarat tables are located in the main casino and have low stakes, players do not handle the cards, and the table can accommodate up to 6-7 players.
・Up to nine players can play Midi-Baccarat; stakes are usually higher than at Mini-Baccarat, and players can handle the cards
・The full-size (or big) Baccarat table is located in the high-roller pit; up to 14 players can play, the stakes are very high, and players can handle the cards.
・Winning Player Hand bets pay 1 to 1.
・Winning Bank Hand bets pay 1 to 1 but you must pay a 5% commission (resulting in a 19 to 20 payout). · Winning Tie bet pays 8 to 1
・Card values .are: 2s through 9s count face value, tens and picture cards count zero, and the ace counts 1.
・Two cards are initially dealt to the Player and Bank Hands. There are house rules that determine whether the Player or Bank Hand requires a third card.
・If the total of a hand exceeds 9, drop the first digit of the total, or subtract 10 from the total, to get the adjusted count of the hand.
・Excluding ties, the Bank Hand wins more times than it loses.
・Including ties, the house edge on the Bank Hand is 1.06%; on the Player Hand it is 1.24%; and for the Tie it’s 14.36%.
・Baccarat’s overall house advantage is about 1.2%, which is one of the lowest in the casino.
・If the commission on a winning Bank Hand is reduced below 5%, the house edge decreases.
・Because the drawing rules are fixed, there is no opportunity for strategic decisions (like in the game of blackjack).

4 Casino Tips for New and Veteran Players

If you like to go to casinos then you know it can be a lot of fun, especially when you get on a hot winning streak.

And, while it’s always more fun to walk away as a winner, unfortunately, that doesn’t always happen. Of course, many people will just chalk up their losing sessions to the old adage “the casino always wins,” but smarter casino players know that phrase isn’t necessarily true and that there actually are ways to get more value for your gambling dollar and also to increase your chances of winning.

Let’s take a quick look at eight ways you can accomplish this with your casino play:

Most casino games require luck for you to be a winner. Examples of these would be: slot machines, keno, roulette, craps, baccarat and most novelty table games, such as let it ride. However, there are some casino games that have an element of skill. Examples of these would be blackjack and video poker. Players who know how to play their hands properly, will achieve a better return on these games, in the long run, than players who guess how to play their hands.

You can get a better return by playing a game of skill such as blackjack or video poker but, as mentioned above, you can only achieve that higher overall payback percentage (in the long run), if you use the proper strategies.

For blackjack players you need to know basic strategy. Computer simulations of millions of blackjack hands have been made and it turns out that there is only one mathematically correct way to play your hand in any given situation. All of these possible situations have been combined into a basic strategy chart for blackjack and you should memorize this chart so you know how to play your hands properly. The chart will tell you exactly what you should do with your hand based on the total of your first two cards and whatever up card the dealer is showing. These basic strategy charts are widely available for free on the Internet. Just do a Google search for “blackjack strategy chart” and you will find numerous sites where you can download them for free.

The strategy chart may change slightly, depending on the number of decks used, and the particular rules of the game, so make sure that you use the correct chart for the game you want to play. By following the correct basic strategy, you can lower the casino advantage from as high as two percent to less than one-half one percent. And, this strategy would also apply to blackjack games played at Internet casinos.

Video poker players are in a similar situation because, once again, there is always only one mathematically correct way to play your hand in any given situation. And, naturally, there is a strategy chart that will show you how to properly play your hands. For instance, if you are dealt 2-3-4-5-5, should you keep the four card open-ended straight (2-3-4-5)? Or, should you keep the pair of 5’s (5-5)? Well, the strategy chart will tell you which choice will give you the highest expected return and that is how you should play your hand. No guessing on your part, just follow the chart!

Keep in mind that the video poker strategy can have major changes, depending on the game you are playing, such as jacks or better, double double bonus, deuces wild, etc. However, once again, these video poker strategy charts are widely available for free on the Internet. Just do a Google search for “video poker strategy chart” and you will find numerous sites where you can download them for free.

