![]() ![]() ![]() This was the approach used by the University of Alberta for years in the Annual Computer Poker Competition, and it crushed the competition there. However - in practice, the strategies produced by CFR for multiplayer games still appear to be quite strong, even if not Nash. If you plot that loss over time while CFR is running, it becomes clear that it does not converge to Nash: it eventually bottoms out and does not improve further. If you take the strategy profile CFR produces and then compute a best response in each position, those best responses each improve over the strategy profile. Like you suggested, we did this with best response calculations. But in a slightly larger toy game, 3p Leduc poker, we empirically found that it does not. In the tiny 3p game of 3p Kuhn poker (3 players, 4 card deck, enough chips for one bet) we found that it does go to Nash (here's the paper. In a multiplayer zero-sum game, there's no theoretical proof that it should go to Nash. Not quite: it really does only go to Nash in a 2p zero sum game. ![]()
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