Craps odds
Gerolamo Cardano (1501-1576), also known as Cardan, spent much time and effort to calculate odds for craps. Being a student at University of Padua, Cardano began collecting material for his work entitled “The Book of gambling” also known as “On Casting the Die”. Not having any living allowance, he had to earn his living by gambling. “The Book of gambling” is a fascinating work, though it is not very consistent. There are practical aspects of casino games, as well as the principles of probability theory. His arguments are based on a strictly logical reasoning. Here is one of them. Die is a cube with six equal faces. While rolling, the chances that any of them would be on the top are exactly the same. Mastery and skill are nothing to do with. In other words, we have “six equal cases.” So the probability of rolling one of the faces can be expressed as1:6.
Therefore, the odds craps can be defined by p = f / c – (where p – the degree of probability, c – the total number of possible variants, f – number of favorable results).
Cardano discovered that one roll of two dice gives 36 different combinations of numbers, because we have to consider all possible combinations of the six faces of one die plus the same number of the second one (6×6 = 36). And in the case of three dice are rolling the maximum number of combinations increases to 216 (6 x 6 x 6 = 216).
Determination of the total number of variants is a simple arithmetic problem. It’s much more difficult to calculate odds on craps with two or three dice. Initially, Cardano did a lot of preparatory work to find all the probabilities of dice rolls to get the required number. Using this information, any player can easily calculate his odds in craps to get the necessary number when rolling two dice.
Odds at craps can be received by comparing the number of all variants of rolls giving this combination to their total number. Each roll of the dice involves six different variants, because the die has six faces. So for one roll of one die your chances to get the required number are 1 to 5. Accordingly, if there are two dice, the number of possible variants increases to 36. There is only one variant, which gives a number 2 or 12. Thus, your odds to roll for once the two dice of 12 or 2 are 1 to 35. Chances to roll the number 11 (or any other number that requires a combination of two digits) are 1 to 17 (or 34 to 2).
It’s easy to understand how important in craps to know in advance what are your dice odds to roll a six before a seven. As you know, in craps, as in roulette, there are only two types of bets: win-lose. Number six can be rolled with five different combinations of numbers. For a seven the number of combinations increases to six. The probability that a six will be rolled before a seven is 5 to 11. Hence, the odds in this case are 5 to 6. The probability that the four (or, a ten) will be rolled before seven is 3 to 9, and odds are 3 to 6 (because there are 3 variants of combinations of numbers giving as a result a four or a ten). For a five or a nine, the odds are 4 to 10 or 4 to 6, and for an eight (as well as a six) – 5 to 11.
Using this information a player can easily calculate craps odds of the desired combination. A seven or an eleven got at the first roll, win, and a two, a three or a dozen lose. If the player rolls the “point”, he or she wins only if it will be repeated before a seven is rolled.