Just make sure that you use the correct strategy chart for the particular video poker game you want to play. And, these strategy charts would also apply to video poker games played at Internet casinos.

“Comp” is short for complimentary and it means anything that the casino will give you for free in return for your play at that particular casino. You’ve probably heard stories of “high rollers” in casinos who bet thousands of dollars per hand and get treated to a huge assortment of lavish freebies, such as: luxury hotel suites with butler service, delicious gourmet meals prepared by private chefs, an endless supply of the finest champagnes, private jet transportation, and more! Not many of us will be gambling at that level of play, but it turns out that even low-limit players can also earn lots of great comps from casinos.

Be sure to sign up for a player’s club card upon your first visit to any casino so that you will eligible to earn those great casino comps. Your card can then be used to track your play on both table games as well on electronic gaming machines, such as slots and video poker. The casino will then track how much you have played and they will give you comps based on your level of play. Comps are a great way to, essentially, lessen the casino advantage over you and you should always use your player’s club card whenever you play in a casino.

An important final note on comps, however, is that you never want to bet extra money in order to earn extra comps. So, if you’re a quarter slots player, don’t start playing dollar machines to get more comps. The vest idea is get comps for gambling that you were going to do anyway.

Many casinos run special promotions where they give bonus points for earning player’s club points. Most will offer double or triple point bonuses as a casino promotion, but some casinos will even go as high as 10 times points on select days. If you can play on these special days you can really rack up points very fast.

Also, sometimes casinos will have gift days where you can get a free gift once you earn a certain number of points on your card. These are also good days to play in the casino, but make sure that the gift you will receive is something that you really want because some might just be totally useless to you. Actually, the best things to play for are gift cards for gas stations, super markets, or drug store chains. Those are great to get because they will save you money that you would normally have to spend anyway.

Be sure to keep all four of these gambling tips in mind when planning your next visit to the casinos. They will all make you a smarter gambler and help you to have more fun!

5 Easy Video Poker Tips That Every Casino Player Should Know

1.Play maximum coins
2.Check pay schedules
3.Know the strategy for the game you are playing
4.Practice before you play
5.Watch your bankroll

Playing maximum coins gives you the full value for the royal flush — typically 800-for-1. Playing fewer coins gives you less for that hand — typically 250-for-1.

You won’t get that royal flush very often (usually once every 40,000 to 45,000 hands on average), but you NEVER know when the next one is coming. So playing maximum coins gets you paid well when the royal comes.

For Video Poker games where you get your money back for a pair of jacks or better, every additional unit you receive for a full house or flush returns an extra 1.1%.

Compare these two Double Double Bonus games.

The first one returns 99.0% with perfect play. The second one returns 97.9%. Most of the plays are the same over the two games, but your money will last longer on the first one. Often you can find both games at the same casino. It’s up to you to know the difference or you’ll be taking the worst of it

If you don’t know how much each pay schedule returns, a good source of this information is my Video Poker for the Intelligent Beginner.

Say you’re playing deuces wild and you’re dealt 4♠ 4♥ 6♣ 6♦ 7♠. How do you play it? Do you hold one pair or both pairs?

Actually either could be correct. Consider the two games below, both of which return approximately 98.9% when played well. In the first game you just hold one pair (it doesn’t matter which one). In the second game you hold both pairs.

How can you tell which is which? Look at the amount you get when you receive a full house. In the first game, you get paid 3-for-1 (15 for a 5-coin bet). Whenever you see that in Deuces Wild, you hold one pair when you’re dealt two.

In the second game you get paid 4-for-1 for the same hand (20 for a 5-coin bet). That’s when you hold both pair.

Computer software is available to tell you how to play any hand. The images you see today are inspired by Video Poker for Winners, which is the one I recommend, but there are other good ones as well.

Here we see a hand dealt in a Bonus Poker game. The player held the jack and the ten to go for the royal flush — certainly a play that looks reasonable. The computer, however, tells you that’s a mistake. Holding the queen and jack is actually better.

After you get corrected a few times, you won’t be making this mistake any more. A little bit of practice can make a big difference in your results!

