Game of Craps Math Puzzle

The rules for a game of craps are:

If a 7 or an 11 is rolled on the first throw of two dice, the player wins.

If a 2, 3, or 12 is rolled, the player loses.

If any other number is rolled, the player continues to roll until

A 7 is rolled. - The player loses.

The original number is rolled. - The player wins.

What is the expected number of rolls per play?

Thanks to Greg A. Qualls.

Click to find the answer to this math puzzle.