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Craps & probability

This is a follow up to my post from the other day on craps. Before we get into actual betting, I want to talk about probability. In craps, you are rolling two dice, each with six sides. This means that there are 6^2 (36) possible combinations of the dice: 1 and 1, 1 and 2, 1 and 3, and so on and so forth.

The reason this matters is that this makes each roll of the dice a random event: each combination is as likely to occur as any other. This is an important concept. If I flip a coin 100 times, there is no way to predict the next result of a coin toss because each event is random. ‘Heads’ is just as likely to come up as ‘tails.’ The coin doesn’t care if the last ten flips were all heads, the next toss still has the same odds of coming up heads: 50%. If you keep track of the result each time that coin is flipped, the more you flip it, the closer you will be to a 50/50 split.

What causes the “streaks” and “runs” of a random system is due to something called ‘distribution variance’ and is the reason why you see people say that a number is “due” for one reason or another. This is because people tend to see patterns even when there aren’t any. It is a random system, and each result is as likely as the other.

The same is true with dice. If I toss them enough times, you will see a pattern emerge. Out of each 36 attempts (on average), two will come up once (a one and a one). So will twelve (a six and a six). Seven will make an appearance six times (1&6, 2&5, 3&4, 4&3, 5&2, 6&1) and is the most likely number to come up. If I make a chart, it will look like this:

  • 2: 1/1
  • 3: 1/2 2/1
  • 4: 1/3 2/2 3/1
  • 5: 1/4 2/3 3/2 4/1
  • 6: 1/5 2/4 3/3 4/2 5/1
  • 7: 1/6 2/5 3/4 4/3 5/2 6/1
  • 8: 2/6 3/5 4/4 5/3 6/2
  • 9: 3/6 4/5 5/4 6/3
  • 10: 4/6 5/5 6/4
  • 11: 5/6 6/5
  • 12: 6/6

This makes the math pretty easy. Let’s go back to the first roll of the dice:

If the shooter rolls a 7 or an 11, they win. There are 8 chances of each 36 rolls on average that will result in a win on the come out roll.

If the shooter rolls a 2, 3, or 12, they lose. There are 4 chances out of each 36 rolls that the shooter will lose.

Any other number becomes the point. That means that 24 of each 36 rolls will result in setting the point.

Now seeing that, you would assume that betting on the shooter would result in you winning twice as often as you lose, and you would be right, if the come out roll was viewed in isolation. The catch here is that if the point is set, the bet must remain in play until the shooter either rolls that number again (and wins) or rolls a seven (and loses). Since seven is more likely than any other number, it is more likely that you will lose your money than it is that you will win. Still, with all of that, betting on the come out roll (called a pass line bet) is the best bet in the casino.

Why is that? Because the come out has the smallest house advantage of any other bet you can make in the entire casino- that includes slots, Blackjack, Roulette, any other bet in any other game. For example: In Nevada, slot machines over the long term pay out 80 cents of every dollar that is wagered. The house keeps 20 cents of every dollar- 20%. This is called the house edge.

In roulette, the house edge is the 0 and 00 spaces on the wheel. This means that the house edge (if you bet black/red or odd/even) is 5.26%. The house keeps 5.26 cents of each dollar wagered.

In Craps, the house edge for a pass line bet is 1.41 percent. That is, out of each dollar, the casino only keeps 1.41 cents.

Still, if the house ALWAYS has an edge, why gamble? Because you CAN win in the short term, thanks to distribution variance. If you find yourself in one of those “hot streaks” you can make a good bit of money. If you are in a cold streak, you can lose a LOT of money.

Let’s go back to our example of flipping a coin. Let’s say I flip a coin 10 times. Even though the odds are 50/50 for heads or tails, it is likely in such a small number of flips that you will see a streak like this: 7 heads, 3 tails. If you are betting heads, you make a lot. If you had bet on the tails, you could lose a lot. This is what makes gambling fun, if you don’t go buck wild. In future posts, I will explain betting and how to do well playing this game.

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