{ "recordType": "dry-side-pot-river-casebook", "schemaVersion": 1, "publicationDate": "2026-09-05", "setup": { "game": "No-Limit Texas Holdem river chip EV", "board": "Kc 9d 7s 4h 2c", "mainPotChips": 300, "currentSidePotChips": 0, "heroBetChips": 150, "allInHand": "As9c", "activePlayers": [ "Hero", "Villain" ], "allInPlayers": [ "All-in" ], "assumptions": [ "The board is complete, so there are no future cards.", "The fixed all-in hand is revealed to the reader for retrospective full-state analysis; during live action, replace an unknown hand with a conditional range.", "Hero may check or bet 150; Villain may fold or call; raises are excluded.", "Villain combinations have equal conditional weight and a declared deterministic response.", "An uncalled bet is returned and is not a contested pot.", "Earlier contributions are sunk; payoffs are decision-point receipts minus any new Hero wager.", "There is no rake, tournament payout conversion, bounty, jackpot, or collusive agreement." ] }, "specialCaseFormula": { "scope": "Hero has zero check EV, loses every main and side pot when called, and q is expected main-pot share conditional on Villain folding.", "expression": "EV(bet) = f*q*M - (1-f)*B", "checkEv": "0", "breakEvenForPositiveQ": "f* = B / (q*M + B)", "zeroShareBoundary": "If q = 0, the bet is never strictly better than checking; it ties only when f = 1." }, "cases": [ { "id": "dead-bluff", "label": "Case A — dead bluff", "claim": "Hero loses to the all-in player and every live-opponent combination.", "hero": "QhJh", "board": "Kc 9d 7s 4h 2c", "allIn": "As9c", "rangeWeights": "equal", "villainCombinationCount": 10, "foldFrequency": 0.4, "callFrequency": 0.6, "checkEvChips": 0, "betEvChips": -90, "betMinusCheckChips": -90, "branches": [ { "villain": "KdQd", "response": "call", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KsQs", "response": "call", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KdJd", "response": "call", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KsJs", "response": "call", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KdTd", "response": "call", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KsTs", "response": "call", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "Kd8d", "response": "fold", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": null, "betPayoffChips": 0 }, { "villain": "Ks8s", "response": "fold", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": null, "betPayoffChips": 0 }, { "villain": "Kd6d", "response": "fold", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": null, "betPayoffChips": 0 }, { "villain": "Ks6s", "response": "fold", "weight": 1, "heroBeatsAllIn": false, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": null, "betPayoffChips": 0 } ] }, { "id": "main-pot-isolation", "label": "Case B — main-pot isolation", "claim": "Hero beats the all-in player but loses to every live-opponent combination.", "hero": "Kh5h", "board": "Kc 9d 7s 4h 2c", "allIn": "As9c", "rangeWeights": "equal", "villainCombinationCount": 10, "foldFrequency": 0.4, "callFrequency": 0.6, "checkEvChips": 0, "betEvChips": 30, "betMinusCheckChips": 30, "branches": [ { "villain": "KdQd", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KsQs", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KdJd", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KsJs", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KdTd", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "KsTs", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 0, "betSideShare": 0, "betPayoffChips": -150 }, { "villain": "Kd8d", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 }, { "villain": "Ks8s", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 }, { "villain": "Kd6d", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 }, { "villain": "Ks6s", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": false, "checkMainShare": 0, "checkPayoffChips": 0, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 } ] }, { "id": "thin-value", "label": "Case C — value against the live opponent", "claim": "Hero beats the all-in player and every live-opponent combination.", "hero": "KhQh", "board": "Kc 9d 7s 4h 2c", "allIn": "As9c", "rangeWeights": "equal", "villainCombinationCount": 10, "foldFrequency": 0.6, "callFrequency": 