Last Updated: May 5, 2011

# Card Craps

## 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%.

## 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.

## Other Number of Decks

I have a report that the Choctaw casino in Oklahoma plays craps using eight decks of cards, using the aces to sixes only. I hear that they deal six face down and the player chooses two of them to represent a roll of the dice.

In an attempt to answer such a game for various number of decks, I present the following table, that shows the house edge of the majority of bets by number of decks used.

### House Edge in Card Craps by Number of Decks

Bet Pays 4 Decks 6 Decks 8 Decks 10 Decks 12 Decks 16 Decks 20 Decks Infinite
Decks
Pass 1 to 1 1.26% 1.31% 1.34% 1.35% 1.36% 1.38% 1.38% 1.41%
Don't pass 1 to 1 1.38% 1.37% 1.37% 1.37% 1.37% 1.37% 1.37% 1.36%
Taking odds 4, 10 2 to 1 1.40% 0.93% 0.70% 0.56% 0.46% 0.35% 0.28% 0.00%
Taking odds 5, 9 3 to 2 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
Taking odds 6, 8 6 to 5 0.69% 0.46% 0.34% 0.27% 0.23% 0.17% 0.14% 0.00%
Laying odds 4, 10 1 to 2 -0.70% -0.47% -0.35% -0.28% -0.23% -0.17% -0.14% 0.00%
Laying odds 5, 9 2 to 3 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
Laying odds 6, 8 5 to 6 -0.57% -0.38% -0.28% -0.23% -0.19% -0.14% -0.11% 0.00%
Place 4, 10 9 to 5 7.97% 7.53% 7.32% 7.19% 7.10% 6.99% 6.93% 6.67%
Place 5, 9 7 to 5 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00% 4.00%
Place 6, 8 7 to 6 2.19% 1.96% 1.85% 1.78% 1.74% 1.68% 1.65% 1.52%
Place to lose 4,10 5 to 11 2.35% 2.58% 2.69% 2.76% 2.81% 2.86% 2.90% 3.03%
Place to lose 5,9 5 to 8 2.50% 2.50% 2.50% 2.50% 2.50% 2.50% 2.50% 2.50%
Place to lose 6,8 4 to 5 1.26% 1.44% 1.54% 1.59% 1.63% 1.68% 1.71% 1.82%
Buy 4, 10 39 to 21 6.09% 5.65% 5.43% 5.29% 5.20% 5.09% 5.03% 4.76%
Buy 5, 9 29 to 21 4.76% 4.76% 4.76% 4.76% 4.76% 4.76% 4.76% 4.76%
Buy 6, 8 23 to 21 5.41% 5.20% 5.09% 5.02% 4.98% 4.92% 4.89% 4.76%
Lay 4, 10 19 to 41 2.35% 2.58% 2.69% 2.76% 2.81% 2.86% 2.90% 3.03%
Lay 5, 9 19 to 31 2.50% 2.50% 2.50% 2.50% 2.50% 2.50% 2.50% 2.50%
Lay 6, 8 19 to 23 1.26% 1.44% 1.54% 1.59% 1.63% 1.68% 1.71% 1.82%
Hard 4,10 7 to 1 16.08% 14.42% 13.59% 13.09% 12.76% 12.35% 12.10% 11.11%
Hard 6,8 9 to 1 14.29% 12.55% 11.68% 11.16% 10.82% 10.38% 10.13% 9.09%
Field (12 pays 2 to 1) 6.32% 6.06% 5.93% 5.86% 5.81% 5.74% 5.71% 5.56%
Field (12 pays 3 to 1) 3.68% 3.38% 3.23% 3.14% 3.08% 3.00% 2.96% 2.78%
2, 12 30 to 1 18.42% 16.90% 16.14% 15.69% 15.39% 15.01% 14.79% 13.89%
3, 11 15 to 1 10.18% 10.49% 10.65% 10.74% 10.80% 10.88% 10.93% 11.11%
Seven 4 to 1 15.79% 16.08% 16.23% 16.32% 16.38% 16.45% 16.49% 16.67%

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