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 6 goes into detail about how several different casinos do it.
Most California casinos have some method of using cards and dice to represent a roll. For example, six cards (the ace to six) may be placed in a random order and the dice determine which cards are flipped over to represent the roll. However, two casinos, the Viejas and San Manuel, use a shoe of only aces to sixes and select two of them to represent a roll of the dice. At the Viejas they refer to this method of playing as Play Craps. At the San Manuel it is just craps.
At the San Manuel I was told they use 312 cards. There is quite a bit of 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. Whenever I’m at Viejas, I always bother everybody about how many cards they use, and nobody can ever give me a straight answer to the question.
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.
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%.
