Push/Fold Nash Chart

A table of which starting hands to move all in with, given your stack in big blinds and your seat. It exists because a short stack has no other meaningful choice: with ten big blinds behind, raising to two and a half leaves you committed anyway, so shoving and folding are the whole decision tree. That makes the spot small enough to solve exactly, which is unusual in poker, and it is why charts like this one exist for short stacks and not for deep ones.

Because a shove is only correct relative to what calls it, and a chart that hides the calling side is asking you to take its shove range on trust. If the big blind calls nine percent of hands you can shove far wider than if they call twenty-five percent, and the equilibrium is the pair of ranges where neither side wants to change. Showing one half of a pair and calling it the answer is the thing this page is built not to do.

That the expected value of shoving and folding that hand differ by less than the precision this chart can honestly claim. The equity figures behind the chart are simulated rather than enumerated, with a stated standard error, and near the indifference line that error is larger than the gap between the two choices. Rather than paint the cell a color and imply a verdict the maths does not support, it is left marked. The indifference band is printed under the grids so you can see exactly how wide it is for the spot you are looking at, and it changes with the stack, the position and the ante.

The equilibrium is solved exactly. The hand-versus-hand equities it is solved from are simulated, and the page says which is which rather than letting one imply the other. Enumerating preflop equity exactly means walking all 1,712,304 board run-outs for each of 14,365 pairs of starting-hand cells, which is roughly twenty hours of computation, and the alternative was to write a second, faster hand evaluator purely for this page. We did not, because a second evaluator is a second source of truth for a number a reader acts on, and this site's whole position is that each published figure has one derivation. So the equities are sampled once with a fixed seed, at a precision stated on the page, and the solve on top of them is exact.

Because an ante is dead money in the middle before anyone acts, so taking the pot uncontested is worth more. At ten big blinds with no ante the blinds are 1.5 big blinds of dead money; add an eighth of a blind from each of nine players and it is 2.6, which is over seventy percent more for the same risk. That is why serious chart sets are indexed by ante structure and why a chart that silently assumes none is wrong for most modern tournaments.

Chips solves for the most chips. Prize equity (ICM) solves for the most money, and they are not the same question. In a tournament the chips you win are worth less per chip than the chips you risk, because doubling your stack does not double your chance of winning the tournament. That asymmetry makes marginal shoves that break even in chips lose money in prize terms, which is why the ICM setting produces a tighter range than the chips one from the same seat and stack. The setting you want depends on whether real money is at stake on this hand's outcome.

You can, and against unknown opponents it is a defensible default, which is what an equilibrium is for. But the range is computed against an opponent who is also playing the equilibrium, and almost nobody is. A big blind who calls far too wide should make you shove tighter than this chart says, and one who folds too much should make you shove wider, and neither adjustment is in here. Treat it as the baseline you deviate from once you know something, not as a rule.