What are the odds against throwing a seven in craps?

Craps, of course, involves rolling two dice, each of which can land on one of six possible numbers, which makes a total of 36 possible number combinations. The odds against throwing a seven or, indeed, any other specific total, in craps is determined by the number of ways to throw that total. Seven can be thrown in six different ways – the highest number of possible combinations for any two-dice total – and, unsurprisingly, is the most frequently rolled number. The probability of rolling a seven is 6/36 or, reduced to the lowest common denominator, 1/6, so mathematically, a player can expect to see a seven once in every six rolls. In other words, the odds of throwing a seven on any roll of two dice, randomly, are 5/1.

Of course, in craps, if you are betting ‘pass’ and you roll a seven on your first, or ‘come-out’, roll you win; if you roll a seven once a point has been established you lose. The pass bet is the fundamental bet in craps, paying even money, with a house edge of 1.41%. Players can also bet on the single-roll ‘Any Seven’ or ‘Big Red’, which wins if the next number thrown is a seven; the winning odds, though, are just 4/1, or a full point lower than the true odds, which equates to a house edge of 16.67%. So, despite the mathematical expectancy of seven occurring more often than any other number, Any Seven is the definitive ‘sucker’ bet in craps.