# The Math of Craps and Playing Wrong

Recently I received an email from a reader stating that they were not into dice setting, but their interests were in the math of the game. Well, with two six sided cubes, the math of craps is about as predictable, for a game of chance, as you can find. What’s not predicable is the outcome of two dice hurled down the layout. It does not matter if the dice are per-arranged in a set or rolled randomly. That’s why it is known as a “crap shoot” Babs!

I started my craps career as a Pass Line player. I struggled playing the Pass Line with inconsistent results. After witnessing Stuart Wilde take down a several thousand dollar win, playing the Don’t Pass at the Princess Casino in Nassau, I decided to switch my game. For the next four years, I consistently won, playing Don’t Pass. So, for those of you in need of some math, here it is, a long with a general description for playing the Don’t Pass. However, make a note, this is how the rules of the Don’t Pass bet translates, not the strategies I necessarily use.

The following is an except from the ** Do’s and Don’ts of Dice™** playbook.

Playing Wrong – The Dice Don’t Pass

Playing “Wrong” is not a judgment it is just another way to play the game. Put on your thinking caps here. Playing wrong or playing the Don’t is opposite to playing “right” or playing the Pass Line. When playing the Don’t Pass, you are betting that the shooter will roll a seven before rolling the point. Hence, the dice do not pass. A “pass” is a win on the “Pass Line.” As a Don’t Pass bettor, you are betting that the result of the hand will be a loser for the Pass Line. The house advantage is about the same for a Don’t Pass bet as it is for the pass line, 1.4%.

Quick Review of a Don’t Pass Line Bet

For the Don’t bettor, 7 or 11 on the come out is a losing roll while 2 or 3, craps is a natural winner and 12 is barred or a push. After a point is established, the Don’t Pass bet wins when a 7 rolls before the point, 4, 5, 6, 8, 9, 10.

We already know the Don’t Pass bet is made during a come out roll. The Don’t Pass bet is not a contract bet. You may pick up the bet anytime you want. Of course, being the odds on favorite to win, you would never want to do that.

That Seems Odd…

Let’s move on to laying odds with a Don’t Pass bet. Do you still have the thinking cap on? When the dice are not passing, not winning for the Pass Line player, playing the don’t pass can make “cents”. Just like a Pass Line bet, the player can make an additional odds bet with the Don’t Pass bet. The tricky part is inverting the odds for the pay off. In other words, you must lay more money in odds to win less money. Yes, that does seem odd. However, it is correct because the bet is favored to win with the seven out. The odds bet has no house advantage other than with the original Don’t Pass bet which is paid even money. When playing the Don’t Pass and you lay odds behind a point, you are favored to win by 2:1 for the 4/10, 3:2 for the 5/9 and 6:5 for the 6/8.

That is why you must lay bet $20 with a $5 don’t pass bet for a point of 4 or 10. You lay $20 to win $10. Get it? It is exactly the opposite of the Pass Line. Follow this…

The Pass Line bet of $5 with $10 double odds wins a total of $25 on a 4 or 10.

The Don’t Pass bet of $5 with $20 double odds wins a total of $15.

So, how does the casino stay in business? Let the accountants worry about that. The casino seems to be doing okay.

The amount you may lay in odds varies from casino to casino. It is recommended that until you have a command of the game that you stick with double odds in the beginning. You will have to learn the math for the odds in order to make the correct lay bet for the established point. The house advantage on a Don’t Pass bet with double odds is about .6%

Quick Review

When the don’t pass bet with odds wins, you are paid even money for the Don’t Pass bet and true odds for the odds portion of the wager. The true odds payoff is determined by the point number. Odds are expressed by the number of ways a point has of winning verses the number of ways of losing to the seven.

Let’s look at the 4/10 for example. If you have a pair of dice handy, get them. Refer to the table below. With two dice, rolling a 4 or 10 has three possible combinations.

The four has 1/3, 3/1, and 2//2.

The ten has 4/6, 6/4, and 5/5.

Those are the three ways of rolling a 4 or a 10.

The seven has six possible combinations of rolling.

1/6, 6/1, 2/5, 5/2, 3/4, 4/3

Some casinos offer “raiser odds”, or odds greater than raiser odds such as 10 times, 20 times or 100 times odds. Again, when you are just learning, double odds will be plenty for you to risk, win or lose.

Raiser odds are 5 times the Pass Line bet for the 6/8, 4 times the Pass Line bet for the 5/9, and 3 times the Pass Line bet for the 4/10.

For you convenience, I present a table for true odds so you can learn the odds for yourself and make the correct bet when laying the odds.

4 | 5 | 6 | 8 | 9 | 10 |

2 to 1 | 3 to 2 | 6 to 5 | 6 to 5 | 3 to 2 | 2 to 1 |

Lay 2 units to win 1 unit. | Lay 3 units to win 2 units. | Lay 6 units to win 5 units. | Lay 6 units to win 5 units. | Lay 3 units to win 2 units. | Lay 2 units to win 1 unit. |

There are six sides to a die and with two dice; there are thirty-six combinations possible. Below is a table of the thirty-six possibilities for rolling the eleven numbers.

Number | Dice Combinations | Possibilities |

2 | 1-1 | 1 |

3 | 1-2, 2-1 | 2 |

4 | 1-3, 3-1, 2-2 | 3 |

5 | 1-4, 4-1, 2-3, 3-2 | 4 |

6 | 1-5, 5-1, 2-4, 4-2, 3-3 | 5 |

7 | 1-6, 6-1, 2-5, 5-2, 3-4, 4-3 | 6 |

8 | 2-6, 6-2, 3-5, 5-3, 4-4 | 5 |

9 | 3-6, 6-3, 4-5, 5-4, | 4 |

10 | 1-3, 3-1, 2-2 | 3 |

11 | 5-6, 6-5 | 2 |

12 | 6-6 | 1 |

The odds are expressed as a ratio of the number of ways of rolling a certain number, divided by the total possible combinations. Examples: There is one possible combination of rolling 12, six/six. Thus the odds of 12 rolling is one in thirty-six or 1/36. There are six possible combinations for 7 to roll, thus the odds of a 7 rolling are 6/36 or 1/6, one out of six.

True odds are an expression of the number of possible winning combinations to the number of losing combinations. Example for a Don’t Pass bet for the 6 or 8: The true odds are 6 to 5. Six ways of winning to five ways of losing. Six 7’s versus five 6’s or five 8’s. Thus 6:5

The Wrap Up

The Don’t Pass bet is often referred to as an opposite play to the Pass Line bet. As you become familiar with and understand the odds, you may agree. The Don’t Pass bets are against the dice passing. This means that the seven will is expected to roll before the established point. The odds portion of the bet (laying the odds) are paid true odds and thus reduces the house advantage to about .6%.

Copyright © 2008 Michael Vernon