Everybody wants to win, and everybody wins some of the time. But we all lose some of the time as well, and we can’t know what’s going to be the result today until we actually play.

If losing a few hundred credits will be a disaster for you, you can’t afford the stakes you’re playing. If you play for a modest amount compared to your overall bankroll, you’ll be able to absorb the swings, both plus and minus, and enjoy the game.

I wish you lots of royal flushes!

How to Play Craps

1.Craps has dozens of wagers available, but the game is structured around the pass line bet.
2.Players bet by placing chips on the pass line on the craps layout. Some other bets require that the dealer move your chips.
3.The pass sequence starts with a comeout roll and the shooter rolls the dice.
4.Pass bettors win if the roll is 7 or 11 and lose if it is 2, 3 or 12. Any other number becomes the point.
5.If the shooter rolls a point number on the comeout, he keeps rolling until either he rolls the same number again to win an even-money payoff, or rolls a 7 to lose.
6.If the shooter makes his point, he keeps rolling with a new comeout. If he doesn’t, he “sevens out,” and the dice rotate to a new shooter

Craps can be as simple as betting on one number and either winning or losing on each roll, or as complex as making a bet, waiting until the shooter rolls a target, or “point” number, then hoping the shooter can roll the same number again. That procedure can go on for any number of rolls.

Let’s start with a look at the craps layout, then explain the available layouts.

Each area of the craps layout signifies a different bet. If your chips are on the pass line, you’re making a pass bet, which is a multi-roll wager. If your chips are in the box that displays images of dice showing a 6 and a 5, you’re making the one-roll bet on 11. When you’re playing online craps, you can make any of the bets by clicking the layout on the screen. It’s different in live casino play. There, you can bet on pass, don’t pass, come, don’t come and the field by putting your own chips on the layout. For other bets, you put your chips directly in front of you on the layout and tell the dealer what you want. If you want to bet $5 on the place bet on 4, you would put $5 in chips in front of you, tell the dealer, “$5 place on 4,” and the dealer then would move your chips to the 4 box.

Let’s take a look at commonly available wagers and break that down into multi-roll and single-roll bets. You can have more than one bet in action at once – in fact most craps players have several bets working at a time. Not every possible wager is listed, though house edges for wagers such as lay bets – betting on 7 to come up before a place number – and horn bets are listed in the chart in the final chapter.

House edge: 1.41%

Winning bets are paid even money, but when non-craps players say the game confuses them, this is usually the bet they have trouble following. It usually takes more than one roll to decide, and while 7 starts out being a good roll for players it ends up being a losing number.

But really, it’s not all that complicated. Casinos aren’t in the business of making rules so intimidating they chase potential players away from the tables. If we don’t play, the operators can’t make money.

The pass line sequence starts with a “comeout roll.” You can tell if the next roll is a comeout by the placing of a disc on the table. If the disc is toward a corner of the layout and is turned so the face-up side is black with the word “off,” then the next roll is a comeout. If the disc is in a numbered box and has a white side saying “on” face up, then the pass sequence already is underway and the next roll is not a comeout.

On the comeout, if the shooter rolls a 7 or 11, pass bets win. If the shooter rolls 2, 3 or 12, pass bets lose. If the shooter rolls 4, 5, 6, 8, 9 or 10, that number becomes the point and the object of the game changes. Now the shooter must roll that number again before rolling a 7.

No other rolls matter in deciding the pass bet. If the point is 6 and the next several rolls are 4, 8, 3, 11, 5, 12, for example, the pass bet just stays in action. The bet isn’t decide until the shooter either rolls the point again or rolls a 7.

House edge: 1.41%

Come is the same bet as pass, except you make it when there already is a point for pass bettors. If the next roll is a comeout, then the bet you want is pass. If there already is a point, then you can bet come and the next roll is treated as a sequence starter for your come bet.

Let’s say that on the comeout the shooter rolls a 6, and that becomes the point. Before the next roll, you bet on come. Then if the shooter rolls a 7 or 11, your come bet wins, if he rolls 2, 3 or 12 the come bet loses and any other number becomes a point for your come bet.

