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Card Craps Simple Explanation

I have had good luck at the Circus Circus bubble craps machine. The place is a dump but their bubble machine is lucky. Report inappropriate content.

I love the card craps at Viejas, not because I’m ever going to win any money there, but because it’s so obviously countable. However, it’s almost impossible to explain to anyone why the odds are different than dice, or why the game is countable. After all, they use a Constant Shuffle Machine (CSM) with 312 cards, right? So, once again, I’m going to explain how the card buffering in the exit chute of the CSM makes the game easily countable.

A picture is worth a thousand words. Example code and simulations are the proof of the pudding. All the code used in this example is available on github, where you can browse or download it.

You can read up on the details of card craps @ Viejas. Here’s how they play it. They use a normal craps layout, but replace the dice with two cards (1 thru 6), dealt out of a 312-card CSM. They take two cards out of the shuffler, call the roll, then muck the two cards back into the CSM. They allow 10x pass/dont odds on all points.

The reason why the CSM screws up the game (favors the dont’s) is that on the comeout, the two cards that just made the point have no chance of coming out on the next roll. Nor do they have any realistic chance of coming out in the next few rolls. This is because a CSM buffers a dozen or more cards in the chute where the dealer pulls the cards from. This buffer is necessary to deal blackjack. (Imagine the dealer waiting for the machine to drop one shuffled card at a time.)

Dice Baseline

Ok, so download the example code, compile and run it with the -d option for normal dice. The results are just as you’d expect. The pass line returns -1.42%, and the dont pass returns -1.36%, and odds and counting don’t make any difference:

It takes billions of games to settle out the averages (especially when playing 10x odds), so don’t worry about the 1/100th of percents.

A) 36-Card Deck Is Same As Dice

At Pala Casino, they use a 36-card deck (one card per roll), and a simple deck shuffler. No buffer. Each card has a picture of two dice. The shuffler spits out one card from the red deck, one card from the blue deck. The player “roll” chooses between the blue or red card. Exact same odds as craps. At Pala, no one ever says anything like “How many cards are in there?”, or “This machine deals a lot of sevens!”.

B) 2-Card Roll Hurts Pass Odds

Now, let’s try the case B in the above diagram. We use the -c option to select an ideal shuffler, and -m 0 option to indicate no buffered cards in the chute.

This shows that even without a buffer, making a dice roll from two cards out of a perfectly shuffled 312-card shoe favors the don’t pass odds. You can use a simple spreadsheet to show this. The point is that you’ll distort the well-known dice roll distribution by using 2 cards dealt from a shoe. It’s a simple exercise to prove (a simple spreadsheet will give you the exact numbers).

Note the pass line player loses more by taking odds. The don’t pass player improves his return by laying 10x odds. That doesn’t happen in a regular dice game. In a dice game, taking or laying odds is fair (0 EV).

C) CSM Is Countable

At Viejas, they use a ShuffleMaster 126 CSM loaded with 312 cards. If you ever open the top (used to happen a lot when they had jams), you’ll see a buffer of approximately 16 cards in the exit chute. This distorts the game, and in general favors the Don’t Pass odds. Sometimes, a good count makes the pass odds +EV.

We’ll run the simulator for the CSM with a minimum buffer depth of 16 cards:

Now you see the pass line player is severely penalised for taking odds. I don’t think someone taking 10x odds on every point would think they’ve increased the house edge from a nominal 1.4% to a whopping 4.2% (of the flat bet). And we see that a don’t pass player laying 10x odds on every point now has a small 0.4% advantage over the house. Of course, there’s a lot of variance laying 10x odds to win an average (0.4%)(flat bet). Using a simple (and fun!) count, the don’t player has a 1.3% advantage over the house.

You can use the -v option in the cardcraps program to generate the statistics on the odds bet vs the count for each point. I ran the program, and plotted the results (don’t pass odds advantage; pass odds are inverted):

The correlation between the count and the next roll out of the CSM is clear. The count is simple and important! Quite often, you have a +/- 1-2% advantage in laying odds or taking odds. Where else can you play a craps game where the previous 6 rolls have a significant effect on the next roll?! The graph was generated with a fair simulator (using a Mersenne Twister 64-bit PRNG with a period of 2^19937-1).

Even though the game is +EV, the edge is small relative to the variance. No one will grind out any money from this game. However, it is a lot of fun to watch the rolls, know the count, and guess the outcome. Plus, the game is dealt on a table, so you get to sit and watch the rolls. And it’s probably 10x faster than a craps game with dice. You could get a roll every 5 seconds if you’re heads up with the dealer.

The count provides a fun, small predictor of the next roll out of the CSM. If you like counting, and/or predicting the next roll in craps, then you have to check out the card craps game. Here’s a video that shows how I play the game @ Viejas:

Introduction

In California the dice alone may not determine the outcome in craps. So a combination of dice and playing cards, or cards alone, are used. There are numerous ways this is done. Here are some methods I am aware of.

Agua Caliente

Twelve cards are used, an ace through six from two separate decks, with different color back sides. The cards will be shuffled and spread across the table face down. The first card of each color from one end shall be used to represent the roll. The odds are the same as with dice.

