perplexus.info :: Probability : A Game of Dice Puzzle

A Game of Dice Puzzle (Posted on 2022-11-14)

Aaron offers Berenice to play a game of dice with him. Aaron explains the game to Berenice as follows:

"We each get one die, the highest one wins. If we tie, I win, but since you always lose when you roll a one, if you roll a one you can roll it again. If you get a one the second time you have to keep it."

What is each person's probability of winning? What are the probabilities of winning if Berenice can keep rolling until she gets something besides a one?

No Solution Yet Submitted by K Sengupta

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soln

| Comment 1 of 7

(original post - I still have a sim error somewhere, but the math seems right). The bold letters are who wins when B does not roll 1.

In the original game, I get

prob A wins: (5/6) (15/30) + (1/6) (21/36) = 0.51389

prob B wins: (5/6) (15/30) + (1/6) (15/36) = 0.48611

B 1 2 3 4 5 6 =A

----------------

1 A A A A A A (this row is used only in round 2 of first game)

2 B A A A A A

3 B B A A A A

4 B B B A A A

5 B B B B A A

6 B B B B B A

In the revised game, it's 50/50 since they each have 15 different ways to win, (15/30)

Edited on November 14, 2022, 11:06 am

Posted by Steven Lord on 2022-11-14 09:30:30

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