A Game of Numbers

Almost all casino games are based on numbers. Even in games such as blackjack and baccarat the non-numbered picture cards are given their own numbers, 10 and 0 respectively. Who says math isn’t important? It certainly is in casino games.

Still many casino players are not fully aware of how all these numbers work. Many players will make bets that the numbers tell us are poor or, to be totally honest, terrible. Players get so caught up in the games that numbers are just some dreamlike side issue when such numbers are in fact the main purpose of the games.

Take a look at the payouts in roulette. A hit on a number pays 35-to-1 when the true payout in a game with no house edge should be 37-to-1 on the American double-zero wheel and 36-to-1 on the European single-zero wheel. The difference in those numbers shows clearly that one game is far better than the other game.

Dollars and cents make sense to the casinos and these should make sense to the players as well. Make bets with the wrong numbers, meaning house edge percentages, and you are asking for trouble if not tonight then as time goes on. Poor bets inevitably lead to poor monetary expectation. Adding more speed to the games, meaning more decisions per hour, will make even small house edges more difficult to overcome.

Craps is a game totally built on the numbers. There are 11 of them 2-3-4-5-6-7-8-9-10-11-12. These are made with two dice, each with six sides showing six pits, one, two, three, four, five and six. The combinations of these pips make up the 11 numbers shown above.

[Please note: With two dice of six sides each, there are 36 possible combinations as six times six equals 36. All of craps exists within those 36 numbers. These 11 numbers are made with combinations of the following pips:

2 = 1:1
3 = 2:1, 1:2
4 = 2:2, 3:1, 1:3
5 = 3:2, 2:3, 4:1, 1:4
6 = 3:3, 4:2, 2:4, 5:1, 1:5
7 = 4:3, 3:4, 5:2, 2:5, 6:1, 1:6
8 = 4:4, 5:3, 3:5, 6:2, 2:6
9 = 5:4, 4:5, 6:3, 3:6
10 = 5:5, 6:4, 4:6
11 = 6:5, 5:6
12 = 6:6

Interestingly enough all these numbers have select nicknames which I will discuss in another column.]

Typical craps players will tend to make combinations of bets. Most will go with three. Such players will make their Pass Line bets with two Come bets and/or Place bets. Some players will go further by consistently putting out Come bets until the Craps shooter sevens-out. Still other players will add “Crazy Crapper” bets such as the Horn, Any Craps, Any Seven, and the Hardway bets among a host of others. These bets come in with astounding house edges – meaning large numbers which will ultimately soak a player’s bankroll.

The more bets a player makes at craps, the less merry that player will be in a relatively short period of time. You can’t beat a game with a house edge by making multiple wagers and you certainly can’t beat such a game by making more and more outrageous selections.

In the past I used to recommend the three-bet wagering technique at the game but over recent years I have changed my mind. I am, in short, an old dog that has learned a new trick. I still use the Captain’s 5-Count before I bet on any shooters other than me, but I no longer subscribe to the multi-bet syndrome. (I shall discuss the Captain’s 5-Count in a future column.)

So what is my new method of playing craps? Strap yourselves in!

I am now suggesting that instead of making multiple bets at the game of craps that you limit yourself to one. That’s correct; one bet on one shooter. My reasoning is simple – your negative expectation is lowered significantly by just going up against the house edge on a single number. Consequently it becomes a completely focused game for you; your single number versus the casino’s single number, the seven.

If the player makes two of the best bets at craps, the Pass Line and Come bet, and goes on three of them at once, he will face a house edge of 1.41 percent on each of the numbers he bets. So a $10 bettor’s expectation is to lose around 42 cents. If the player only makes one such bet, his expectation is to lose 14 cents.

Take a look at players who make more than three bets; say these players go up on four numbers? Five numbers? Six numbers? Throw in some Crazy Crapper bets for icing on the poisonous cake and what have you? The casino’s dream player.

