When your stack 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 maneuver — so 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

Heads-up — 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 Nash-equilibrium threshold for each seat, and the shape is what matters, not the 169 individual cells: pairs and aces always, then broadways, then suited connectors, and finally the offsuit junk that only the shortest stacks reach. Antes widen everything — more dead money makes a successful shove worth more, so both the jamming and the calling ranges stretch.

Where people go wrong

Min-raising when short. A 2x open at eight blinds commits a quarter of your stack and folds out nothing. Jam or fold — nothing in between.
Calling shoves too light. The most expensive short-stack leak. Out of the big blind you need real equity against the jamming range; "I had an ace" is not a reason on its own.
Ignoring antes. Antes are dead money that widen every range. Shoving nine blinds to collect a fat pile of blinds-plus-antes is a better proposition than shoving to collect the blinds alone — so jam wider, and call wider.
Forgetting the model is chip-EV. Nash push-fold charts assume chips equal money. Near a pay jump they do not — so tighten your calls hard when busting costs real dollars, not just chips.
Memorising cells instead of the shape. You do not need to recite a chart. You need to feel where the frontier sits at five, ten, and fifteen blinds.

A rule of thumb that travels: under roughly fifteen big blinds, never just-call or min-raise — jam or fold. Shove wide, call tighter.

How the push-fold puzzle trains this

The puzzle drops you into a heads-up short-stack spot: your stack in big blinds, your seat (small or big blind), the ante structure, and your two cards. You choose to commit your stack or fold, and we grade against a Nash-equilibrium solver's exact answer for that spot — then show you how much expected value, in big blinds, the wrong button would have cost. It deliberately serves you marginal hands, the ones sitting on the frontier where intuition actually breaks, so you drill the close decisions instead of the obvious snap-jams. Filter by stack depth and ante to rehearse the exact spots you keep facing. (In the big blind, "jam" means calling the shove all in.)

Go deeper

Push-fold is where the whole series converges. A big-blind call weighs your equity against the jammer's range at the price the pot odds lay you. And the moment real money is on the line, the chip-EV frontier bends to ICM: near a pay jump you fold hands the Nash chart says to call, because surviving is worth more than the chips suggest.