Nash Push/Fold Charts and ICM
Nash push/fold charts assume chip EV — but ICM changes the answer near pay jumps. See how ICM tightens your calls and reshapes shove ranges.
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Nash push/fold charts tell a short stack which hands to shove and which to call a shove with — but they’re built on a hidden assumption: every chip is worth the same. That’s chip EV, and it’s only true deep in a field or heads-up. Near a pay jump, ICM makes chips diminish in value, and the chart’s answers shift. The rule of thumb: ICM tightens your calling range and leaves your shoving range roughly intact or wider.
What a Nash chart actually is
A Nash push/fold chart is a game-theory-optimal solution for the shove-or-fold stage — typically under about 15–20 big blinds, where raising to anything but all-in leaves you pot-committed anyway. At a Nash equilibrium, neither the shover nor the caller can improve by changing their range, given the other’s range. Charts give you two grids by stack depth: a shoving range (which hands to jam) and a calling range (which hands to call a jam).
The catch is that these charts are computed in chip EV. They maximize chips won, treating a chip you win as equal in value to a chip you lose. That’s a fine assumption in a cash game or deep in a tournament — and a dangerous one on the bubble.
Where ICM breaks the chart
ICM introduces the risk premium: the extra equity you need to call an all-in in dollars versus chips. Because busting near a pay jump forfeits a payout, the chips you’d win are worth less than the ones you’d lose, so your break-even calling requirement rises above what the chip-EV chart assumes.
This hits the two sides of the chart very differently:
- Calling ranges shrink — sometimes drastically. A chip-EV chart might say call a shove with the top 25% of hands; under heavy ICM pressure that can collapse to the top 8–10%. Calling risks your whole tournament life for chips worth less than they seem.
- Shoving ranges hold or widen — because the shover has fold equity, and near a pay jump opponents fold more, so jamming stays profitable. You collect blinds and antes without a showdown.
The asymmetry is the whole story: shove about the same or more, call far less.
ICM adjustment at a glance
| Situation | Shove range vs. Nash chart | Call range vs. Nash chart |
|---|---|---|
| Deep / early | Same (chart is accurate) | Same |
| Money bubble, covered | Same or wider | Much tighter |
| Steep FT pay jump | Slightly wider | Dramatically tighter |
| Heads-up | Same (ICM off) | Same |
Notice heads-up and deep spots return the chart to full accuracy — that’s where chips and dollars nearly agree, so the chip-EV Nash chart is correct. The chart only misleads in the ICM-heavy zone, and only on the calling side.
Worked spot: chart says call, ICM says fold
You’re the big blind with 12 BB, on the bubble, and a covering stack shoves from the small blind. Your hand is a marginal ace — the kind a chip-EV Nash chart says is a comfortable call against a wide small-blind shoving range (call it ~48% equity).
In chips, calling 12 BB as a 48% underdog is roughly break-even to slightly profitable — the chart’s logic. But apply ICM. On the bubble, covered, your risk premium might be 20 points, meaning you need about 68% equity to call, not 50%. Your marginal ace at 48% is nowhere near that bar. The chip-EV chart says call; the dollar math says snap-fold. You wait for a hand above the ICM threshold — roughly the top tier — or you fold and keep your equity intact.
Using charts the right way
Treat a Nash chart as a chip-EV baseline, not gospel. Deep and early, follow it closely — it’s accurate there. As pay jumps approach, keep shoving near the chart’s shove range but tighten your calls hard, guided by your risk premium and who covers whom. Short-stack formats where this matters most are covered in the sit & go strategy hub, and the pressure that drives the calling-range collapse is detailed in ICM pressure.
The takeaway
Nash push/fold charts are a powerful default, but they speak chips, not dollars. Near a pay jump, ICM keeps your shoves honest while it slashes your calls — so lean on the chart for jamming and override it for calling. Start from the ICM hub to see the full model behind the adjustment.
Frequently asked
What is a Nash push/fold chart?
A Nash push/fold chart is a game-theory-optimal guide for short stacks, showing which hands to shove all-in and which to call a shove with, by stack depth. It assumes both players play perfectly, so neither can profit by deviating. Standard charts are calculated in chip EV, not dollars.
Do Nash charts account for ICM?
Standard Nash push/fold charts do not — they assume every chip is worth the same, which is only true deep in a big field or heads-up. Near a pay jump, ICM makes chips diminish in value, so you must tighten your calling range below what the chip-EV chart says.
How does ICM change push/fold ranges?
ICM mainly tightens your calling range, because busting near a pay jump is disastrous, while leaving your shoving range close to the chip-EV chart or even wider, since fold equity is worth more. The net effect is: shove about the same or more, call much less.
Should beginners use Nash charts?
Yes, as a baseline. A chip-EV Nash chart is a strong default when you're deep or far from the money. Just remember to tighten your calls on the bubble and at final-table pay jumps, where ICM overrides the chart and calling a shove costs more in dollars than the chart assumes.