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Nash equilibria in Ballmer's binary-search interview game
Yesterday John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question,” and in the Hacker News discussion, among the predictable “interview culture is flawed!!” complaints, there was some discussion of whether binary search was even the right way to solve Ballmer’s puzzle. Here’s a stab at an answer.
HN rightly points out that the intangible value of getting to play such a game against Steve Ballmer is very high regardless of how many dollars you expect to win or lose at it. But, as Ballmer points out in the linked video, if he knows you’re going to do a plain old binary search, then he certainly won’t ever choose 50 as his secret number. If Ballmer avoids those eleven numbers, and chooses uniformly at random from among the rest, that alone is enough to lower the expected value of the game from $952 to about $949.55.
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