One situation. A different decision for every hand.
The model predicts how often a population folds, calls, and raises. An equity gate distributes those actions across the hands that could have reached this spot.
Public situation →Population frequencies →Hand probabilities →Updated range
THE IMPORTANT DISTINCTION
Equity is the input. Rank is a way to view it.
The gate uses a hand’s equity value, rather than its percentile rank. Equity here means expected showdown pot share against a uniform heads-up opponent, including ties.
A 30% fold target means the range-weighted average fold probability is 30%. It does not mean the weakest 30% always fold, or that the hand at the 30th percentile folds exactly half the time. The curves overlap, and their position adjusts to the candidate range.
THE SPOT / TURN / FACING A BET
A♠ A♥ on Q♥ 7♠ 2♣ 9♦
Cutoff raised to 3 BB preflop, then bet 3 BB on the flop. Big blind called both, then led 4 BB on the turn.
16.4 BBPot before decision
4 BBBet to face
1,128Candidate combos
01 / FROM THE POPULATION TO EACH HAND
Three probabilities. One equity axis.
Solid lines show the fitted gates for hands with zero measured draw potential. The dashed raise line shows the same gate with a 30% next-card improvement estimate. Dots show the selected candidate’s actual probabilities, using its own draw estimate.
● Fold32.4%Weighted gate average: 32.37%
● Call53.2%Weighted gate average: 53.17%
● Raise14.5%Weighted gate average: 14.46%
Matching 30 / 40 / 30 is an average constraint. The curves are shifted until the sum of each candidate’s prior weight × its action probability matches the target. Empty parts of the equity axis contribute nothing. Changing slope changes which hands supply those actions, while the three averages stay fixed.
Improvement means the estimated probability that the next board card increases equity by at least 10 percentage points. It is a sampled feature, not exact outs or the chance to win. Dashed and solid lines are slices through this two-input gate; no single line describes every real candidate.
02 / CONDITION THE RANGE ON AN ACTION
Choose an action. Watch its hands gain weight.
The prior range has already been updated by the preflop raise and flop bet, then filtered for this turn board. Choose a hypothetical action below to see its conditional range. The recorded action was call.
Diagonal = pairs; upper triangle = suited; lower triangle = offsuit. Cells sum compatible physical suit combos. Before/after share one linear probability color scale; the change chart uses a symmetric linear ±1.12 pp scale. Color scales refit when controls change. Rounded 0.00 values can remain positive.
THE EXACT UPDATE / AsAh
Prior × action likelihood ÷ action frequency
0.4179% × 72.03% ÷ 53.17% = 0.5661%
AsAh becomes 1.35× as likely after observing call. This is a probability of holding that hand, not its probability of winning.
SELECTED CLASS / AA
2.505% → 3.395%
+0.89 percentage points across 6 compatible combos.
Carry this posterior forward only if that action was executed. The API’s returned range is conditioned on its sampled chosenAction. It does not condition on the eventual bet size. Without passing a range on the next request, the API starts from uniform again.
WHY THE CURVES OVERLAP
Value, bluffs, and everything between.
Postflop, the gate allocates aggression first. Its score combines a low-equity bluff arm with a high-equity value arm. Draw potential boosts the bluff arm; it is a separate input, not a region on the equity axis.
The remaining probability is divided between calling and folding with an increasing equity sigmoid. Consequently, very weak hands can sometimes raise, middle hands can favor calling, and strong hands can favor raising. The exact shape depends on the situation, the range, and the calibration.
WHAT CHANGES BEFORE THE FLOP
Preflop has a different gate.
Preflop uses an increasing continuation sigmoid, then an increasing aggression sigmoid among continuing hands. It has no postflop bluff arm or draw boost.
Neither version assigns each hand a fixed action. Every candidate receives a probability distribution. The actual hand is used to sample an action only after the whole candidate population has been allocated.