Card Craps

Introduction

As per California's state constitution, the outcome in craps cannot be determined solely by dice. Therefore, casinos typically employ a mix of dice and playing cards or sometimes just cards to mimic the effect of rolling two dice. My craps appendix 6 details the various approaches taken by different casinos in this regard.

In California, most casinos implement some version of using both cards and dice to represent the roll state. For instance, they may shuffle six cards numbered from ace to six in a random sequence, with the dice deciding which of those cards will be flipped over to reflect the roll. However, there are two casinos, Viejas and San Manuel, that utilize a shoe containing just the aces through sixes, selecting two of these to replicate a dice roll. At Viejas, this method is referred to as Play Craps, while at San Manuel, it is simply known as craps.

During my visit to San Manuel, I learned they employ 312 cards. There's much discussion regarding the exact number of cards used at Viejas. The game's proprietor asserts they use six decks totaling 54 cards each, resulting in 324 cards in total. On the other hand, Discount Gambling claims they utilize five decks of 44 cards, leading to a collective total of 264 cards. Each time I’m at Viejas, I tend to question everyone about the card count and no one seems to provide a clear response.

The total number of cards is significant due to the concept of removal. Whenever the first card is dealt, the probability of the second card matching is less than 1 in 6. With the dice, there's a 1 in 6 or 16.667% chance of a pair appearing. In the case of 324 cards, the probability is (53/323)=16.409%, whereas with 264 cards it stands at 43/263=16.350%.

I am going to demonstrate the calculations for both scenarios, utilizing 324 cards and 264 cards, so you can come to your own conclusion regarding the actual count.

324-Card Shoe

The subsequent table illustrates the house edge for most bets under the rules of Viejas compared to a traditional dice game.

The notable takeaway from the previous table is that when laying odds on points 4, 6, 8, and 10, the house edge is shown as negative, indicating that the player has a favorable position! However, this is contingent on first making a don’t pass bet with negative expectations. Viejas is quite friendly to players, permitting them to lay odds up to 10 times, capped at a maximum payout of $1,000. If a player opts for the max odds on points 4, 6, 8, and 10, the total house edge between don’t pass and laying odds turns out to be 0.016%. In the event of laying full odds on all points, the overall house edge would be as low as 0.011%.

264-Card Shoe

The subsequent table illustrates the house edge for most bets under the rules of Viejas compared to a traditional dice game.

The key point highlighted in the prior table suggests that laying odds on the points of 4, 6, 8, and 10 results in a negative house edge, signifying an advantageous position for the player! However, it's essential to first place a don’t pass bet that inherently carries a negative expectation. At Viejas, players can generously lay odds up to 10 times the bet, with the potential for a maximum win capped at $1,000. If a player takes the maximum odds for points 4, 6, 8, and 10, then the player edge against the house would be calculated at 0.022%.

These calculations assume that each 'roll' originates from two random cards drawn from the 264-card shoe. However, in reality, the game uses a continuous shuffling machine. This type of shuffler works by using shelves, and any new cards introduced cannot be placed in the top shelf, which is where new cards are dealt from. Therefore, unless a new shelf is reached, the effective play depth is greater than just two cards. It’s quite apparent that even a slight increase in depth would favor the don’t pass bet. The very cards used to establish a point during the come out roll might not be available for re-draw until a new shelf is hit, making it considerably more likely to roll a seven instead—resulting in a win.

The brilliant new site discountgambling.net analyzes the implications of the shuffling device and calculates a player advantage of 1.8% for each don’t pass line wager placed. Furthermore, he introduces a card counting strategy that could enhance the advantage even more. Even if you reside miles away from San Diego, this site is worth exploring, as it also features excellent resources on games like Mississippi Stud and Ultimate Texas Hold 'Em.

Other Number of Decks

I received information that the Choctaw casino in Oklahoma conducts their craps games using eight decks of cards that only include aces through sixes. Reportedly, they deal six cards face down, allowing players to select two of those to represent a dice roll.

To address the gameplay features related to varying deck counts, I have compiled the following table that displays the house edge for the majority of bets according to the number of decks in play.

Written by: Michael Shackleford