Heads-up SB vs BB · chip EV, no ICM · solved live in your browser
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Two players: the small blind (SB) and the big blind (BB) with the same effective stack. The SB can only shove all-in or fold; facing the shove, the BB can only call or fold. No limps, no min-raises. Results are measured in chips (chip EV), with no ICM — tournament payouts are ignored.
For this game the tool finds the Nash equilibrium — a pair of strategies where neither player gains by deviating. The solver covers all 169 hand classes, takes the exact equity of every pair of hands from a 169×169 table and accounts for card removal (your cards remove some of the opponent's combos). Strategies are refined iteratively with CFR+, a close relative of fictitious play in which both players keep adapting to each other. It stops once neither player can gain more than 0.00001 BB per hand by deviating; the iteration count is shown under the charts.
The stack is counted before blinds and antes are posted; both players post the ante. If a hand is played at a frequency rather than always (this happens to 1–3 borderline hands), its cell is partly filled.
The 13×13 grid follows the usual poker chart layout: pairs on the diagonal, suited hands (s) above it, offsuit hands (o) below it. Aces are in the first row and column.
Shows what to do at the selected stack. Green cells are the SB's shoving hands, blue cells the BB's calling hands. The header shows what share of all 1,326 combos is in the range. Hover over a hand (tap on a phone) to see the EV of shoving and folding, the equity against the opponent's range and the stack up to which the hand is played.
The classic Nash push/fold chart: each cell holds the largest stack in BB at which the hand is still a shove (left chart) or a call (right chart). The rule is simple: your stack ≤ the number — shove (call); above it — fold. The table is built from 49 separate solves, 1 to 25 BB in 0.5 BB steps, so it is accurate to ±0.5 BB. Bright cells are hands played at the stack selected with the slider.
A few weak suited hands (53s, 43s, 63s) are non-monotonic: they shove at very short stacks, fold at roughly 2.5–5 BB and shove again at bigger stacks — 53s up to 12.5 BB. Those cells carry a yellow dot, and the exact gaps show on hover.
Share of all starting hands in the equilibrium ranges, SB = 0.5 BB. No ante, and a 12.5% ante (of the big blind) from each player:
| Stack | SB shove | BB call | SB shove, ante | BB call, ante |
|---|---|---|---|---|
| 3 BB | 77.7% | 92.4% | 83.6% | 100.0% |
| 5 BB | 71.6% | 62.0% | 75.3% | 69.0% |
| 8 BB | 61.9% | 45.0% | 67.5% | 49.7% |
| 10 BB | 58.2% | 37.4% | 62.9% | 42.4% |
| 12 BB | 53.3% | 33.0% | 58.1% | 36.8% |
| 15 BB | 45.6% | 28.5% | 52.0% | 31.4% |
| 20 BB | 40.2% | 21.7% | 43.3% | 24.8% |
| 25 BB | 36.3% | 17.3% | 38.4% | 20.4% |
At 1 BB with no ante the small blind shoves any two cards: folding costs more than losing the all-in. By 2 BB the weakest offsuit hands — 32o, 42o, 52o, 72o — already drop out.
That's why short-stack MTT charts usually stop at 15–20 BB; this page goes up to 25 BB to complete the Nash table.
Antes are dead money. When the SB shoves and the BB folds, the SB wins 1 BB plus the ante; when the SB folds, he loses 0.5 BB plus his ante. Bigger antes make stealing more profitable and calling cheaper.
At 10 BB a 12.5% ante widens the SB shove from 58% to 63% of hands and the BB call from 37% to 42%. At 15 BB — from 46% to 52% and from 29% to 31%. A big blind ante (BB ante, 1 BB for the whole table) is not modelled here: it puts even more dead money in the pot, so real ranges are wider than with a 12.5% ante.
True heads-up spots are rare at a full table, but late positions come close. When everyone folds to the small blind, it is exactly SB vs BB. From the button or cutoff two or three players are left behind, and the chart works as an approximation with adjustments:
This is a heuristic, not a solution. Multi-way spots need multi-player Nash charts or an ICM calculator.
13×13 tables of all 169 starting hands that show which hands to move all-in with (push), which to fold, and which to call an all-in with. Nash push/fold charts are equilibrium ranges: neither the small blind nor the big blind can win more by deviating from them as long as the opponent plays the chart too.
Find your hand: the number in its cell is the largest effective stack in big blinds at which the hand is still a shove (or a call). If your stack is at or below that number — shove (call); above it — fold. For example, K2o shows 11.5 in the no-ante shove chart: shove it from the small blind with up to 11.5 BB. “25+” means the hand is played at every stack up to 25 BB.
Pure push/fold works up to about 10–12 BB, where limping or min-raising gains little. At 12–20 BB push/fold is still a solid baseline, but strong players mix in min-raises and limps with part of their range. Above 20–25 BB, an open shove usually risks too much — standard opens and 3-bets take over.
These are heads-up charts: small blind vs big blind. At a full table they work as an approximation when everyone folds to you and one or two players are left behind, with adjustments: the more players behind you, the tighter your shoving range must be, and in the money ICM tightens it further. See the late-position section above.
Sklansky–Chubukov numbers assume the opponent sees your cards and only calls when ahead — a very conservative lower bound. Nash charts are an equilibrium for both players: the shove is computed against the optimal calling range and the call against the optimal shove. That's why Nash ranges are much wider — at 10 BB the small blind shoves about 58% of hands.
Heads-up against a random hand, 32o, 42o and 52o are worse: 72o has a seven-high card, and against a single hand high cards matter more than connectedness. That's why 32o and 42o are the last hands to leave the shoving range at 1–1.5 BB. For the big blind call, all weak offsuit hands drop out at about the same stack — around 2.5 BB without antes.
Antes grow the pot you pick up when the opponent folds and make folding more expensive. Both ranges widen: with a 12.5% ante at 10 BB the small blind shoves about 63% of hands instead of 58%, and the big blind calls about 42% instead of 37%.
Equities between all 169 hand classes come from an exact table with card removal. The equilibrium is iterated until neither player can gain more than 0.00001 BB per hand by deviating. The real limits are in the model itself: heads-up, chips rather than money (chip EV), no ICM, and no limps or min-raises.
Model: heads-up SB vs BB, shove or fold only, chip EV, no ICM. The charts are a guide for short stacks, not a substitute for analysing a specific tournament.