IBM Ponder This #135 · July 2009

What is the probability that the last move in a backgammon (link resides outside of ibm.com) game will be a double? To make things easier, we assume that all the 15 checkers of each player are at their 1-point (just ready to bear-off); so each player, in its turn, removes (bear-off) two checkers for every non-double throw and four checkers for every double.

Hint: The solution is *not* the trivial 1/6.

07/01: Note that there are two players.

07/21: The game is played till its end, even if the result is already determined. For example, when a player has only one checker left, he still throws the dices and game is defined to end with a double if the dices come up equal.

Solution

Best opened after a real attempt

To be added.