Methodology: How the Push/Fold Ranges Are Computed

The model

• Game. The action folds to you; you either shove all-in or fold. Each player left to act then calls or folds. Payoffs are in chips (chip-EV) — no ICM, no antes (the big blind ante variant is solved separately).
• Pots. Every player starts the hand with the same total stack. An uncalled shove wins the 1.5bb of blinds. When someone calls, the pot holds both matched stacks plus any blind that is not in the hand, and a posted blind counts toward its owner's call, so each caller type (an unposted seat, the Small Blind, the Big Blind) has its own break-even equity and its own calling range.
• Equity. A 169×169 table of all-in equities between hand classes, estimated by Monte Carlo with 6,000 samples per matchup and a fixed seed, so every build reproduces the same numbers.
• Solver. Fictitious play for 220 iterations: each round the shover best-responds to the callers' average range and vice versa. A hand's push frequency is the share of rounds in which shoving beat folding.
• Fold equity. With k players behind, the shove takes the pot uncalled with probability (1 − c)^k, where c is the share of hands a caller continues with. Each caller is modelled heads-up; multiway all-ins are not.
• Big Blind. Excluded: when the action folds to the Big Blind there is no shove-or-fold decision.

Players behind each seat

Fold equity depends on how many players can still call, so k is the real seat count behind the shover — the Button always has exactly the two blinds behind it, whatever the table size.

Stack convention — read this before comparing charts

“10bb” on RangeMyHand means every player starts the hand with 10 big blinds in total, before posting blinds. That is the convention HoldemResources, ICMIZER and most published Nash charts use, so the numbers compare directly. Heads-up, the Small Blind shove and Big Blind call ranges match the HoldemResources Nash table within 2 percentage points at 5, 10, 15 and 20bb.

Changed in data version 0.3.0 (October 2026). Earlier versions counted stacks behind the posted blinds and treated the blinds as dead in every pot. That made most ranges a few points too wide, by up to 14 points for a short-stacked Button. Every chart, hand page and dataset row was re-solved together; version 0.2.1 stays available as a tagged release of the dataset repository. The iPhone app and the Chrome extension switch to 0.3.0 with their next store updates; until then they still show the earlier numbers.

Verdicts

A hand is a shove when the solution pushes it at least 95% of the time, a fold at 5% or less, and mixed in between. Solved stacks run from 1 to 25bb; the charts publish 5, 8, 10, 12, 15, 20bb, and each hand page reports how deep the hand stays a shove across the full range.

Big blind ante variant

With a big blind ante the Big Blind posts 1 extra big blind for the whole table, so 2.5bb is in the pot before anyone acts instead of 1.5bb. More dead money makes a successful steal worth more, so every seat shoves wider: 3 to 23 percentage points more hands across the 54 published spots.

• Same equity matrix. The ante ranges (data version 0.2.0, generated 2026-10-12) are solved from the same 169×169 equity table as the no-ante ranges, version 0.3.0: same seed, 6,000 samples per matchup, 220 solver iterations. The only change is the ante: dead money goes from 1.5bb to 2.5bb, and the Big Blind pays it out of its own stack.
• Stack convention. N bb is still each player's total stack before the blinds and the ante. The Big Blind has N − 1bb left to play with after its ante, so it calls wider, and against that wider call a few small connectors stop being shoves at the shortest stacks even though every range gets wider overall.
• Charts. Push/fold charts with a big blind ante compare both variants seat by seat.
• Dataset. push-fold-ranges-bb-ante.json and push-fold-ranges-bb-ante.csv, in the same format and under the same license as the files below.

Open dataset (CC BY 4.0)

Chip-EV Nash push/fold (shove-or-fold) frequencies for all 169 starting-hand classes, every seat that can open-shove in 6-max and 9-max, at stacks from 1 to 25 big blinds. Each row gives the push frequency and a shove/mixed/fold verdict. 38,025 rows in total. Free to use, including commercially, with attribution.

• push-fold-ranges.json — one entry per seat and stack, with 169 push frequencies in the order of the hands array.
• push-fold-ranges.csv — one row per hand, seat, and stack.
• github.com/hasuwini77/push-fold-ranges — the same JSON and CSV as a public GitHub repository, to clone, fork, or cite.

CSV columns:

Attribution (link back to this page):

License: Creative Commons Attribution 4.0.

How to cite

Limits

Chip-EV ignores payout pressure, so near the bubble and at final tables correct ranges are usually tighter than these. The ranges are a study baseline for learning short-stack play away from the table, not a substitute for judgement about specific opponents.