The hardness of the butter is proportional to the softness of the bread.

You’re looking at the solution to one of our math puzzles. There are several other puzzles to enjoy. Please click to see 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.

Home Brain Teasers Cryptic Math Puzzles Logic Puzzles Math Puzzles Hard Math Puzzles Word Picture Puzzles

### Logic Games

Play Mastermind Same Game Play ShisenSho

### Other Games

Car Games Skiing Games Football Games Free Kid Puzzles Magic Grid Game
Dog Jokes Funny Blonde Jokes I have Learned...
Astroid Games Play Tic-Tac-Toe Play Kuzushi Play 3D Driver Wermz Online Game Antaris Free Game
How Stereograms Work Optical Illusions Visual Optical Illusions

### Play a Game

Outpost Game
Report A Broken Link Contact Information

 Brain-Fun.com Site Map | Terms of Use | Privacy & Security | Contact Us | Purchase Agreement | Send Feedback Brain Teasers, Logic Puzzles, and other Fun Brain Activities © 1996-2005 by Brain-Fun.com All Rights Reserved.