In the context of rounds of poker, where actions include a call, a raise, or fold, CFR computes at each moment of action which would have been better to play, by having the computer play against itself and analyze as it proceeds how good or bad outcomes were. Pluribus uses a familiar approach to Libratus and DeepStack in its training of the machine, something called 'counterfactual regret minimization,' or CFR. So, Brown and Sandholm had to suffice with an approach to machine learning that is 'not guaranteed to converge to a Nash equilibrium.' It's a venture into the unknown in a sense, but one that wins nevertheless: 'ven though the techniques do not have known strong theoretical guarantees on performance outside of the two-player zero-sum setting, they are nevertheless capable of producing superhuman strategies in a wider class of strategic settings.'

As the authors write, 'Even approximating a Nash equilibrium is hard (except in special cases) in theory, and in games with more than two players, even the best complete algorithm can only address games with a handful of possible strategies per player.' Here's how it's related to artificial intelligence, how it works and why it matters.īut in multi-player Texas hold'em poker, the Nash Equilibrium becomes intractable computationally. What is machine learning? Everything you need to know

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