[a-dub]

agree about the EV stuff. it only makes sense over many draws and the problem states that he is thinking of "a number", that sounds like one game.

that said, the problem screams binary search and you know your opponent is a computer person, so i guess the question is: if you make a bet that your opponent is making an adversarial choice that assumes you're going to do a vanilla binary search, can you improve your odds of coming out ahead by modifying your own binary search to always assume the target is an adversarial one?

[nighthawk454]

That is an interesting question. I suppose it's equivalent to the 'worst case' performance for binary search, which would be a relevant topic. Finding the optimal strategy in the case where the opponent _may_ be adversarial could be interesting. I don't imagine the odds improve compared to the base situation, but not sure

[a-dub]

what if you, say, decided to make the bet that your opponent is adversarial and just did binary search, but restricted high, low and mid to snap to the nearest adversarial numbers when adjusting them?