[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.

[gregdeon]

I know that it minimizes the expected number of moves. But, the goal is to maximize the probability that you win in fewer moves than your opponent, not minimize the expected number of moves. Given that your opponent is playing some riskier strategy, it's not intuitively obvious to me that your optimal moves for those two objectives are the same.

[baobun]

If it helps your intuition: Even at 3-4 remaining, you'll still win at the next turn. Above that your chances of getting it right are too low compared to the reduction (assuming there is an option eliminating enough).

This could be made more complicated/interesting if you play a series of games and are awarded points based on either how many rounds it took to win or how many remaining cards you still had.