Push or fold: the short-stack endgame, solved
When your (The smaller of two players' stacks in a confrontation, since that is the most either side can actually win or lose in the hand.) drops to about fifteen big blinds and below, poker stops being a game of postflop finesse. There is no room to raise, get raised, and still have chips to manoeuvre. The winning strategy collapses to two buttons: jam all in, or fold. The happy part: this corner of the game is essentially solved. Learn the jam-or-fold frontier and you will never again agonise over a nine-blind spot.
Why it collapses to two buttons
A small raise when you are short is the worst of both worlds: it commits a chunk of your stack and folds nothing out, so you get shoved on and called off anyway. Going all in fixes both problems at once.
- Shoving wins the blinds and antes outright a large share of the time, and when you do get called you still have live equity. You also take away your opponent's chance to outplay you after the flop: there is no flop.
- Folding risks nothing beyond the blind you already posted.
So the decision is a clean comparison: the expected value of jamming versus the expected value of folding. Pick the bigger number. That is the whole game when you are short.
Two seats, two ranges
Played (A hand, or an entire match, played between exactly two players.) (the spot the puzzle drills), there are two roles, and they do not use the same range.
- You shove (the small blind). You jam wide, because much of your profit comes from simply taking the blinds and antes uncontested. The shorter your stack and the more dead money in the middle, the wider you go, toward any two cards at the very bottom depths.
- You face a shove (the big blind). You call tighter. Calling has no fold equity: you can only win at showdown, so you need genuine equity against the whole range that just jammed, at the price the pot is offering. This is pot odds and hand reading, all in one decision.
Every stack depth has a (The unexploitable strategy for a spot: the one no opponent can profit from by deviating away from, regardless of how they adjust.) threshold for each seat: the unexploitable strategy that no opponent can profit from by deviating. Nash is the correct starting point, not the final answer: against a caller who folds too much you can jam even wider, and against one who calls too much you tighten.
What matters is the shape, not the 169 individual cells: pairs and aces always, then (Any card ranked ten or higher: ten, jack, queen, king, or ace. A broadway hand holds two of them.)s, then suited connectors, and finally the offsuit junk that only the shortest stacks reach.
Antes widen everything. More dead money from (A small forced bet posted by every player before the hand starts, on top of the blinds, adding dead money to the pot regardless of who wins it.)s makes a successful shove worth more, so both the jamming and the calling ranges stretch.