Week 7: Fish

I finished revising the calculations for when you start with 6 cards, 5 cards, or 4 cards from a set. This has been so much work and pain. Now I think about it, looking at the results, there are a few things I could’ve simplified: using recursion to calculate the expected values, especially when 5 or more cards from the set is split between your opponent and you; doing more computations and shortening expressions using the fact that the game is symmetric and has a constant sum, etc.

One problem I encountered is that using our current model, the opponent does not adjust their strategies based on your trolling frequencies, and does not change their own strategies based on how often you think they troll. This sometimes leads to very obvious dominant strategies of to troll versus not to troll, trivializing the entire project. So, I thought, instead of maybe computing the amount of information given in Fish without trolling, I should do another analysis on Fish, but both players play “optimally”.

In fact, there is a clear dominant strategy in Fish without trolling, which is already summarized by experienced players: always work on the same set as your teammates, if a card from the set has been asked and you don’t have the card, ask a player on the other team for that card. If otherwise, start a new set. I will skip the proof in the blog, but it isn’t long. In fact, I already have examples of why it works: my friend won the Fish tournament with this precise strategy and good memory.