Note that the same 7 that wins on your come bet could lose on the pass line, and a 2, 3 or 12 that loses on come will have no effect on pass. Say 6 is established as a point on craps and you follow with a come bet. If the next roll is 7, you win on come but lose on pass. If it’s 11, you win on come and your pass bet stays in action, and if it’s 2, 3 or 12 you lose on come and your pass be stays in action.

House edge: 1.36%

These are the near opposites of pass and come. Like them, you bet don’t pass if the next roll is a comeout and don’t come if it isn’t.

On the comeout for a don’t pass bet or on the first roll after making a don’t come bet, you win if the roll is 2 or 3 and lose if the roll is 7 or 11. You don’t win if the roll is 12 even though 12 is a loser at the start of pass or come sequences. Instead, the bet is a push and you can take your money back after a 12. If the roll is any other number, it becomes the point. If a 7 rolls before the point is repeated, don’t bettors win, and if the point comes first, they lose – the opposite of pass or come.

Most players prefer playing the pass side so they are rooting for the shooter and have the camaraderie of winning together. They refer to don’t players as “wrong bettors” and “the dark side.” But the house edge is slightly lower on the don’ts and the dark side has its followers.

House edge: 0%

Winning bets are paid at true odds, varying according to point number. It’s rare that you get an even break on casinos games, but the odds give you just that. They’re called “free odds,” but it’s not a free bet – you still have to but money at risk. The “free” just signifies that there is no commission or other method of making this bet profitable for the house.

In order to take free odds, you must first make a pass or come bet. After a point is established, you may back your pass or come bet with a second wager. Originally, that free odds bet had to be equal to your pass or come bet, but today most casinos allow you to bet multiples of your original bet.

The great part is that the free odds are paid at true odds. If the point number is 6 or 8, a winning free odds bet is paid at 6-5 odds. Payoffs are 3-2 on points of 5 or 9 and 3-1 on 4 or 10.

Those reflect the actual odds of rolling those numbers. Using two six-sided dice, there are 36 possible combinations. Six of them total 7, with there are five each if 6 and 8, four each of 5 and 9 and three each of 4 and 10.

Six ways to roll 7 and 5 ways to roll 6 means the true odds against rolling 6 before 7 are 6-5, exactly the same as the payoff on winners. Hence, no house edge. It works the same way on all the point numbers. Payoffs are the same as the odds against winning the bet. There is no house edge on the odds themselves, though the house retains its edge on the pass or come bet you must make before betting the odds.

If a casino offers single odds, then your odds bet must be equal to your pass or come bet. If the casino offers multiple odds, then your odds bet may be any multiple of the original up to the maximum. When 10x odds are offered for example, your odds bet may be 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 times your original bet.

Many casinos today offer 3, 4x, 5x odds meaning you may make an odds bet of three times your original wager if the point is 4 or 10, four times if the point is 5 or 9 or five times if the point is 6 or 8. This makes calculating payoffs easy – with maximum odds, total payoffs are the same on any point. If you bet $5 on pass, then a $15 odds bet on 4 or 10 pays 2-1, or $30; a $20 odds bet on 5 or 9 pays 3-2, or $30; and a $25 odds bet on 6 or 8 pays 6-5, or $30.

Don’t pass and don’t come bettors can lay the odds instead. To use a point number of 6 as an example, once that point is established, the don’t bettor has six ways to win – the six possible ways to make 7 – and only five ways to lose – the five ways to make 6. When you lay the odds, you win $5 for every $6 you bet on 6 or 8, $2 for every $3 you bet if the point is 5 or 9, and $1 for every $2 you bet when the point is 4 or 10.

The payoffs reflect the true odds, just as when a pass/come bettor takes free odds. There is no house edge on the lay odds, but the house has an overall edge because you must bet don’t pass or don’t come first.

