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Nash equilibrium

8 steps · read as text
↑ how often you call
100%50%0%
← you foldyou call →
↑ they stop bluffing↓ they bluff more
equilibrium
0%33%60%
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One spot, two players. They bet $100 into a $100 pot, with strong hands or bluffs. You call or fold.

the idea

A Nash equilibrium is a pair of strategies where neither player gains by changing their own, as long as the other keeps theirs.

GTO, in poker

"Game theory optimal" means playing your side of an equilibrium. It can’t be exploited, but it also doesn’t punish mistakes as hard as a strategy built for one opponent.

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06Bluffing & MDF08Variance & bankroll→Practice: play or fold
sources & further reading
Non-Cooperative Games ↗John Nash · Annals of Mathematics · 1951 · paper
A Simplified Two-Person PokerHarold W. Kuhn · Contributions to the Theory of Games · 1950 · paper
Heads-up limit hold’em poker is solved ↗Bowling, Burch, Johanson, Tammelin · Science · 2015 · paper
Superhuman AI for heads-up no-limit poker ↗Noam Brown, Tuomas Sandholm · Science · 2018 · paper