{
  "schema_version": "1.3",
  "rebuild": "v2",
  "provenance_class": "model_spot",
  "table_size": 6,
  "id": "nut-straight-fold-diamond-jam",
  "format": "call_fold",
  "free": true,
  "updated_at": "2026-08-08T00:00:00Z",
  "source": {
    "session_id": "StackoffValues",
    "verdict_audio": "quiz/audio/nut-straight-fold-diamond-jam.m4a",
    "lesson_slug": null,
    "solver_node": {
      "tool": "GTO Wizard (line, pot, stacks, sizings) + PioViewer 2.0.7.21 used as an equity calculator (the 91.364) + Windows Calculator (the $278 and the -19.975) + PokerTracker 4 replayer (the source hand the node mirrors; frames READ-ONLY)",
      "file": "app.gtowizard.com/solutions?gametype=Cash6m500zComplex&depth=100&preflop_actions=F-F-R2.5-F-F-C&history_spot=11 (frame t=2984) and history_spot=10 (frame t=3056); config panel CASH / 6max / NL500 / Complex GTO / 100bb / 3b: GTO; browser tab title 'Qd5d4hAd8h - Solutions - GTO Wizard'. PioViewer scratch tree 'Unnamed', header 'Pot: 0 0 1 (1) Starting Stacks:1' - no money tree, pure equity calculator (frames t=3180, t=3186).",
      "node": "UTG Fold / HJ Fold / CO Raise 2.5 / BTN Fold / SB Fold / BB Call (ribbon stacks CO 100, BTN 100, SB 99.5, BB 99) -> FLOP Q(d)5(d)4(h), pot 5.5, BB Check + CO Check both selected -> TURN A(d), pot 5.5, BB Bet 2 + CO Call both selected -> RIVER, pot 9.5, both 95.5 behind. BB river menu (history_spot=10, Actions panel): Check 27.9% / Bet 2.5 43.1% / Bet 5.5 20.1% / Bet 12.5 3% (the selected branch - it mirrors the source hand's $63 bet) / Bet 28.5 5.9% / Allin 95.5 0%, 0 combos. CO's menu facing the selected bet (history_spot=11): Fold / Call / Raise 27 / Raise 40 / Allin 95.5. The staged decision is the BB's Allin 95.5 branch - the exact hypothetical Eric poses at s764 ('if he's all in, if he's all in') and Tyler rules on at s765-766 and s779-800. The equilibrium itself never takes that branch (0%), and the fixture claims no equilibrium frequency for it.",
      "source_hand": "PokerTracker 4 replayer, hand #4495111649, $5 NL 6-max (title bar, frames t=2030/t=2040/t=2340): CO (Hero, A(s)9(s)) raises to 12.50, BB (P6, 9(d)8(d)) calls 7.50; flop [Qd 5d 4h] check-check; turn [Ad] BB bets 8.58, CO calls; river [8c], pot $44.66, BB bets $63 (calculator 8.58 + 63 = 71.58, t=2410/2460). Tyler substitutes 7-6 of spades into the CO seat at s772 ('let's say hypothetically you accidentally stack something like... 7-6 of spades here') - the fixture's hero hand IS that substitution, and no displayed string claims the hand was played.",
      "equity_node": "PioViewer node r:0, board typed A(d) 5(d) 4(h) Q(d) 8(c) (Pio build log 'River: Ad5d4hQd8c', frame t=3155); one range hand-typed via Select range as '77,66,55,44,AKo,AQs,A9s,KJ,87s,86s,76s,75s,65s,64s,54s' (76.0 combos / 5.73%, frame t=3155) into the IP slot, read against the 320.4-combo OOP range (header 'CHECK 320.4 combos (100.00%)', total equity 60.638); panel legend 'IP Equity in % of the pot' (frame t=3180). 7(s)6(s) cell 91.364; siblings 7(h)6(h) 91.408, 7(c)6(c) 91.400, 7(d)6(d) 96.323 (a flush - excluded; the hero combo holds no diamond).",
      "video_t": {
        "replayer_hand": [2010, 2350],
        "gto_wizard_node": [2960, 3150],
        "pio_equity_calc": [3155, 3316],
        "windows_calculator": [3244, 3252, 3308],
        "raise_counter_ruling": [3420, 3460],
        "verdict_beats": [3209.6, 3214.5, 3223.9, 3304.0]
      },
      "board": "Felt: Q(d) 5(d) 4(h) / A(d) / 8(c). Flop and turn order per the replayer action log ('Flop: [Qd 5d 4h] ... Turn: [Ad] ... River: [8c]', frames t=2030/t=2040) and the GTO Wizard ribbon (FLOP Q 5 4, TURN A). River shown as the source hand's (and Pio board's) 8(c); the GTO Wizard mirror node deals 8(h) there (tab 'Qd5d4hAd8h'). Neither eight is a diamond and no displayed figure depends on the suit - every number was computed on the 8(c) board.",
      "pot_chips": 47.5,
      "turn_baseline_pot_chips": 27.5,
      "stacks_chips": 477.5,
      "chips_per_bb": 5.0,
