You can read more about crapless craps here High Point Craps This version of Craps is pretty simple, but a much larger deviation from standard craps than craps variants other variants. Variants can be divided into equivalence classes based which variants can reach each other using only outcome preserving operations. It seems a moderate and amusing challenge to characterize this group and count the number of equivalence classes of games, but I will have to leave that to a future article.

The cards is each deck are only those cards which can be used to represent the faces of the dice I. In exchange, you lose the 11 as a sure win on the come out roll; instead, any other number other than 7 becomes the point.

The functional definition of the craps game will simply serve as a guide to the Python implementation, which will perhaps be much easier to read. Fraction 1, 68: The player then has three more rolls to try and hit the point number again without rolling a 1; if he fails, the die is passed to the next player and the cycle repeats.

This game of California Craps can be a little confusing to understand as first and there are several variants of the game and in this section of the website we shall take a look at each of them.

Nevertheless, my conjecture that craps had been explicitly designed as a maximally fair game was thoroughly disproved when we were able to construct thousands of variants that were all fairer than craps variants original. Conclusion Craps is a suprisingly fair game.

The house edge here is 2. However it must be pointed out that the house edge attached to both these side bets are enormous and should be avoided at all costs! However, it is important to consider the odds of these rolls.

With this parameterization, every craps-variant has the same rules. The player then repeatedly rolls until one of two things happen: Fraction 5, 367: If the player gets 11 or 12, he or she wins automatically.

Any other total is established as the point. For example, if two games are the same except one has an out of 5 and the other an out of 9, they will always have the exact same probability winning the whole game because 5 and 9 have the same probability.

A full generalization would not have any specific magic numbers hard-coded in, but would instead treat all numbers used in the rules as parameters. On the other hand, a come out roll of 1 is a loser.

Bubble Craps Machines Since several of our readers have asked us about the bubble craps machines that is found in some casinos, we decided to explain what exactly is bubble craps. Any of the middle numbers establishes the point.

The player then must roll a total higher than the point to win. If you would like to see the full list, here it is in compressed format. Fraction 1, 363: The odds of making a point on the 2 or 12 are only 1 in 7, and the odds of craps variants a 3 or 11 are 1 in 4 — that is, you are not gaining as much as it seems by scrapping the craps numbers, and you are losing one of your big chances to win on the come out roll.

Note that while all of these games are unique under our definition, they exhibit several kinds of symmetry. A win on the come out roll that is, the shooter rolled a 6 pays 1 to 1; a thrown point on the second or fourth rolls pays 2 to 1; and a win on the third roll pays 1 to 1 again.

The game is played by two cards being dealt out to replicate the rolling of the dice, however it should be pointed out that when playing this game as the cards are not returned to the shoe after being used the overall odds attached via the remaining cards left to be dealt in the shoe will change accordingly much like in Blackjack where a card counter will use the history of the cards dealt out to determine what cards are left.

When the shooter first rolls, a roll of 2 or 3 is ignored completely and the dice are returned to be thrown again. Pauma Craps Variant - This is an interesting version of Craps which uses 73 cards in the shoe, the make up of these cards are an equal division between the Ace to Sixes and one addition card that card being a Joker.

Fraction 1, 9 Fraction 1, 184: A full solution may also be found, for example, in the book Fifty Challenging Problems in Probability with Solutions. Play Craps Online for Money Are you ready to play craps online? The shooter only throws one roll of the dice: It was later adopted by French gamblers and eventually morphed into the high-energy attraction it is today.