I mathematically proved the best "Guess Who?" strategy [video]
5 comments
·November 22, 2025abetusk
gregdeon
I find it somewhat surprising that the optimal play when you're ahead is still just binary search. Is there an intuitive reason why it's not productive to make riskier guesses? Why not use my lead to have some chance of sealing my victory immediately, while still maintaining my lead if I'm wrong?
ironSkillet
Binary search minimizes the number of expected moves until you find the target. If you are already ahead, this is a natural thing to want to do. The reason why this doesn't work when you're behind is that your opponent can also do that and probabilistically maintain their lead.
IncreasePosts
If you're behind and you're doing the same strategy as your opponent, you'll never catch up. If you're behind doing the risky bet strategy, most times you will never catch up either because your risky bets don't pay off, but a few times they will pay off.
null
The idea is that if you're winning you can just do a binary search, but if you're losing, it's better to take some risks by making narrower guesses.
For example, let's say it's the last turn and your opponent is about to win. Say you may have 2 options but your opponent has 4 options. Instead of whittling it down to 2 options, it's better to guess one of the four. How outrageous should your guesses be is the content of the result and paper.
Paper is on archive (and linked from the video):
https://arxiv.org/abs/1509.03327