A backgammon ending

You have reached an end-game position in backgammon where it is your roll.

You have a 19/36 chance to win on this roll. If you are given a second roll, you will win with 100% chance.

If you do not win on your first roll, your opponent has a 29/36 chance to win with his lone roll.

What is your total chance to win the game, to four decimal places? For instance, if you think your overall chance of winning is 15/16, you would enter 0.9375.

The answer is 0.6196.

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1 solution

Denton Young
Jun 12, 2018

Your total chance of winning is 19/36 (on first roll) + (17/36 * 7/36), the chance of missing your first roll and getting a second roll.

Adding those up and converting to a decimal yields 0.6196

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