House edge 1.52% on 6 or 8; 4% on 5 or 9; 6.67% on 4 or 10

Winning bets are paid at 7-6 odds if you’re betting on 6 or 8, 7-5 on 5 or 9 and 9-5 on 4 or 10. Want to choose your number without waiting for the shooter to establish a point on the comeout? Place bets enable you to do just that. When you make a place bet, you’re betting the shooter will roll your number before he rolls a 7. As on pass, no other numbers matter. If you place 6 and the next several rolls are 5, 4, 12, 3, 9, 8, then there is no decision on your bet. You win only if the shooter rolls your number, and lose if he rolls 7. These pay more than even money, but less than true odds. Instead of the 6-5 true odds of making a 6 or 8, those numbers pay 7-6, giving the house it’s 1.52% edge.

One important point: If you place 6 or 8, be sure to bet in multiples of $6 so the house can make that 7-6 payoff. If you bet $5 instead, the house will pay at even money.

Many players like to place 6 and 8, the most frequently rolled winning numbers. Other place numbers, with higher house edges, are less popular.

House edge: 4.76%, or less if commission is only on winners.

Winning bets are paid at true odds, but you have to pay the house a 5% commission to get that deal. For example, if you buy the 4 for $20, you must also pay the house a $1 commission. Then if you win, you’re paid at the 2-1 true odds. That lowers the house edge from 6.67% to 4.67% on 4 or 10, but raises the house edge on other numbers.

However, some casinos charge the commission only if you win. That drops the house edge to 2% if you buy 5 or 9 and 1.67% on 4 or 10, making buying a better option than placing. The house edge on buying 6 and 8 under these conditions is 2.27%, so you’re still better off with the 1.52% for a place bet.

House edge 9.09% on 6 or 8; 11.11% on 4 or 10

Payoffs are 9-1 on 6 or 8 and 7-1 on 4 or 10. A number rolled the hard way means that both dice show the same number. A hard 4 is a 2 on each die. Hard 6 is 3 on each die, and so on. To win a hardway bet, your number must come up the hard way before the shooter rolls either the 7 or your number any other way. If you bet hard 8 and the roll is 2-6 or 3-5, you lose. Only 4-4 is a winner.

Before getting into the individual bets, the payoffs listed below are the most common. A one-roll bet on 2 usually pays 30-1, but some casinos, especially in the United Kingdom and Australia, pay 31-1, 32-1 or, rarely, 33-1. The higher the payoff, the lower the house edge.
Also, the listings are odds-to-1. Some casinos pay odds-for-1, which essentially means your bet is included in the payoff. If you bet $1 and are paid 30-to-1, you keep your $1 bet and get $30 in winnings. If you’re paid 30-for-1, $29 in winnings are added to your $1 to give you a total of $30. Beware tables that pay odds-for-1.

House edge 5.56% or 2.78%: You win if the next roll is 2, 3, 4, 9, 10, 11 or 12.

Winners are paid even money most of the time, but are paid 2-1 if the roll is 2 and either 2-1 or 3-1 if the roll is 12. Some casinos, especially in Reno, Nevada, reverse that and pay 3-1 on 2 and 2-1 on 12. If both 2 and 12 pay 2-1, the house edge is 5.56%. If either pays 3-1, that cuts the edge in half to 2.78%.

2 OR 12
House edge 13.89%

Winners are paid 30-1. If you bet on 2 the next roll must be 2. If you bet on 12, the next roll must be 12. All other numbers lose.

3 OR 11
House edge 11.11%

Winners are paid 15-1. If you bet on 3 the next roll must be 3, and if you bet on 11, the next roll must be 11. All other rolls lose.

House edge 16.67%:

Winners are paid 4-1.

House edge 11.11%:

Winners are paid 7-1.

You get three numbers on this bet – you win if the next roll is 2, 3 or 12.

House edge 13.89% or 11.11%.

Winners are paid 30-1 on hard hop bets and 15-1 on easy hop bets.

On hop bet, you’re betting each die will land on a specific number. You tell the dealer,”6-3 hopping” or “4-2 on the hop,” and you win only if the dice show those specific numbers.