0.4, "checkEvChips": 300, "betEvChips": 360, "betMinusCheckChips": 60, "branches": [ { "villain": "KdJd", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": 1, "betPayoffChips": 450 }, { "villain": "KsJs", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": 1, "betPayoffChips": 450 }, { "villain": "KdTd", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": 1, "betPayoffChips": 450 }, { "villain": "KsTs", "response": "call", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": 1, "betPayoffChips": 450 }, { "villain": "Kd8d", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 }, { "villain": "Ks8s", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 }, { "villain": "Kd6d", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 }, { "villain": "Ks6s", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 }, { "villain": "Kd3d", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 }, { "villain": "Ks3s", "response": "fold", "weight": 1, "heroBeatsAllIn": true, "heroBeatsVillain": true, "checkMainShare": 1, "checkPayoffChips": 300, "betMainShare": 1, "betSideShare": null, "betPayoffChips": 300 } ] } ], "thresholdRows": [ { "mainPotChips": 300, "betChips": 75, "betAsMainPotFraction": "1/4", "conditionalMainPotShare": "1/4", "breakEvenFoldFrequency": "1/2", "breakEvenFoldPercent": 50 }, { "mainPotChips": 300, "betChips": 75, "betAsMainPotFraction": "1/4", "conditionalMainPotShare": "1/2", "breakEvenFoldFrequency": "1/3", "breakEvenFoldPercent": 33.3333 }, { "mainPotChips": 300, "betChips": 75, "betAsMainPotFraction": "1/4", "conditionalMainPotShare": "3/4", "breakEvenFoldFrequency": "1/4", "breakEvenFoldPercent": 25 }, { "mainPotChips": 300, "betChips": 75, "betAsMainPotFraction": "1/4", "conditionalMainPotShare": "1/1", "breakEvenFoldFrequency": "1/5", "breakEvenFoldPercent": 20 }, { "mainPotChips": 300, "betChips": 150, "betAsMainPotFraction": "1/2", "conditionalMainPotShare": "1/4", "breakEvenFoldFrequency": "2/3", "breakEvenFoldPercent": 66.6667 }, { "mainPotChips": 300, "betChips": 150, "betAsMainPotFraction": "1/2", "conditionalMainPotShare": "1/2", "breakEvenFoldFrequency": "1/2", "breakEvenFoldPercent": 50 }, { "mainPotChips": 300, "betChips": 150, "betAsMainPotFraction": "1/2", "conditionalMainPotShare": "3/4", "breakEvenFoldFrequency": "2/5", "breakEvenFoldPercent": 40 }, { "mainPotChips": 300, "betChips": 150, "betAsMainPotFraction": "1/2", "conditionalMainPotShare": "1/1", "breakEvenFoldFrequency": "1/3", "breakEvenFoldPercent": 33.3333 }, { "mainPotChips": 300, "betChips": 300, "betAsMainPotFraction": "1/1", "conditionalMainPotShare": "1/4", "breakEvenFoldFrequency": "4/5", "breakEvenFoldPercent": 80 }, { "mainPotChips": 300, "betChips": 300, "betAsMainPotFraction": "1/1", "conditionalMainPotShare": "1/2", "breakEvenFoldFrequency": "2/3", "breakEvenFoldPercent": 66.6667 }, { "mainPotChips": 300, "betChips": 300, "betAsMainPotFraction": "1/1", "conditionalMainPotShare": "3/4", "breakEvenFoldFrequency": "4/7", "breakEvenFoldPercent": 57.1429 }, { "mainPotChips": 300, "betChips": 300, "betAsMainPotFraction": "1/1", "conditionalMainPotShare": "1/1", "breakEvenFoldFrequency": "1/2", "breakEvenFoldPercent": 50 } ], "sources": [ { "url": "https://www.pokertda.com/view-poker-tda-rules/", "accessed": "2026-09-05T03:14:00+02:00", "use": "Current published 2024 rules: continued action after an all-in, separate side pots, and individual-play/soft-play boundaries." }, { "url": "https://www.pokerstars.com/help/articles/poker-rules-master/217448/", "accessed": "2026-09-05T03:09:00+02:00", "use": "Official side-pot creation and contributor-eligibility explanation." }, { "url": "https://assets.wsopcdn.com/wsop/1a72ba28-781c-409d-a9c3-5ca13c4c5718.pdf", "accessed": "2026-09-05", "use": "2026 WSOP rules: separate side-pot settlement, return of an uncalled amount, and collusion/soft-play rules." } ], "limitations": [ "This is a disclosed casebook, not an equilibrium solve or population model.", "The response policies are synthetic inputs, not claims about optimal or observed fold frequencies.", "Turn and flop incentives require future-card and future-betting branches that this river model excludes.", "Tournament ICM, bounty value, rake, raises, ties, side pots already in existence, and room-specific procedures can change decisions." ] }