How Push/Fold Works
Every tournament reaches a stack depth where standard poker stops functioning. Open-raising, continuation betting, and multi-street pot navigation all assume you have chips behind to apply on a later street. Below roughly 15 big blinds you do not, and the decision collapses to a binary: shove or fold.
The reason is leverage rather than caution. A 2.5 big blind open costs 8.3% of a 30 big blind stack and 31.3% of an 8 big blind stack, and the percentage is only the visible half of the problem. Open to 2.5 with 12 behind, get called by the big blind, and the pot is roughly 5.5 with 9.5 left in front of you. Any continuation bet of half pot or more commits the rest. You cannot credibly fold to a check-raise, because a fifth of your stack is already in the middle, and you cannot apply pressure, because what remains no longer threatens anyone.
| Stack depth | 2.5bb open | Postflop SPR |
|---|---|---|
| 30 bb | 8.3% | 5.5 |
| 20 bb | 12.5% | 3.5 |
| 15 bb | 16.7% | 2.5 |
| 12 bb | 20.8% | 1.9 |
| 10 bb | 25.0% | 1.5 |
| 8 bb | 31.3% | 1.1 |
| 5 bb | 50.0% | 0.5 |
The stack-to-pot ratio column carries the argument. At 30 big blinds an SPR near 5.5 leaves room for two or three meaningful bets. At 12 big blinds the SPR is under 2, so any half-pot flop bet is past the point of return. At 8 big blinds you are functionally all in the moment you raise.
Shoving resolves all of that at once. It captures the maximum fold equity the stack can generate, deletes every postflop decision, and removes the multi-street skill edge a stronger opponent would otherwise exercise against you. That is the whole case for the framework, and it is why the solver above returns a single action per hand instead of a sizing.
Ranges Widen as Stacks Shorten
Two variables move a pushing range: how many players are still to act, and how short you are. Fewer players behind means fewer chances of running into a real hand. Shorter stacks mean the blinds and antes are a larger share of what you have left, so the cost of folding another orbit rises.
At 10 big blinds on the button you are shoving something like a third of all hands: every pair, most aces, suited broadways, suited connectors down to 76s, and a spread of offsuit broadways. From the first seat at the same depth the range contracts to premium pairs, strong aces, and a handful of suited broadways. At 5 big blinds in the small blind you are shoving close to three quarters of the deck, because hands like J4o clear the bar not on strength but on the combination of dead money and fold equity.
Calling Is Tighter Than Pushing
The most common misreading of a push/fold chart is that a hand good enough to shove is good enough to call. Fold equity is the entire difference. When you shove there are two ways to win: the opponent folds, or you hold at showdown. When you call, the first one is gone. K9o can be a profitable button shove at 8 big blinds because the blinds fold often enough to pay for the times you get called and are behind. The same hand facing a shove has to beat the shoving range outright, and it does not.
The gap is structural, and the solver shows it directly. Set an opponent to shove, put yourself in the big blind, and the call range it returns will be narrower than the push range that provoked it at every stack depth. The practical rule that follows: if you are going to play a short-stack hand, be the one shoving.
Where the Chips Actually Are
Blinds and antes are the prize. Every orbit that folds to you in late position is dead money, and every hand that folds to the small blind is a direct confrontation over it. Blind versus blind is where the largest share of short-stack EV changes hands, and it is also where passive play leaks fastest. Limping the small blind and over-folding the big blind cost a measurable amount per orbit, compounded across dozens of orbits per tournament.
Opponent tendencies move the ranges from there. Against a big blind who folds too often, push wider than the solution. Against one calling everything, tighten and shove for value. The RFI percentages in the left panel exist so you can encode that read rather than assume everyone at the table is playing the equilibrium.
Reading the Ranges
The grid is the standard 13 by 13 hand matrix. Pairs run down the diagonal, suited hands sit above it, offsuit hands below. Colour encodes the recommended action and its strength: green for a shove, purple for a raise where one is still available, a faint purple wash for hands that fold at equilibrium but carry positive shove EV on their own, and neutral grey for a fold. The counter in the header reports combos rather than hand classes, because 22 and A2s are not the same amount of range.
The left panel is the scenario. Set the number of players, the blind and ante structure, then a stack in big blinds for each seat. The star marks your position; click any seat to move it. Seats in front of you carry an action dropdown, so you can leave the table folded, put a specific seat all in, or give it an open raise at your chosen size. That last case splits the result into two tabs: your shove range against that open, and the opener's calling range against your shove.
Nash Is a Baseline, Not a Bible
A Nash equilibrium is a pair of strategies where neither side can improve by changing alone. That makes it unexploitable, which is the upside, and it is why the badge in the result header reads NASH until you edit something. The downside is symmetrical: an unexploitable strategy also does not exploit. If the big blind folds 80% of the time to your shove, equilibrium does not tell you to widen. You should widen anyway.
That is what the editable cells are for. Click a hand to force it into or out of a range, and the solver recomputes the other side against your edit rather than against the equilibrium assumption. The badge flips to ADJUSTED so you always know which numbers you are looking at, and Reset to Nash restores the solution.
Chip EV Is Not the Whole Answer
Every range on this page is solved in chip EV, where winning a thousand chips and losing a thousand chips are worth the same. Near a pay jump that stops being true. The Independent Chip Model prices a stack against the payout structure, and under ICM the loss side of an all-in costs more equity than the win side gains.
The adjustments run in predictable directions. Chip leaders push wider, because busting a short stack barely changes their equity while the blinds accumulate. Short stacks push tighter, because tournament life carries value the chip count does not show. Medium stacks tighten the most, since they are neither large enough to absorb a loss nor short enough to profit from other players busting first. A bubble factor of 1.5 means you need 50% more equity than chip EV to justify a call, and on a real bubble that number reaches 3. At those levels, hands that are clear shoves here are clear folds at the table. Model the spot in the ICM deal calculator before trusting a chip EV range on a pay jump.
Where This Stops
This solver is calibrated for 6-max and lands within about a percent of Nash across the stack depths that matter. At 8-max and full ring, short-stack multiway play is where our caller model drifts, and BBZ's all-in threshold charts remain the authority.
Two further limits are worth stating outright. The solution assumes chip EV, so every range it returns needs the ICM adjustment described above before it is used near money. And it solves the preflop game only: it prices fold equity and showdown equity, not the postflop edge you might hold at 20 big blinds where shoving is no longer forced.
Where Sklansky-Chubukov Fits
Nash is not the only way to price a shove. Sklansky-Chubukov numbers answer a different question: the deepest stack at which a small-blind shove still profits against an opponent who can see your cards. Neither model contains the other, so treat them as two instruments rather than a strict and a loose version of one.
All 169 hands, ranked by threshold →
