I've been generally wondering about what sort of winrate good players can expect vs. worse players, and thought of an interesting limit to this winrate. In NLHE, if the worse player just blindly shoves all-in before the flop every turn, what kind of winrate can an optimal player hope to have against them? Their strategy probably amounts to just waiting for a good enough hand to call; at best you get AA and have a 85% chance to with the hand, but in practice you probably end up having to call with worse hands. Has anyone done the math and figured this out?
EDIT: After some discussions with answerers, I want to clarify some points in this question:
- Each player starts with 50BB, and the shover starts as BB
- Each player stays until one player runs out of chips, at which point the game ends
- The goal of the pro player is to win this single game with as high a probability as possible, knowing their opponent's strategy is to shove pre-flop every hand