In the two-player game of Go Fish, using a standard desk of 52 cards, where a set consists of all four cards of a given rank, is there a known optimal strategy?
When I play, if I can ask for a rank that I know the other player has, then I'll ask for it; but if not, I'll ask for the rank that I have asked for least-recently, on the grounds that my opponent has had most time to pick up that rank.
However, it might be better to bias the choice towards ranks I already have three or two cards of.
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$\begingroup$This is not a rigorous answer, sorry, but I believe there is not a single optimal solution, because it depends on the strategies of your opponents.
[I will note that I grew up with the version where a set consists of a pair of cards of the same rank, so I might be missing some subtleties here.]
The least-recently used approach would help increase the chance of an lucky match, but it also broadcasts to other players what cards you have.
If you opponents are naive, and do not note which ranks you have, then that is no problem.
If your opponents have mastered the strategy of remembering the locations of cards, then your improved strategy might be to stick to repeatedly asking about one card, and gathering more cards, until you learn of the location of another card you need.
(With the four cards to a set rule, it might be worth holding off until you are confident that you have located all the cards in the complete the set. Grouping three of the same card just makes you a bigger target.)
What happens when all of your opponents follow the strategy of sticking to one card? The flow of information is so limited, it might enter a stalemate (which I assume means everyone loses) In which case, returning to a less strict strategy at least gives a chance you will win.
I haven't modelled these thoroughly, but I am leaning toward there being no Nash Equilibrium here.
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