Quote:
Originally Posted by robert_utk
GTO always has blinds. Folding as a pure strategy always has the EV of losing your blind, or whatever you have invested in the pot for whatever reason. Folding as a mixed strategy is the GTO solution when continuing has an even larger negative EV.
Theoretical GTO versus multiple opponents means that Hero loses the least possible.
In heads-up this also equates to winning the most possible.
That's it. Statements beyond these two may or may not be true, or at least provably true.
No. Game theory, and game theory optimal solutions to games, aren't limited to poker. There are a lot more theoretical situations that game theory can be applied to than just poker, so clearly, gto would not always have blinds, as it would not always apply to poker. Poker, on the other hand, may well always have blinds, I don't know. That's why you can get a valid equilibrium strategy for rps, and you can get at least one equilibrium for a poker game without blinds. Which I correctly explained. You can even have any number of equilibrium strategies for choosing heads or tails for a coin flip. It's pretty pointless though, as any strategy you choose will be optimal.
For a game such as poker, assuming no rake, any equilibrium strategy will have an overall EV (when playing against any number of players playing an equilibrium strategy) of exactly 0. The only way that the EV of an equilibrium poker strategy Vs another equilibrium poker strategy (again assuming no rake) would have an EV different to 0 would be if the sequentiality of the game was changed, i.e. if players were at certain positions more frequently than others. So, for example, in hu, if one player was always the SB.
I felt my explanation as to why the gto solution to playing rps didn't really translate to poker (because poker is played with blinds) made intuitive sense, and helped to provide an answer to the question. Whether the theoretical point I made is useful (beyond the strictly theoretical) is up for debate, and it may even be incorrect (although I highly doubt it). If you do want to show it is correct or not, I'd consider looking into game theory for zero sum games (poker without rake is zero sum, with rake, negative sum, obviously), and not making wild statements which are just not true. I count 2 incorrect assertions in what you've written, and I'm not even commenting on your last sentence, and the one about losing the least possible in multiway settings is only true assuming rake. Actually, the hu statement is true assuming positive rake, I.e. the rake is paid to the players, rather than the players paying the rake.