      "stake_source": "Replayer title '$5 NL (6 max)' + the log's 'Hero raises to 12.50' / 'P6 calls 7.50' (blinds $2.50/$5) + preflop pot $27.50 = 5.5 bb (frames t=2030/t=2040). The GTO Wizard ribbon (NL500, 100bb) mirrors the hand bb-for-bb: pot 5.5 -> 9.5, stacks 97.5 -> 95.5. So 1 bb = $5: the 9.5 bb river pot = $47.50, the 5.5 bb turn-baseline pot = $27.50, and 95.5 bb behind = $477.50.",
      "rounding_note": "Tyler prices the full stack-off at a round $500 (calculator, frame t=3308); the node's exact stack behind at the river is 95.5 bb = $477.50. The rounding is his and does not move the verdict. He likewise rounds the Pio 91.364 to 0.91/0.09 in both calculator lines."
    }
  },
  "context": "SOLVER SPOT · 6-MAX NL500 · 100 BB",
  "hero": {
    "pos": "CO",
    "cards": [
      "7s",
      "6s"
    ],
    "stack_bb": 95.5,
    "avatar": "lono_ghoul"
  },
  "seats": [
    {
      "pos": "BTN",
      "avatar": "ghoul_4167",
      "folded": true
    },
    {
      "pos": "SB",
      "avatar": "ghoul_4174",
      "folded": true
    },
    {
      "pos": "BB",
      "avatar": "ghoul_5242",
      "stack_bb": 0,
      "villain": true
    },
    {
      "pos": "UTG",
      "avatar": "ghoul_104",
      "folded": true
    },
    {
      "pos": "HJ",
      "avatar": "ghoul_4526",
      "folded": true
    }
  ],
  "streets": [
    {
      "name": "preflop",
      "actions": [
        {
          "pos": "UTG",
          "act": "fold"
        },
        {
          "pos": "HJ",
          "act": "fold"
        },
        {
          "pos": "hero",
          "act": "open",
          "to_bb": 2.5
        },
        {
          "pos": "BTN",
          "act": "fold"
        },
        {
          "pos": "SB",
          "act": "fold"
        },
        {
          "pos": "BB",
          "act": "call"
        }
      ],
      "pot_bb": 5.5
    },
    {
      "name": "flop",
      "board": [
        "Qd",
        "5d",
        "4h"
      ],
      "actions": [
        {
          "pos": "BB",
          "act": "check"
        },
        {
          "pos": "hero",
          "act": "check"
        }
      ],
      "pot_bb": 5.5
    },
    {
      "name": "turn",
      "board": [
        "Qd",
        "5d",
        "4h",
        "Ad"
      ],
      "actions": [
        {
          "pos": "BB",
          "act": "bet",
          "to_bb": 2
        },
        {
          "pos": "hero",
          "act": "call"
        }
      ],
      "pot_bb": 9.5
    },
    {
      "name": "river",
      "board": [
        "Qd",
        "5d",
        "4h",
        "Ad",
        "8c"
      ],
      "actions": [
        {
          "pos": "BB",
          "act": "allin",
          "to_bb": 95.5
        }
      ]
    }
  ],
  "prompt": "7♠6♠ · NUT STRAIGHT ON THE RIVER · BB JAMS 95.5 BB INTO A 9.5 BB POT — CALL OR FOLD?",
  "pot_bb": 105.0,
  "options": [
    {
      "id": "call",
      "label": "CALL"
    },
    {
      "id": "fold",
      "label": "FOLD"
    }
  ],
  "correct": "fold",
  "option_feedback": {
    "call": "The straight is the nuts against everything except a flush, and it beats 91.4% of the whole range Tyler typed into the equity calculator. But the jam range is not that range — 'You're thinking flush. Definitely a flush.' Only two-diamond hands, about 9% of it, ever play for stacks on this board, and even the solver's BB never open-jams this river. Calling 95.5 to win the 105 out there needs ~48% against the range that is actually all-in — the no-diamond nut straight is nowhere near that against flushes.",
    "fold": "Correct. The all-in range is not the checking range: 'You're thinking flush. Definitely a flush.' Tyler prices the stack-off from the 5.5 bb pot entering the turn — $27.50 at NL500: 27.5 × 0.91 ÷ 0.09 = $278, about 56 bb, the most this straight can voluntarily put in (he rounds his Pio read to 0.91). The jam plays for roughly $500, and paying it off runs −500 × 0.09 + 27.5 × 0.91 = −$20 on a hand Tyler says should be worth 'plus 40 or so'. Facing a normal-sized bet instead, this hand raises — 'we can never screw up raising seven six here.'"
