Card Craps

Last update: Nov. 3, 2009

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 Card Craps. 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 Card Craps. It is my understanding that they use a 264-card shoe, consisting of 44 cards each numbered 1 to 6. They take two cards out of a shuffling machine to represent a roll of the dice. What makes the odds different from a game with dice is the effect of removal. Whatever the first card removed is, there will be 43 out of 263 of that card left in the shoe. So, the probability of getting a pair is 43/263 = 16.35%, a little less than the 16.67% you would have in a game with dice.

The following table shows the probability of each total from 2 to 12 under the 264-card shoe rules at Viejas and a standard game using dice.

The next table shows the house edge for most bets under both the Viejas rules and a standard game with dice.

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. However, the Viejas generously allows the player to lay up to 10X odds, up to a maximum win of $1,000. That turns out to be enough to overcome the loss on the don't pass bet. To be specific, if the player lays the full odds on all points except 5 and 9, he can expect to win 0.001631 units per come out roll. The average wager per come out roll is 7.6515 units. So, the overall player advantage is 0.001631/7.6515 = 0.000213. It is pretty small, but how often does the player have a chance to have the odds in his favor at all?

The 0.16% profit per don't pass bet may actually be understated. That is 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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