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Respond to the question: Guess Who game and theory probability?

11/06/2005 09:57 AM by Sam Gong; Guess Who game and theory / probability

I recently played the child's game of Guess Who against a girl. The objective is simple, there are 24 characters defined by varying characteristics. Each player picks a character card at random and then you alternate asking questions to try to find out who the other person is ('Does your person have red hair?') etc. Being a computer scientist, I used a binary search whereby I asked questions that eliminated half of the remaining possible characters at a time. This gurantees guessing the answer in 6 questions, in the worst case.
Using this method, I lost the first 7 straight games because she would ask questions such as 'Does your character have glasses?'
Assuming she doesn't include her character, only 5/23 possible characters wear galsses. If I did have glasses, then after the first question her pool is down to 5 while mine is at 12.
If she was wrong about the glasses, she would follow up with an equally unlikely question. Say it was a 4/17.
Anyway. After losing to this seemingly luck-based strategy 7 straight tmes I had to ask myself if it didn't have some mathematical validity. I hope it's not inappropriate to ask how I would go about solving this game. What is the best strategy to guess their character faster than they can guess yours? Is it different if you have to go 2nd and start out a question behind? Like I said, my background isn't in game theory or probability. Any pointers, and especially the solution, would be greatly appreciated. [Manage messages]