How the charts and grades are made

The preflop charts are solver output for a six-handed table. A counterfactual regret minimization (CFR) solver plays the whole preflop tree (opens, 3-bets, 4-bets, 5-bet jams, cold calls and squeezes) on the 169 starting hand classes, over many rounds, each seat adjusting to the others until the strategies settle. The 100 big blind charts have no ante; the 60, 40, 25, 20 and 15 big blind charts have an ante of 12.5% of the big blind.

A hand that is called goes to the flop, and the solver does not play the flop out. It gives each hand its showdown equity, scaled by an equity realization factor for the seat it is in. Each chart page names its own factors.

Where it stops being right: the factors are a model of postflop play, not a solve of it, which is why the shorter-stack charts are labeled approximate. The charts are chipEV, so they ignore tournament payouts, and they assume six players.

The push/fold charts solve a smaller game: everyone before you folds, you either go all in or fold, and each player behind either calls or folds. The trainer's solver runs 1,200 rounds of that game toward a equilibrium, in the browser for the calculator and ahead of time for the chart pages. Its tests check it against the published ten big blind heads-up chart, and a test solves every chart page again and fails if the page and the solver disagree. With payouts set, the calculator turns chips into prize equity with ICM.

Where it stops being right: real players also min-raise, limp and call, which this game leaves out, and the deeper the stacks the more those plays matter. Everyone behind a caller is assumed to fold.

The equity of every starting hand against every other is counted exactly, by dealing out every possible board for each pair of hand classes, not by sampling. Poker math uses the same code for its worked examples.

In the full trainer, flop decisions in 13 heads-up spots are graded against exact solutions for 575 flops: solved until neither player could gain more than 0.75% of the pot by changing strategy. On any other flop, the app's engine, Turnstone, searches the flop and asks a network trained on 100,000 exact turn solves what each hand is worth. Measured over those 575 flops it comes within about 0.3% of the pot of the exact answer on average, and 0.79% in its worst spot, 3-bet pots at 40 big blinds. The turn and the river are solved exactly while you play, for the trainer's own bet sizes.

Where it stops being right: the engine answers heads-up pots after a raise and a call or a 3-bet and a call, at the trainer's bet sizes. Pots with three or more players, limped pots and 4-bet pots are graded by rules of thumb, and the grade says so.

Where the trainer knows what each action is worth, a decision is graded by its EV loss as a share of the pot: Best up to 0.25%, Correct up to 2%, Inaccuracy up to 5%, Wrong up to 15%, and Blunder beyond.

Where a chart gives only how often each action is taken, the grade follows that frequency: Best if the chart takes your action at least 50% of the time or more often than any other, Correct from 25%, Inaccuracy from 10%, Wrong below that, and Blunder if the chart never takes it. Every grade at the table names its source: an exact solve, an engine estimate with its measured loss, an approximate chart or a rule of thumb.

Where it stops being right: a grade measures a decision against a model of the game, not against the players you will meet. Against a player who plays badly in a known way, the best play can differ from the chart.

The worked examples on poker math are computed by the same code that grades your play. Each psychology idea names its source and is labeled well supported, contested or table lore, with a line on what it does not mean.