Heuristics & draws

Fast equity estimates (rule of 2/4), hypergeometric and flop→river hit math, runner–runner patterns, implied-odds breakeven targets, and multiway out duplication. Exact straight-on-river probability is under Monte Carlo (straightMadeFlopToRiverExactProbability).

Use this group in draw trainers and study apps where exact enumeration is overkill but you need principled probabilities from out counts and unseen cards.

Export	Summary
ruleOfFourEquity	Out-count × 4% cap heuristic (turn+river).
ruleOfTwoEquity	Out-count × 2% cap heuristic (one card).
estimatedOutsFromRuleOfTwo	Inverse-style equity×unseen/2 clamped.
estimatedOutsFromRuleOfFour	Same for two streets: equity×unseen/4 clamped.
impliedBreakevenFutureWin	Extra future win needed for neutral call.
hypergeometricOneCardHitProbability	One-card draw: outs / unseenCards.
runnerRunnerBackdoorFlushTwoCardProbability	C(s,2)/C(u,2) runner flush.
flopToRiverAtLeastOneHitProbability	Two streets, single out count.
flopToRiverAtLeastOneHitUnionTwoCategories	Two overlapping out categories.
flopToRiverAtLeastOneHitUnionThreeCategories	Three categories with inclusion–exclusion.
flopToRiverAtLeastOneHitUnionFourCategories	Four categories with full inclusion–exclusion.
flopToRiverAtLeastOneHitDisjointOutsSum	Sum disjoint categories, then two-street formula.
runnerRunnerStraightDrawHitProbability	Runner–runner straight pattern model.
duplicationAdjustedOuts	Heuristic outs / (1 + weight × villains).
equityDeltaIfCardRemoved	Δ exact range equity when a card is dead.
flopToTurnAtLeastOneHitProbability	One-street flop→turn hit: outs/unseen.
turnToRiverAtLeastOneHitProbability	One-street turn→river hit: outs/unseen.
flopToTurnAtLeastOneHitUnionTwoCategories	Two overlapping categories, one street (flop→turn).
turnToRiverAtLeastOneHitUnionTwoCategories	Two overlapping categories, turn→river.
flopToTurnAtLeastOneHitUnionThreeCategories	Three categories with inclusion–exclusion, one street.
turnToRiverAtLeastOneHitUnionThreeCategories	Three categories, turn→river.
flopToTurnAtLeastOneHitUnionFourCategories	Four categories with inclusion–exclusion, one street.
turnToRiverAtLeastOneHitUnionFourCategories	Four categories, turn→river.
flopToTurnAtLeastOneHitDisjointOutsSum	Sum disjoint outs, then one-street hit formula.
turnToRiverAtLeastOneHitDisjointOutsSum	Sum disjoint outs, turn→river.
hypergeometricTwoCardHitProbability	Two-card hypergeometric hit rate.
hypergeometricTwoCardMissProbability	Complement of two-card hit.
runnerRunnerBackdoorFlushOneCardProbability	One-card backdoor flush probability.
blockerAdjustedOuts	Scale outs by blocker fraction.
suitBlockerFraction	Dead suit cards divided by unseen.
impliedBreakevenTotalPot	Total pot needed: (pot+call)/equity.
impliedOddsRequiredEquityFromFutureWin	Equity needed given extra future win.