Play Craps
Last update: Dec. 29, 2009
Introduction
According to the constitution of the state of California, dice alone may not determine the outcome in craps. So what the casinos usually do is use some combination of dice and playing cards, or playing cards alone, to simulate the roll of two dice. My craps appendix 5 goes into detail about how several different casinos do it.
Every six months, I make a trip to the San Diego area casinos. On October 25, 2009, I noticed a new game at the Viejas Casino called Play CrapsTM. Normally, when the California casinos offer craps, they are careful to keep the odds the same as the conventional game. However, this is not the case with Play Craps. There is some debate about how many cards they use at Viejas. The game owner claims they use six packs of 54 cards, for a total of 6×54=324 cards. However, Discount Gambling claims they use five packs of 44 cards each, for a total of 5×44=264 cards.
What makes the number of cards important is the effect of removal. Whatever the first card dealt is, there is less than a 1 in 6 chance of the second one matching it. With dice, there is a 1/6=16.667% chance of getting a pair. With 324 cards it is (53/323)=16.409%. With 264 cards it is 43/263=16.350%.
I'm going to present the math both ways, with 324 cards and 264 cards. You'll have to determine yourself how many they actually use. I have a trip there planned in May 2010, to hopefully put this question to rest.
324-Card Shoe
| Probabilities in Play Craps |
| Dice Total |
324 Cards |
Dice |
| 2 | 2.7348% | 2.7778% |
| 3 | 5.5728% | 5.5556% |
| 4 | 8.3075% | 8.3333% |
| 5 | 11.1455% | 11.1111% |
| 6 | 13.8803% | 13.8889% |
| 7 | 16.7183% | 16.6667% |
| 8 | 13.8803% | 13.8889% |
| 9 | 11.1455% | 11.1111% |
| 10 | 8.3075% | 8.3333% |
| 11 | 5.5728% | 5.5556% |
| 12 | 2.7348% | 2.7778% |
| Total | 100.0000% | 100.0000% |
The next table shows the house edge for most bets under both the Viejas rules and a standard game with dice.
| Probabilities in Play Craps |
| Bet |
Pays |
324 Cards |
Dice |
| Pass | 1 to 1 | 1.368% | 1.414% |
| Don't pass | 1 to 1 | 1.366% | 1.364% |
| Taking odds 4, 10 | 2 to 1 | 0.412% | 0.000% |
| Taking odds 5, 9 | 3 to 2 | 0.000% | 0.000% |
| Taking odds 6, 8 | 6 to 5 | 0.202% | 0.000% |
| Laying odds 4, 10 | 1 to 2 | -0.206% | 0.000% |
| Laying odds 5, 9 | 2 to 3 | 0.000% | 0.000% |
| Laying odds 6, 8 | 5 to 6 | -0.169% | 0.000% |
| Place 4, 10 | 9 to 5 | 7.052% | 6.667% |
| Place 5, 9 | 7 to 5 | 4.000% | 4.000% |
| Place 6, 8 | 7 to 6 | 1.714% | 1.515% |
| Place to lose 4,10 | 5 to 11 | 2.830% | 3.030% |
| Place to lose 5,9 | 5 to 8 | 2.500% | 2.500% |
| Place to lose 6,8 | 4 to 5 | 1.653% | 1.818% |
| Buy 4, 10 | 39 to 21 | 5.155% | 4.762% |
| Buy 5, 9 | 29 to 21 | 4.762% | 4.762% |
| Buy 6, 8 | 23 to 21 | 4.955% | 4.762% |
| Lay 4, 10 | 19 to 41 | 2.830% | 3.030% |
| Lay 5, 9 | 19 to 31 | 2.500% | 2.500% |
| Lay 6, 8 | 19 to 23 | 1.653% | 1.818% |
| Hard 4,10 | 7 to 1 | 12.577% | 11.111% |
| Hard 6,8 | 9 to 1 | 10.624% | 9.091% |
| Field (12 pays 3 to 1) | | 3.044% | 2.778% |
| 2, 12 | 30 to 1 | 15.222% | 13.889% |
| 3, 11 | 15 to 1 | 10.836% | 11.111% |
| 7 | 4 to 1 | 16.409% | 16.667% |
What stands out in the table above is that laying odds on points of 4, 6, 8, and 10 show the house edge in negative. In other words, the player has an advantage! Of course, you have to make a negative expectation don't pass bet first. The Viejas generously allows the player to lay up to 10X odds, up to a maximum win of $1,000. If the player laid the maximum odds on points of 4, 6, 8, and 10, then the overall house edge between the don't pass and laying odds would be 0.016%. If the player laid full odds on all points, then the overall house edge would be 0.011%.
