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Some intuition

Posted By: Timothy Chow
Date: Thursday, 22 August 2024, at 2:32 a.m.

In Response To: My best probability puzzle (Max Stockslager)

My colleague Emma Cohen suggested the following way of thinking about the 2x5 case, or really the 2xk case.

If the two prizes are in the second row, then Barbara wins.

If the two prizes are in the first row, then Andrew wins (unless one of the prizes is in the first box, when it's a tie). So far it's almost a wash, with a slight edge to Barbara.

But if there is one prize in each row, then Andrew usually wins. He loses only if the prize in the first row is more than twice as far to the right as the prize in the second row, which is a relatively rare occurrence. Andrew's advantage in this case more than wipes out the slight edge to Barbara that we noted above.

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