This might be the right thread for this.
I was musing this morning on how the Secretary Problem might be modified to handle "who should I main" in MOBAs.
For this, you'd want some same assumptions, some different assumptions:
I. You are going to play N games testing A applicants before selecting your applicant (the same, people tend to have an idea of how much time they want to waste experimenting)
II. Unlike the Secretary problem, you are free to go ahead and play all N games (though it'd be nice to have a strategy where you quit early if you can completely rule out all but one hero.)
III. Like the secretary problem, the process of gathering information about applicants is sequential in nature, but unlike the secretary problem, you can make up to P passes through the list, revisiting only sufficiently impressive cantidates (The way most players enjoy/efficiently learn suggests that games on the same hero be consecutive. The large number of characters in a MOBA game requires that P be small.. definitely less than ten. In Starcraft A=three so P can equal, like, twenty.
It seems like this may need to be revised or cleaned up to reflect that playing a large number of games on a champion, leaving it, then returning it for another long string of games, creates far less testing bias then playing a champion once on first pass, once on second past, etc.)
IV. Like the secretary problem, each applicant has a true value V. V is your winrate over an infinite number of games with the champion, so it ranges from 0 to 1. You could probably use practical knowledge about the game to clamp the values to at least .1 through .9 and probably something even smarter than that, but there's lots of parameters already.
V. Like the secretary problem, you gather information about V when you spend time with an applicant. Unlike the secretary problem, your knowledge is imperfect, and dependent on the amount of time you spend with an applicant. You'll get a value of wins over games played, and that will have an imperfect correspondence with V, but it gives you some information about V.
VI. Unlike the secretary problem, the final choice does not have to be last champ you played. Due to the consequences of rule III and rule I you still might have to reject choices early on in a manner somewhat reminiscent of how those secretaries get very indignant if you don't hire them on the spot.
VII. The optimal solution to the problem maximizes the V of the final champion selected. The value of V is more important than how V is relative to the other champions, though, unlike the secretary problem (all though if the secretary problem were made more practical, it would probably also be more concerned with V)(Unless there's all the ones you don't hire join other company's and then you lose the intramural between company's secretary-off).
The idea interest me a bit, and as MOBAs get more stable and balanced there might be more interest in playing the game in a style that sort of chases the solution here.
I find it rather fascinating that the optimal solution quite possibly excludes some applicants entirely when A is small, and N is large. Maybe even if P is still large or infinite. Because getting accurate information could be so much more important than being open to every possibility. The interesting question is, how many applicants will get excluded? If it proves best to clamp the lowest to highest winrates as something like 15%-60%, it might, paradoxically, sometimes be correct to ignore a totally unplayed virgin champion while you continue to explore a champion you are are 1-1 with, even if the algorithm is doing much better than a .5 V on average, just because you can build a reliable source of information without being two games behind and have ruled against the champion being awful.
Idk just some musings in b4 no1 reads