On a “hard hop,” both numbers are the same, such as 1-1 or 4-4. When the two numbers are different, the bet is an “easy hop.”

Craps is the same game online and in live casinos, but some rules and procedures are a little different. Here are a few point every player should know before playing.

Two six-sided dice are used, and you are betting on the total of the numbers that land face up on both dice.

If one die lands on 2 and the other on 4, then the number on that roll is 6. If the numbers are 1 and 1, then the roll is 2.

You cannot bet on each die separately. There is no wager that one die will show No. 1, for example. All craps bets are on two-dice totals.

At online casinos, as in other games, you start by making a deposit, or if you already have funds on deposit, you may draw on them for money to play.

At live casinos, most players buy in at the table. Some already have chips from previous play and some who have credit accounts at the casino may have chips from having cashed a credit marker.

But most pay as they play. You do so by putting cash on the layout and telling the dealer you want to buy chips. The dealer is not permitted to take cash directly out of you hand. You must put your cash on the table and the dealer then will take it and give you chips.

Online, all decisions and payouts are done automatically, but in live casinos there’s a human crew. The common complement is four people: the boxman, the stickman and two dealers.

The boxman is in charge of the table, watching to make sure players follow rules and that dealers make proper payoffs. When you buy in by putting cash on the table, a dealer gives the cash to the boxman, who lays it flat, face down on the table, then watches as the dealer gives you chips. When the transaction in complete, the boxman then uses a flat plastic paddle to push the cash into a drop box, which later will be taken by guards for transport to the count room.

The stickman holds a long hooked stick, which he uses to push dice around the table. When it’s your turn to shoot, the stickman pushes the dice to you. He also handles the proposition bets at the center of the table.

The dealers each are in charge of one end of the table, giving you chips when you buy in, moving your wagers to the appropriate spots on their ends of the table and making payoffs.

At most online casinos, your screen will include a graphic of the craps layout. You may click on chip images to determine how much you want to bet, then again on the screen to place the chips on the bet you want. If you want to make the bet labeled “Pass Line,” you would click on the pass line area. If you want to bet on 11, you would click on a box depicting 11 with images of one die on 6 and one on 5.

At live casinos, you may place your own chips on the pass line and in areas marked “Come” and “Field,” but for must bets, your chips must be placed by the dealer. You push chips in front of you on the layout and tell the dealer, “$6 each on 6 and 8.” The dealer then moves your chips to the appropriate box and positions it in accordance to your position at the table, so he knows both what the bet is and who made it.


Online, you’ll usually be asked to choose from a range of minimum and maximum bets. For example, you might be presented with options of minimum bet $1, maximum $100; minimum $5, maximum $500; or minimum $10, maximum $1,000. You choose the range that’s within your comfort zone. In live casinos, there will be a placard on the table detailing minimum and maximum bets. If the placard lists a minimum wager of $10 and you only want to put $5 on the line, then you need to look around and see if there’s another table that’s more friendly to your bankroll.

At online casinos, virtual dice are rolled and results determined by a random number generator. In live casinos, shooters take turns. To see how that works, we need to revisit the pass line.

You’ll remember from chapter 2, the pass line sequence starts with a comeout roll. If the shooter rolls 7 or 11, pass bets win, and if he rolls 2, 3 or 12, pass bets lose. Any other number becomes the point. If the shooter rolls the point number again before 7, pass bets win, but if a 7 comes first, pass bets lose.

When the shooter rolls a loser 7 after establishing a point, he’s said to “seven out.” At that point, the dice rotate to a new shooter. Not all losing rolls bring a new shooter. If pass loses with a 2, 3 or 12 on the comeout, the shooter has not sevened out and keeps shooting.

Similarly, not all 7s are seven out. If the shooter makes a point, the sequence starts all over with a new comeout, and on that comeout 7 and 11 again are winners.

As long as the shooter keeps making points and avoids seven out, he keeps shooting. In the longest streak on record, Patricia Demauro rolled 154 times without sevening out in 2009 at the Borgata in Atlantic City. That streak took four hours, 18 minutes before the dice passed to the next shooter.


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