Now start multiplying, not bets, but how much a player comparatively loses over time based on the number of bets he makes. When I write one Pass and one Come bet (or more) that can actually be multiple Come bets with no Pass Line bet. Now watch how scary this can get:

[Please note: Obviously winning and losing is not a smooth process. It’s up and down, in and out, but the above figures give you an idea of how bad the best bets can get over a rather short period of time. Most craps players, even those only betting $10 on the Pass and Come wagers, can see a lot of money being worked on by a rather small house edge.]

The above totals are indicative of how the losses grow based on the amount of money being wagered. A $10 bettor of the best bets will get to that $1,000 mark quite quickly.

Now think of attaching poorer bets such as Place bets instead of Come bets. The Place bets will come in with the following edges: 6.67 percent on the 4 and 10; four percent on the 5 and 9, and 1.52 percent on the 6 and 8. These edges will add significantly to a player’s losses.

Okay, let me go the route: Think of adding Crazy Crapper bets with edges of 16.67 percent, 13.89 percent, 12.5 percent, 11.11 percent, 9.09 and 5.56 percent, etc., to get an idea of how hard it is to come out just a little behind, or even or perhaps slightly ahead with a multiple bet approach to the game. A player trying that approach is just asking for trouble and he will get it too.

Now look at this chart and see how a single bet works based on what number you are betting. Dead time is the appearance of all numbers except the two that count for you, meaning the 7 and your specific number.

Question: Shouldn’t I go up on some other numbers because watching all those other numbers appearing will cause me to be bored?

Answer: The key is not to think of those numbers as actual numbers. They are not a part of your game. Right now as you read this article numbers are being rolled all over the world. Those numbers are dead time to you right now. You aren’t concerned with them. You aren’t even thinking about them. The numbers rolled while you are at your table don’t count; it’s as if they are being rolled on another table. By the way, the same holds true if you are taking a break and while you are away from the table a friend of yours tells you about his or her great roll. So what? There’s a great rolls going on right now in many casinos across the world and you really don’t care about them.

Question: Do I take Odds on the number that is mine or do I just go with a plain Pass Line or Come bet?

Answer: I recommend taking Odds on your bet. If you are playing at a 5X Odds game and you want to bet $60, you are better doing that with a $10 Pass or Come bet with $50 in Odds. Your expected loss is only 14 cents. If you bet $60 on the 6 or 8 your expected loss is 91 cents. That’s a big difference. The differences are much bigger using Place bets on the 4, 5, 9 and 10.

Question: What if my number doesn’t hit? How will that make me feel? I’ll be missing out on something.

Answer: Once you get used to playing this way, you will feel nothing. You will also feel nothing when the shooter sevens-out and everyone takes a thumping at the table and you have lost only a single bet. You will also feel nothing when your number hits and then a quick seven-out occurs and everyone is moaning and groaning because they have lost multiple bets. The key thing to remember: Play your game and ignore what happens to everyone else. They don’t exist and those other numbers don’t exist either. Getting in that mindset will take a little while but you’ll hopefully get there.

Question: Won’t I lose comp time if I bet this way?

Answer: Probably. Remember that your comps are based on the size and number of bets you make and how much time you are at the table. But so what? Comps are given based on your expected losses over time. They aren’t given to you because you are a heck of a nice person. You’re better off buying your own sandwich or gourmet dinner than losing so much money you could be a partner in the restaurant.

Question: How did you come up with this idea? It is as radical as I can think and I have a feeling very, very few craps players ever think of playing this way. What gave you this concept?

Answer: Over the years I looked at various gamblers and types of gambling and one thing stuck in my mind; part of the fun of gambling is the anticipation of the decision or event. Lottery players dream about winning the big one and they can’t wait for the drawing of the numbers. Slot players can’t wait to get to the casinos to play. This holds true of sports bettors, craps players and every other type of gambling. The anticipation is a large part of the fun!

But something happens when you play too much, you become somewhat numb to what’s happening. Before you go to the craps table you are supercharged but once you make countless multiple bets you seemingly become immune to that anticipatory set. You have too much happening. You are kind of numb. So playing that one-number bet continues the anticipatory set more strongly than throwing multiple bets out time and again.

Aside from being the best money-management system, the single bet rewards you in a more emotional context. Anyway that’s the origin of the idea, a mixture of emotion and math.

All the best in and out of the casinos!