A backgammon settlement

Probability Level 2

You've reached the very end of a backgammon game. The stake (how much the loser pays the winner) is $8, and it is your opponent's roll. He has a 25/36 chance of winning with his roll: if he does not, and you get a roll, you are certain to win.

He offers to settle the game. How much should you pay him?

Choose the closest option.

$3 $4 $5 $2 $1

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Jun 18, 2018

Your opponent's mathematical expectation is (25/36 - 11/36) * $8, or 14/36 * $8, which is $112/36 or $3.11. So to the nearest dollar, you should pay him $3.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

you might clarify what you mean by "the stake is $8" for the ones of us who are not native English speakers. I understood that the pot was $8 meaning each player had bet $4.

Jose Fernandez Goycoolea - 2 years, 11 months ago

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Wording clarified.

Denton Young - 2 years, 11 months ago

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