I'm currently setting up a model using data from the game "Hearthstone". Those familiar with the game know that it can (for the most part) be described as a zero-sum game, where players choose a deck before being randomly matched against another player. These decks have over-all winrates against all players, as well as winrates for each specific matchup (Deck A vs Deck B).
Let's assume there are only 5 decks that can be played (there are a lot more). We could then form a 5x5 expected payoff matrix for each matchup using the respective winrates of all decks.
My question is this: how would the probability of encountering a certain deck factor in? We could technically calculate an optimal strategy from the payoff matrix, but it doesn't seem like that takes into account the likelihood of encountering a certain deck more than another.
At first I thought it could be a type of signaling game, where the matchmaking process was a "type" drawn randomly, but that isn't the case here, since the players are making their decisions before this occurs.
I should have specified. I mention MSNE since I'm trying to see if you can better your chances of winning statistically by playing a number decks in a number of sequential games, rather than just choosing one deck and sticking with it.