{"dataset":"push-fold-heads-up","title":"Heads-up push or fold charts","license":"CC BY 4.0","licenseUrl":"https://creativecommons.org/licenses/by/4.0/","credit":"George Li, georgelipoker.com","description":"The small blind shove frequency and the big blind call frequency for every starting hand at every stack from 1 to 20 big blinds in half steps, with the EV of acting and the equity behind it. Chips only, no ante, solved to an exploitability of at most 0.001 big blind.","data":{"schema":"georgelipoker/pushfold-hu/1","description":"Heads-up push or fold equilibrium, chips only. The small blind moves all in or folds; facing the shove the big blind calls or folds. push[k] and call[k] are the frequencies of class k (grid order, see classes) at each effective stack. EVs are in big blinds, the chip change from the start of the hand before the blinds go in.","game":{"smallBlind":0.5,"bigBlind":1,"ante":0,"depths":"effective stacks 1 to 20 big blinds in steps of 0.5","sbFoldEv":-0.5,"bbFoldEv":-1,"calledEv":"S x (2e - 1) for a stack S and the player's share e of the pot at showdown, ties split"},"method":{"hands":"the 169 starting-hand classes; the small blind holds class i while the big blind holds class j in proportion to compat[i][j] (pairs of specific hands that share no card, so blockers count)","equity":"win plus half of tie from equity-matrix.json, small blind against big blind","solver":"fictitious play (each round, each player takes the best response to the other's average so far), then the hands on the edge are made exactly indifferent with a small linear solve; the profile with the lower exploitability is kept","exploitability":"what the two players together would gain by each switching to a best response against the published strategies, in big blinds per hand, rounded up to 9 decimals; at most 0.001 at every depth","rounding":"frequencies to 4 decimals, frequencies of all hands, EVs and equities to 5; every figure is computed from the rounded strategies","fields":{"pushFrequency":"share of all 1,326 hands the small blind shoves","callFrequency":"share of all 1,326 hands the big blind calls a shove with","sbValue":"small blind's EV per hand dealt","sbPushEv":"small blind's EV of shoving each class against the call strategy (folding is sbFoldEv)","bbCallEv":"big blind's EV of calling the shove with each class (folding is bbFoldEv); null when no shove can meet the class","sbEquityWhenCalled":"small blind's equity with each class against the hands that call; null when none can","bbEquityVsPush":"big blind's equity with each class against the hands that shove; null when none can","method":"exact when the indifference solve gave the profile, average when the fictitious-play averages did","iterations":"fictitious-play rounds 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