264-Card Shoe
| Probabilities in Play Craps |
| Dice Total |
264 Cards |
Dice |
| 2 | 2.725% | 2.7778% |
| 3 | 5.5767% | 5.5556% |
| 4 | 8.3016% | 8.3333% |
| 5 | 11.1534% | 11.1111% |
| 6 | 13.8783% | 13.8889% |
| 7 | 16.73% | 16.6667% |
| 8 | 13.8783% | 13.8889% |
| 9 | 11.1534% | 11.1111% |
| 10 | 8.3016% | 8.3333% |
| 11 | 5.5767% | 5.5556% |
| 12 | 2.725% | 2.7778% |
| Total | 100% | 100% |
The next table shows the house edge for most bets under both the Viejas rules and a standard game with dice.
| Probabilities in Play Craps |
| Bet |
Pays |
264 Cards |
Dice |
| Pass | 1 to 1 | 1.358% | 1.414% |
| Don't pass | 1 to 1 | 1.367% | 1.364% |
| Taking odds 4, 10 | 2 to 1 | 0.506% | 0.000% |
| Taking odds 5, 9 | 3 to 2 | 0.000% | 0.000% |
| Taking odds 6, 8 | 6 to 5 | 0.248% | 0.000% |
| Laying odds 4, 10 | 1 to 2 | -0.253% | 0.000% |
| Laying odds 5, 9 | 2 to 3 | 0.000% | 0.000% |
| Laying odds 6, 8 | 5 to 6 | -0.207% | 0.000% |
| Place 4, 10 | 9 to 5 | 7.139% | 6.667% |
| Place 5, 9 | 7 to 5 | 4.000% | 4.000% |
| Place 6, 8 | 7 to 6 | 1.760% | 1.515% |
| Place to lose 4,10 | 5 to 11 | 2.785% | 3.030% |
| Place to lose 5,9 | 5 to 8 | 2.500% | 2.500% |
| Place to lose 6,8 | 4 to 5 | 1.615% | 1.818% |
| Buy 4, 10 | 39 to 21 | 5.244% | 4.762% |
| Buy 5, 9 | 29 to 21 | 4.762% | 4.762% |
| Buy 6, 8 | 23 to 21 | 4.999% | 4.762% |
| Lay 4, 10 | 19 to 41 | 2.785% | 3.030% |
| Lay 5, 9 | 19 to 31 | 2.500% | 2.500% |
| Lay 6, 8 | 19 to 23 | 1.615% | 1.818% |
| Hard 4,10 | 7 to 1 | 12.911% | 11.111% |
| Hard 6,8 | 9 to 1 | 10.973% | 9.091% |
| Field (12 pays 3 to 1) | | 3.105% | 2.778% |
| 2, 12 | 30 to 1 | 15.526% | 13.889% |
| 3, 11 | 15 to 1 | 10.773% | 11.111% |
| 7 | 4 to 1 | 16.350% | 16.667% |
What stands out in the table above is that laying odds on points of 4, 6, 8, and 10 show the house edge in negative. In other words, the player has an advantage! Of course, you have to make a negative expectation don't pass bet first. The Viejas generously allows the player to lay up to 10X odds, up to a maximum win of $1,000. If the player laid the maximum odds on points of 4, 6, 8, and 10, then the overall PLAYER edge between the don't pass and laying odds would be 0.022%.
Those figures are based on every "throw" coming from two random cards out of the 264-card shoe. However, the game uses a continuous shuffler. The way these shufflers work is with shelves. Any new cards coming in cannot be put into the top shelf, where new cards are dealt from. So, unless a new shelf is reached, there is a deeper penetration than just two cards. It is fairly obvious that even a slight penetration will work in the favor of the don't pass bet. The same cards used to get a point on the come out roll may not be available to be drawn again until a new shelf is hit, making it disproportionately likely to throw a seven instead, resulting in a win.
The brilliant new site discountgambling.net analyzes the effect of the shuffler and calculates a player advantage of 1.8% per don't pass line bet made. He goes on to introduce a card counting strategy to increase the advantage even more. Even if you don't live anywhere near San Diego, this site merits a visit. He has great material on Mississippi Stud and Ultimate Texas Hold 'Em too.
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