Week 8: Fish

This week I had an epiphany. Instead of wondering what a logical opponent would do, or what variables I should add to my recursion, I should just assume that my strategy is optimal, and both sides would follow it perfectly. In other words, I will hold the assumptions constant, and try to minimize or maximize expected payoffs from both sides. The difference is that no matter what you do, the opponent will follow the exact same strategy, or in other words, troll, ask randomly, and ask for a card already asked for, with the same probability as you for every situation.

The reason this works is the symmetric properties of the game. If both players play optimally, then they should have the exact same optimal strategy, assuming it is unique. Combining this with the fact that it is sort of a zero-sum game, a mixed strategy nash equilibrium must exist.

From here, I continued working on the computations of the version where the opponent follows a fixed strategy, and I am almost done with the case where you start with 3 cards of the set.