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My best probability puzzle

Posted By: Bob Koca
Date: Friday, 16 August 2024, at 1:59 p.m.

In Response To: My best probability puzzle (Timothy Chow)

Andrew is more likely to win.

Suppose instead that they were guessing randomly and simultaneously announcing their guess to each other at each step. Then the organizer informs at each step if someone has one. As long as the new guesses are not stupidly chosen to be a previous guess any guess is equally likely to win and any guess is as good as another.

The actual game is like that but with stupid guesses being made. If the game lasts that long a stupid guess comes from Barbara at steps 4, 7, 10, 11, 13, 14 and from Andrew at steps 6, 7, 11, 12, 13, 14.

Earlier stupid guesses are more important and we can match them as

4 < 6

7 = 7

10 = 11

11 < 12

13 = 13

14 = 14.

Barbara's stupid guesses coming earlier are more impactful. The same analysis applies if there had been only 1 hidden prize or up to 11 hidden prizes. If 11 or more someone would have necessarily won by step 3 so the stupid guesses do not come into play.

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