Push or fold: the chart, and how to read it

In push/fold, the first player to act either shoves or folds, and each player behind either calls or folds. Nobody makes a small raise. The charts are numerical solutions to a restricted model. A Nash equilibrium is a set of strategies where no player gains by changing theirs alone; limiting everyone to two actions does not make the model identical to unrestricted poker.

The trainer's charts are solved for six players with everyone at the same stack, an ante of an eighth of a big blind from each player, and the action folded to the shover. They are in chips: they ignore prize money, so they fit a cash game, or a tournament far from the payouts.

Each hand on the chart has a frequency. Most are 100% or 0%. A few near the edge show a share, such as K6o shoved 87% of the time from the button at 10 big blinds. Those hands are close to break-even, and shoving or folding them costs very little either way.

As in the opening charts, you can shove more hands when fewer players are left to act. The small blind shoves more than two hands in three, because only the big blind can call.

The small blind's shove is wide for a second reason. A shove does not have to be a strong hand, because it wins the blinds and antes whenever everyone folds. The pot before anyone acts here is the two blinds plus six antes:

This is an illustration for an opener who has not posted a blind. A blind's posted chips reduce its additional risk, and the actual break-even point depends on who can call and on the hand's equity when called.

In every row, the big blind calls with fewer hands than the shover shoves. Against the small blind's 69.6% shove, the big blind calls 50.0%. Against the lojack's 21.5%, it calls 18.5%.

Calling cannot make the shover fold. A call only wins at showdown, so it needs a hand that does well against the shover's range, not against a random hand. The shover gets the blinds and antes every time the caller folds, which lets it play weaker cards.

Mixing up the two ranges is an easy mistake to make: a player learns that a short stack shoves wide, then calls shoves with the same hands. A hand like K6o is a shove from the button at 10 big blinds, but the big blind folds it 96% of the time against that shove.

In these charts, the shoving ranges widen as stacks get shorter. The blinds and antes become a bigger share of what you risk, and a shove has more to win compared with what it costs.

At 5 big blinds the lojack shoves almost two hands in five. At 20 it shoves about one in nine. Small raises and limps are worth studying alongside shoves at these depths. The trainer's opening charts cover a broader action model; there is no universal depth at which one chart replaces the other.

Real tables rarely have six equal stacks, and near the money the payouts change every range. The explorer below solves the same game for any stacks, ante and payouts you enter, and shows the chip ranges next to the ICM ranges. Try the bubble preset and compare each seat. Payout pressure can tighten calls and widen some shoves, but the direction depends on the stack arrangement.