  },
  "verdict_text": "That would actually be probably a blunder — because essentially you could get all-in here roughly 18% of the time. That's far more aggressive than anyone you've ever seen. You actually lost more than the pot with a 91st-percentile hand.",
  "principle": "Max voluntary stack-off = pot × equity ÷ (1 − equity), priced from the pot you are protecting: 27.5 × 0.91 ÷ 0.09 = $278, about 56 bb. That caps money you choose to put in — it is not a bluff-catch price — and a 95.5 bb jam is far past it when the only range stacking off on three diamonds is flushes. Against a normal-sized river bet the same nut straight raises.",
  "pct_provenance": {
    "91.4": {
      "role": "range_composition",
      "referent": "7♠6♠'s equity against the FULL 320.4-combo range Tyler built for the BB in his PioViewer scratch tree (r:0, header 'Pot: 0 0 1 (1) Starting Stacks:1' — an equity calculator, no money tree), on the board he typed as A♦5♦4♥Q♦8♣ — the same five cards as the felt's Q♦5♦4♥/A♦/8♣. The cell reads 91.364 under the legend 'IP Equity in % of the pot'; siblings 7♥6♥ 91.408, 7♣6♣ 91.400, 7♦6♦ 96.323 (a flush — excluded; the hero combo holds no diamond). It is equity against his WHOLE checking range, NOT against the range that jams 95.5 bb — the whole lesson is that those two differ.",
      "source": "frames t=3180 (combo panel + legend), t=3186 (node header), t=3155 (Select range, 76.0 combos / 5.73%; Pio log 'River: Ad5d4hQd8c')"
    },
    "18": {
      "role": "frequency",
      "referent": "Tyler's spoken estimate of how often the money would have to be going all-in here for paying off the jam to be defensible — roughly his ~9% flush share doubled, since at this price (95.5 to win 200.5, 47.6% breakeven) flushes can be at most about half the all-in range. The aired tape itself dismisses it: 'That's far more aggressive than anyone you've ever seen.' No 18 appears on any screen in the segment.",
      "source": "SER StackoffValues s780 (t=3214.5-3218.6) + s781-782 (t=3222.4-3226.5); s780 and s782 are aired verdict beats"
    },
    "9": {
      "role": "range_composition",
      "referent": "the flush share of the BB's full range — the 1 − 0.91 = 0.09 Tyler types into both calculator lines, his rounding of the Pio read (100 − 91.4). On a three-diamond board only two-diamond hands beat the nut straight (A♦, 5♦, Q♦ are already out there).",
      "source": "frames t=3244 / t=3252 / t=3308 (the 0.09 in the typed expressions); SER s787"
    },
    "48": {
      "role": "price",
      "referent": "breakeven equity of the staged call: 95.5 to win the 9.5 + 95.5 = 105 out there, i.e. 95.5 / 200.5 = 47.6%, displayed rounded. Derived from the displayed felt state (streets/decision block), not from any screen.",
      "source": "fixture arithmetic"
    }
  },
  "size_claims": {},
  "claims": [
    {
      "text": "you actually lost more than the pot with a 91st-percentile hand",
      "basis": "Tyler's photographed arithmetic: −500 × 0.09 + 27.5 × 0.91 = −19.975 (Windows calculator, frame t=3308), set against the spoken 'plus 40 or so' the hand should be worth (s797) — a ~$60 swing on the $27.50 turn-baseline pot. s799-800 scope it as the ledger of the stack-off strategy ('this is your actual EV with 7-6 if that's your strategy choice'), not as the price of one call.",
      "source": "frame t=3308; SER s794-800"
    },
    {
