Welcome to lesson 7, narrated by Hermes.
Push-fold is the discipline that turns 15bb stacks from "death row" into "easily exploitable spots". When you're short, post-flop play stops mattering, what matters is whether you shove the right hands.
The framework
Sklansky and Chubukov (2005) gave us the first solved push-fold framework: each starting hand has a maximum profitable shove depth versus a random calling range. Above that stack depth, fold. At or below, push, and against perfect defence you cannot lose money.
Modern Nash equilibrium charts refine this with actual ranges on both sides, the SB shover and BB caller both play GTO. The results are similar but the ranges widen slightly because real opponents can't defend perfectly.
Train the most common spot (SB vs BB, 15bb) live with the push-fold trainer. Look up specific hand depths in the SC rankings table.
Push-fold charts by stack size
The right shoving range depends on how many big blinds you have left, your position, and what the caller can profitably defend with. Here is what solved play looks like at the six stack depths that come up most in real tournaments.
20bb: the late reg zone
At 20bb effective, you are past the point where a min-raise-fold makes sense, but not yet at pure push-fold. The clean rule: shove your bottom of range (small pairs, weak aces, suited kings, all suited connectors T9s and up) rather than opening them, because the reshove risk becomes too expensive to fold to. Open-raise your premium hands (JJ+, AQ+), because you want them in a pot bigger than 5bb.
SB shove range vs BB: ~35% of hands. That is any pair, any ace, any suited king, KQ, KJo, QJs, JTs, T9s. Full lookups on the Sklansky-Chubukov table.
15bb: the classic Nash spot
This is where push-fold theory was born. Every study of tournament play converges on the same conclusion: at 15bb, in the small blind vs a competent big blind, you shove ~52% of hands. That is any two cards with an ace, any pair, K5s+, K9o+, Q8s+, QTo+, J8s+, JTo, T8s+, 98s, 87s.
Practise this exact spot until it is automatic. In a $100 buy-in tournament, the difference between correct 15bb push-fold and the amateur "tight when short" default is roughly $12 ROI per 100 buy-ins. That is real money.
10bb: the shove machine
At 10bb, you have one move: shove or fold. Min-raising 10bb into someone who can call with 60% of hands and set-mine or flop-shove-back is just donating chips. From the small blind versus big blind, correct range widens to ~63% of hands. From other positions the range tightens with stack depth to the blinds.
The pushbot trainer drills the exact ranges by position at 10bb. Do 20 hands a day for a week and your instinct will be right ~90% of the time.
7bb: any-two territory from the button
At 7bb effective, from the button, the correct shove range is ~76% of hands. From the small blind vs big blind, it is closer to 78%. This is the depth where the phrase "any two cards" starts being technically accurate for late-position steals.
Callers face a 3.5:1 pot-odds price and need ~35% equity to call correctly. Against a 78% shove range, hands as weak as A5o, KJo, and 88 clear that bar. Everything worse folds. That defence range is much tighter than most casual players realise.
5bb: the survival stack
At 5bb, ICM pressure evaporates and correct play is aggressive to the point of feeling reckless. From the button, shove any hand better than 72o. From the small blind vs big blind, shove ~95% of hands. The math is straightforward: winning the blinds without a fight adds 30% to your stack, and even when called your equity averages ~35% against the caller's range.
Ranges from every position and stack depth are indexed in the Sklansky-Chubukov rankings table.
3bb: any two, always
Below 5bb the game is over except for the paperwork. Shove any two cards, from any position, into any opponent. The math no longer allows anything else. Fold 32o here and you have shipped four tournaments of expected value into the muck.
Common push-fold mistakes
Limping short. Any limp at 15bb or less is a leak. You either want the blinds now, or you want to see all five cards. Limp-folding a small pair to a 12bb reshove is the largest single mistake a tournament player can make.
Calling too tight. When the small blind shoves 15bb into you in the big blind, they are shoving ~52% of hands. You need to be calling ~40% of the time to defend that price. Folding 88 or A7s in the big blind vs a 15bb SB shove is a fundamental error.
Ignoring ICM at the final table. All the above assumes chip EV. On the money bubble and at the final table, ICM tightens shove ranges by roughly 5 to 15 percentage points depending on payout distribution. Run the spot through the ICM deal calculator to feel the pressure.
Playing your M instead of BB. The M-ratio (Harrington's "stack in orbits") is a mental shortcut, not a strategy. Below M of 5, push-fold logic dominates regardless. Above M of 20, standard stack-depth play applies. In between, effective BB versus the specific opponent you're facing matters more than any orbit count.
Push-fold vs open-shove: which is which
The terminology confuses beginners so let us make it clean:
- Push-fold is the equilibrium concept: at low stack depths, every hand either shoves or folds preflop. There is no open-raise-fold, no 3-bet-fold, no post-flop play. The whole game reduces to two decisions.
- Open-shove is the specific action of moving all-in as the first-to-act player, distinct from calling all-in or reshoving.
- Reshove is moving all-in over someone else's open-raise. Reshove stacks are typically 8 to 20bb, deep enough to make an open, shallow enough that the reshove is committing.
The Sklansky-Chubukov shortcut
Not every hand has a solved Nash range at your exact stack depth. Sklansky-Chubukov numbers give you a fallback rule: if the number for your hand is greater than your stack in blinds, you can shove and mathematically cannot lose money to any calling range. The full lookup lives on the Sklansky-Chubukov rankings page, but here are the anchor points:
- AA: SC number 6127 (effectively infinite)
- KK: 549
- QQ: 179
- AKs: 122
- JJ: 74
- TT: 40
- 99: 26
- 88: 18
- 77: 13
- ATs: 12
- 66: 9.3
- 22: 3.6
- 72o: 1.3
So with 12bb, you can shove ATs and any pair 77+ and be theoretically break-even or better against any calling range. Reality is better still because opponents fold more than they should.
Related calculators and lessons
- Push-fold trainer for live drilling
- Sklansky-Chubukov rankings table for full lookups
- M-ratio calculator for orbit-based stack context
- ICM deal calculator for final-table adjustments
- ICM explained for the theory of why final-table push-fold ranges tighten
- Variance for the reality that push-fold is high-variance even when correct
Hermes gut-check
One question, friend. Pass it and lesson 8 unlocks.
You're in a tournament with twelve big blinds. Action folds to you in the small blind. The big blind is a tight regular. What is the spot called and what's usually the right play with a wide chunk of hands?
Continue to lesson 8