Short-stacked: push/fold and the Nash game

When your stack gets short, a standard 2.2bb open commits a big chunk of your chips but leaves you with an awkward, foldable stack if you get raised. Going all-in instead removes your post-flop mistakes entirely and adds *fold equity* — the chance everyone folds and you bank the blinds and antes risk-free.

The rule of thumb: once your stack is ~12bb or less, shoving open beats min-raising in most spots. From the small blind it kicks in even higher (15bb+) because there's only one player left to get through.

• Open-shove zone: roughly 1–12bb effective.
• Why not limp/min-raise? With 8bb you can't profitably fold to a 3-bet, so you're committed anyway — take the fold equity now.
• Effective stack is what matters: if you have 30bb but the big blind covers you with 7bb, the *meaningful* short stack for a shove-decision is the smaller one in the pot.

The Nash equilibrium push/fold charts (HoldemResources, ICMIZER) tell you the unexploitable shoving and calling ranges assuming both players play perfectly. They're your baseline, not gospel.

The driver is risk premium from antes. With antes in play, the pot you're stealing is large relative to your shove, so the math rewards aggression. A quick sanity check for an open-shove from the button into two blinds + antes: you typically need fold equity around 50–55% for a marginal hand to print.

A few anchor points worth memorizing (full-ring, with antes):

• 10bb on the button: shove roughly the top 35–40% of hands — any pair, any ace, any two Broadway, K9s+, suited connectors down to 65s.
• 10bb under the gun: much tighter, ~12–14% — 55+, ATs+/AJo+, KQs.
• From the small blind, 10bb: very wide, 45%+, because you only fight one player.

You won't carry a chart to the table, so internalize a handful of hand-class cutoffs by stack depth. These are open-shove ranges from late position (cutoff/button) with antes:

• 15bb: pairs 77+, AJo+/ATs+, KQ. Tighter than people think — at 15bb you still have room to raise-fold, so don't over-shove trash.
• 12bb: 55+, any suited ace, ATo+, KJs+, QJs, suited connectors 76s+.
• 8bb: any pair, any ace, any two Broadway, K8s+, Q9s+, J9s+, T8s+, 65s+.
• 5bb: any ace, any king, any pair, most suited hands, any two cards 8+. You're shoving ~55–60%.
• 3bb or less: any two cards from the button or SB. The blinds you win matter more than your equity when called.

Position compresses everything: from early position, cut these roughly in half. From the small blind, widen them substantially.

The single most common push/fold leak is calling too wide. When *you* shove, fold equity helps you. When you *call*, there is no fold equity — you must simply be ahead of their range often enough to cover the pot odds.

Rule of thumb at 10–15bb facing a late-position shove:

• Call off ~JJ+/AQ+ tight, AKo/AKs always. Add TT, 99, AQ, AJs as the shover's range widens (button/SB shoves).
• Pocket pairs are coin-flips at best against two overcards — calling 77 off a 12bb shove is fine vs a wide button, a trap vs an UTG shove.
• Dominated aces are the killer: A9o looks callable and is a disaster — when called you're often crushed by a better ace. Fold it unless the shove is very wide and your odds are excellent.

Quick odds anchor: getting 2-to-1, you need ~33% equity. Even A2o has ~33% vs two random cards but only ~30% vs a tight UTG range — so the *shover's range* decides the call, not your hand in a vacuum.

Nash charts assume chip-EV (every chip equal). In real tournaments, especially near the bubble and at the final table, chips you lose hurt more than chips you win help. This is ICM, and it makes correct play *tighter than the chart* when busting is costly.

Practical adjustments:

• Near the money / pay jumps: tighten your *calling* range hard. A call that's +chipEV can be a clear fold once a bust-out costs you a guaranteed pay jump. Folding AQ to a big-stack shove on the bubble is often correct.
• As the short stack with everyone else medium: you have license to shove wider — opponents can't call lightly because *their* ICM risk is high. Pressure flows from big and short stacks onto the mediums.
• Covering vs covered: shoving into players who cover you is more dangerous (you can bust); shoving into players you cover is cheap pressure.
• Pay-jump test: before calling off, ask "if I lose this, do I drop a pay tier?" If yes, demand a noticeably stronger hand than Nash suggests.

Nash is unexploitable, but your opponents aren't playing it, so deviate to punish their leaks:

• Tables that fold too much: widen your open-shoves toward *any two* — you're printing on fold equity, not showdowns. Live and low-stakes tables fold far too often to a short-stack jam.
• Tables that call too wide (calling stations): tighten your shoves toward value (pairs, strong aces, Broadways) and stop bluff-jamming junk like 84s — they'll snap with K7o.
• Stack-size targeting: prefer shoving over a covered big stack who's pot-committed to fold marginal hands, and avoid jamming into a clear calling station who covers you.
• Re-shove (re-steal) spots: when a late-position player min-opens and you have 10–18bb, jamming over them is one of the highest-EV plays in tournaments — they open wide, can't call your shove profitably, and you reclaim fold equity. Good re-shove hands: small/medium pairs, suited aces, KQ/KJs.