John Graham-Cumming tackled the issue of Steve Ballmer’s incorrect binary search interview question. While the expected value of the game is seemingly $952, interestingly, strategic variations by Ballmer can substantially affect this number. Binary search appears the best method at first, yet the game’s Nash equilibrium is more complex. The analysis delves into a simplified three-number version before expanding on a four-number and five-number scenario. Surprisingly, the Nash equilibrium results in a conformist strategy, where the best option for both parties is to uniformly pick numbers. The process reveals how variations can impact the game outcomes significantly.
https://quuxplusone.github.io/blog/2024/09/04/the-game-is-flawed/