Math Puzzle Answer

Here is the solution to one of our math puzzles. There are several other puzzles for you to solve. Please click to find all of our math puzzles.

Game of Craps - Answer

The number of rolls of the dice you can expect in a game of craps is 3.376. Here's the solution:

The frequency (F) of each number (N) rolled is F(N) = (6 - lN - 7l) / 36.

Of all 36 possibilities, the 12 which have an N of 2, 3, 7, 11, or 12 end on the first roll.

For other values or N, the probability of ending on the next roll is P(N) = F(N) + F(7). So the expected number of rolls after the first roll for these values of N is 1 / P(N).

For all possibilities, the expected number of rolls is
E = 1 + ∑(F(N)/P(N)) = 1 + 2(3/9 + 4/10 + 5/11) = 557/165 = 3.376.