Quote:
collusion is ruled out.
i am too lazy to dig it out, but this was the gist of the reply to some weakish prove attempt on why GTO can not exist in multi player situations and thus sno**e could always be beat in theory (discussed in this subforum not long ago)
Derailing a bit, but to clarify what I meant:
My understanding of the problem is that two or more more players can sometimes increase their EV's by changing their strategies together, even if neither one could have achieved that by changing his strategy alone. This is called an "alliance".
An alliance is not collusion (as in information sharing), each player operates on his own, but can anticipate certain actions from his opponents, because it makes sense for them to do so. Like everybody checking to showdown when a short-stack is all-in at a tournament FT, because everybody gain when he is eliminated, and they maximize the chance of that happening by not forcing out each other before showdown.
You can always find a Nash equilibrium (where one player can not increase his EV by deviating alone), but the forming of alliances can lead to some players gaining by deviating from it.
So the question is: Is "GTO" well-defined for multiway pots? If it isn't, how can you claim that your algorithm can get there? And if it is, how can you approximate it well in a 6-max game, when even HU NL is nowhere near solved? Smart people with math degrees are encouraged to comment.
Last edited by ZenFish; 11-12-2013 at 08:01 PM.