Barona

Six cards are used, numbered one to six. They are randomly placed in six positions on the table. The roll of two dice will determine which card(s) are turned over, that shall deterine the outcome for betting purposes. With each new shooter, the cards are re-arranged. The odds are the same as conventional craps.

Fantasy Springs

Same method as the Agua Caliente.

Harrah's

Two separate six-card decks, one red and one green, are used. Each shoe consists one each of ranks A, 2, 3, 4, 5, and 6. Aces count as one, all other ranks count according to its pip value. Six cards are dealt from each shoe. Two ordinary dice are thrown, one red and one green. The outcome of the dice determine which cards are turned over, which represent the roll. The odds are the same as conventional craps.

Normandie

Two partial decks are mixed together, each consisting of all four suits ranked ace to six. So, there are 48 cards total. Two cards are drawn without replacement. If they are the same suit, then there is no action. Otherwise, the two cards represent the roll. This is mathematically equivalent to using dice. There is also a 'No Call' bet, which pays 3 to 1 on two cards of the same suit. The house edge on that bet is 6.38%. As usual with the Los Angeles county casinos, the player must also pay about a 1% fee on all bets.

Pala

The following equipment is used: (A) A red die numbered with three 1's, and three 4's, (B) a blue die numbered with three 2's, and three 3's, and (C) A 36-card deck featuring all possible permutations of two dice. Two cards are drawn at random and placed face down over red and blue regions of the table. The dice are thrown. If the red die is higher then the red card is turned over and used as the roll, if the blue die is higher then the blue card is used. Note that there can be no ties. Also the blue die is irrelevant. A 1 on the red die will always lose to the blue die, and a 4 will always win. The odds are the same as conventional craps.

The 'Super Field' pays if both cards are the 1-1 and 6-6, in either order. Wins pay 500 to 1. The probability of winning is 0.154%, for a house edge of 22.685%.

Pechanga

Pechanga currently follows the Barona method (at least as of 7/26/16). They have previously used other methods so please don't write in to correct me unless you have very current information.

Pauma

A 73-card deck is used, consisting of 12 each of cards ace to six, and one joker. Two cards are drawn to determine the roll. If the first card is the joker, there is no action, and two new cards are drawn. If the second card is the joker, it shall match the first card. The odds are the same as conventional craps.

San Manuel Bubble Craps

The joker side bet pays 60 FOR 1 if the first card is a joker. The probability of winning is 1.389%, for a house edge of 16.67%.

The four suit bets, one for each suit, win if both cards are the suit specified, and pays 14 FOR 1. The probability of winning is 5.822%, for a house edge of 18.493%.

San Manuel

Same procedure as Viejas, except 312 cards are in the shuffler and they call it just 'craps.'

Sycuan

The Sycuan follows the same procedure as Barona.

Viejas

The game is dealt at a blackjack-size table called 'Card Craps.' I'm told a 264-card shoe is used, consisting of 44 cards each of ranks ace to six. They start with five 54-card decks (9 cards each numbered 1 to 6), and then remove one of each face (5×54-6=264), to accomodate the shuffler. Two cards are drawn to represent the roll. Due to the effect of non-replacement, the odds will be slightly different from conventional craps.

Bubble Craps San Manuel Zeno

The maximum win on odds bets is $1,000. If the player wishes to get that limit, with 10X odds after a pass or come bet, then he should not bet more than $10 on a pass or come bet, and $100 on a don't pass or don't come.

For more information, see my page on Card Craps.

Southern California Odds Survey

Here is what I know of the odds allowed in the casinos of southern California.

San Diego County Craps Survey

* The Viejas 10X odds game has a maximum odds bet of $600.

'3x-4x-5x' means the player can bet 3 times his pass/come bet with a point of 4 or 10, 4 times with a 5 or 9, and 5 times with a 6 or 8. Assuming the player always takes the maximum odds, under this rule, his odds win will always be 6 times his pass line bet. The house edge column is the combined house edge between the pass/come bet and full odds.

Disclaimer: The Barona Casino hired me to perform surveys of San Diego casinos for backjack, roulette, and craps. The table above summarizes my findings.

Oklahoma

It seems that Oklahoma also has card craps. Here is what little I know about it.

Winstar

The Winstar uses a 36-card deck, one card for each two-dice combination. It is my understanding that the cards look ordinary, except for a bar code, which corresponds to the dice roll.

Internal Links

• How the house edge for each bet is derived, in brief.
• The house edge of all the major bets on both a per-bet made and per-roll basis
• Dice Control Experiments. The results of two experiments on skillful dice throwing.
• Dice Control Advantage. The player advantage, assuming he can influence the dice.
• Craps variants. Alternative rules and bets such as the Fire Bet, Crapless Craps, and Card Craps.
• California craps. How craps is played in California using playing cards.
• Play Craps. Craps game using cards at the Viejas casino in San Diego.
• Number of Rolls Table. Probability of a shooter lasting 1 to 200 rolls before a seven-out.
• Ask the Wizard. See craps questions I've answered about:
  
• Simple Craps game. My simple Java craps game.

External Links

• Las Vegas craps survey — The max odds bet allowed at each casino.

Bubble Craps San Manuel Cardoso