[jogsxyz]

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It's not only likely, it's proven. (von Neumann and Morganstern, and then Nash proved the existence of equilibria in games with more than two players). I don't really understand your comments about "different games" - the turn and the river are part of "in every sequence" from my comments above. To specify a strategy for the game, you must specify an action in every possible sequence, from preflop through all possible flops, turns, and rivers, and all betting sequences with nonzero realization weight (ie, any sequences you allow to happen.)

jerrod

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In hold'em the relative pot equity of the two players change with every street. Does the proof includes games with a randomizing mechanism that changes relative pot equity?

Isn't changing the relative pot equity the same as changing the rules of the games? Thus a new game.