Credits and Licences

Push/fold equilibrium (computed here) v1.0.0 (approximate)

Computed here: Built a head-to-head equity table for all 169 hands (seeded Monte Carlo, 30,000 runs per pairing, averaged with the mirrored value to smooth out noise), then solved the all-in-or-fold subgame numerically over 2,000 iterations of fictitious play. Card removal is counted exactly, not approximated.

Not a transcription of a published Nash table, but a numerical solution to a simplified model inside this repository. The equity matrix itself is Monte Carlo (largest gap against published values: 0.26%), and the simplifications below (no multiway, calling ranges not position-dependent) move it further from a true equilibrium.

• Assumes an unopened pot: everyone before the hero has folded
• Applies from 1 to 25BB. Deeper than that you need options other than push/fold, which this chart cannot judge
• The hero may only shove or fold. Middling raise sizes are not modelled
• Players behind act in order and the hand ends at the first call (multiway calls are not modelled)
• Calling ranges are solved separately for each (caller, shover) pair
• A further cold call from a seat behind the caller is not modelled
• Chip EV only. ICM is not applied (ICM decisions are handled separately in M5)
• Everyone is assumed to have the same effective stack as the hero
• Antes use the big-blind ante format: one player posts for the table

Preflop range charts (approximate) v2.1.0 (approximate)

Built from heuristics: Hands are ordered by all-in equity against a random hand across all 169 combinations, adjusted for playability (suited +0.035 / pair +0.02 / connectedness up to +0.025 / weak-kicker offsuit ace -0.02). Opening, calling, 3-bet and 4-bet frequencies and sizes are set from common values, and the actual hand sets are cut from that ordering by percentage. 3-bets and 4-bets are split into a value portion and a bluff portion (weak suited aces and connected hands).

No equilibrium including postflop play has been solved, so this will not match a GTO solver. The ordering of hands is computed, but where the line is drawn, which hands bluff, and the sizes are all heuristics.

• Assumes a tournament with antes
• No equilibrium including postflop play is solved. This is an approximation from an ordering plus percentages
• Opening frequencies (about 15% under the gun through 45% on the button) are common values and move a few points by school of thought
• Calling, 3-bet and 4-bet frequencies are set heuristically from the opener’s width and position
• Bluffing hands are picked mechanically from weak suited aces and suited connectors
• The value portion of a raise is cut from an ordering that promotes suited AK and AQ above the middling pairs (going by raw equity alone produces a range that never 3-bets AKs)
• The stack-depth adjustment is a flat factor: 0.85x from 15 to 25BB, 1.1x at 50BB and above
• Multiway pots (more than one caller) are not modelled

Preflop all-in equity matrix v1.0.0 (approximate)

Computed here: Seeded Monte Carlo, 30,000 runs per pairing. The value and its mirror are averaged to smooth out noise.

Monte Carlo estimates. The largest gap against nine reference values computed by full enumeration is 0.26%.

• All-in preflop equity between each of the 169 hand classes
• Averaged over every combination in a class, so not the value for one specific suit pairing
• Ties count as half a win

Postflop c-bet model (simplified) v1.0.0 (approximate)

Computed here: Computes the chip EV of each action (check, 1/3, 2/3 and pot-sized bet) under the assumptions above, and recommends whichever has the highest EV. This is not a solver output.

Not a solver: a single-street model built on the five assumptions above. Ignoring raises and later streets makes checking look better and bluffing look worse than it is. This is not GTO.

• Only one street is evaluated (play from the turn onward is not modelled)
• The opponent never raises; they only call or fold
• The opponent defends exactly MDF = pot / (pot + bet), taking the hands with most equity first
• A check goes to showdown and the pot is split according to equity
• A bet that gets called also goes to showdown there
• Assumes a heads-up single-raised pot