      "text": "max stack-off = pot x equity / (1 - equity) = 27.5 x 0.91 / 0.09 = $278, about 56 bb",
      "basis": "Typed by Tyler in two steps: 27.5 * 0.91 = 25.025 (frame t=3244), then 25.025 / 0.09 = 278.0555 (frame t=3252); spoken at s787: 'if you put in more than $278 here with a straight, it could be a mathematical mistake.' The baseline is the 5.5 bb ($27.50) pot entering the turn — the ceiling caps total voluntary turn+river investment, which is why the felt keeps the turn bet-call visible. $278 / $5 = 55.6 bb, displayed as 'about 56 bb'.",
      "source": "frames t=3244, t=3252; SER s787"
    },
    {
      "text": "the all-in range is a flush",
      "basis": "Eric: 'If he's all in, if he's all in' (s764); Tyler: 'You're thinking flush. Definitely a flush.' (s765-766). With A♦ 5♦ Q♦ on board the read means two diamonds in hand.",
      "source": "SER s763-766"
    },
    {
      "text": "even the solver's BB never open-jams this river",
      "basis": "GTO Wizard BB river node (history_spot=10): Actions panel Allin 95.5 = 0%, 0 combos; the equilibrium spreads Check 27.9 / Bet 2.5 43.1 / Bet 5.5 20.1 / Bet 12.5 3 / Bet 28.5 5.9. The staged jam is that tree's real Allin 95.5 branch taken by a human — exactly the hypothetical Eric posed.",
      "source": "frames t=2984, t=3056"
    },
    {
      "text": "facing a normal-sized bet instead, this hand raises",
      "basis": "Tyler, minutes later, over the replayer's real river bet: 'if your bet's a normal sizing, I can guarantee a raise that's coming in with seven six... we're not even close to minus 278... we can never screw up raising seven six here' (s820-828; replayer river on screen at t=3430). The fold this quiz grades is bounded to the stack-size jam.",
      "source": "SER s820-828; frame t=3430"
    }
  ],
  "unverifiable_claims": [
    "'plus 40 or so' (s797) — Tyler's spoken baseline for what 7♠6♠ should be worth in this scenario; it appears on no screen and is displayed only as an attributed quote in the fold feedback.",
    "The 18% (s780) is a spoken estimate, never a solver or screen read-out; its arithmetic referent (~2× the 9% flush share at a near-half-stack price) is recorded in pct_provenance.",
    "The villain framing that tempts the call — 'this guy's been super aggressive and just really, really good' (s775) — is Tyler's hypothetical, not a read on a real opponent; the felt seats an unnamed VILLAIN."
  ],
  "cosmetic_invention": [
    "Seat ghouls/avatars for hero and the four folded seats, and the felt render itself. Positions, stacks, sizings, line and board come off the GTO Wizard node (frames t=2984, t=3056).",
    "River card shown as 8♣ — the source hand's river and the exact board every displayed figure was computed on (Pio log 'River: Ad5d4hQd8c') — where the GTO Wizard mirror node deals 8♥ (tab 'Qd5d4hAd8h'). Neither eight is a diamond; no displayed number depends on the suit.",
    "The all-in itself: villain takes the node's real Allin 95.5 branch (0% at equilibrium, 0 combos). It is staged because it is the exact hypothetical Eric asks at s764 ('if he's all in, if he's all in') and Tyler rules on (s765-766, s779-800); claims[3] records that the equilibrium never takes it."
  ],
  "concept": "max-stackoff-threshold",
  "concepts_secondary": [],
  "topic": "river-defense",
  "difficulty": 4,
  "decision": {
    "pot_settled_bb": 9.5,
    "bets": {
      "BB": 95.5
    }
  }
}