Theory Foundation — Cash NLHE

• LIT-2 (Probe Betting): "An in-position raiser has a much stronger preflop range than a BB caller, carrying this range advantage forward to the flop" [PRB-1]
• LIT-3 (Delayed C-Betting): raiser-favorable vs unfavorable flop dichotomy [DCB-2, DCB-6]
• LIT-7 (Equity Realization): "Stronger ranges realize more equity because they generate more fold equity" [EQR-5, EQR-7]
• LIT-8 (Protection): dual EV source from range strength [PRT-12]
• Model (B1 A1 Position → Range Width): PASS on Cash

C-HIGH (4 lit citations + B1 A1 PASS = 5+ sources)

LIT CORR

Cash CO open → BB call, flop c-bet % by board class (high-dry vs low-connected). Expect high-dry > low-connected by a wide margin (>20pp).

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• LIT-2 (Probe Betting): "AK8 flop: BB enjoys nuts advantage but NOT equity advantage" [PRB-6]; "BB bets a polarized range at large sizing to leverage nuts advantage" [PRB-8]
• LIT-4 (Donk Betting): "654r flop: BB holds more of the Best Hands and Good Hands despite equal equity" [DNK-6]
• Model (B1 D2 Nut Advantage → Betting): PASS on Cash
• Model batch: sizing_per_combo (AK6r 18.75% overbet), a2_sizing_overbet_xval (AK8r 18.3%, A72r 0%) 2026-04-14

C-HIGH (2 lit + B1 D2 PASS + 2-board overbet confirmation = 4 sources)

LIT CORR [MODEL-BATCH] Batch ref: cash/data/batches_cash_sizing_per_combo/R_cash_a2_sizing_overbet_xval.json (2026-04-14)

• LIT-7 (Equity Realization): "When your range consists mostly of weak hands, the rare strong hands realize MORE equity" [EQR-5]; "Medium-strength hands under-realize equity most dramatically" [EQR-10]; "Stronger ranges realize more equity because they generate more fold equity" [EQR-7]
• Model (no direct B1 test — EQR is not exposed as a first-class field in the strategy_grid API)

C-MED (LIT-7 + LIT-18 (EQD-1..7) + LIT-19 (EQB-1..4) via IA-3 expansion = 2 source-article citations; Model does not count — EQR not exposed by API)

LIT CORR

Medium-strength hands (e.g., 9-high on low boards, bottom pair on high boards) in BB's range defending vs CO 33% pot c-bet should fold at a higher rate than raw pot-odds equity would suggest.

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• LIT-2 (Probe Betting): "A check from the preflop raiser is a condensing action, making nutty hands less likely for them" [PRB-4]
• LIT-3 (Delayed C-Betting): "By declining to bet the flop, you have not allowed opponent to fold weak hands" [DCB-1]
• LIT-5 (Turn Strategy): "After BB checks and calls a 33% pot c-bet, BB has folded away equity disadvantage and now has a stronger range on most turns" [TRN-18]
• Model (B1 A9 Street → Range Narrowing): PASS on Cash (range narrows monotonically as street progresses, consistent with the condensing mechanism)

C-HIGH (3 lit + B1 A9 PASS = 4 sources)

LIT CORR

BB probe rate after CO flop check on A94r (condensed range) > BB donk rate on same board with no flop action (full range).

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• LIT-7 (Equity Realization): EQR formula definition [EQR-1]; "EQR depends on position, board texture, stack sizes, and composition of each player's range" [EQR-18]; "EQR depends on how well you and your opponents play later streets" [EQR-19]; BB Ad2d vs HJ Ad2d example [EQR-4]

C-LOW (1 lit source; Model does not count — no B1 EQR property)

LIT CORR NOT APPLICABLE in Artifact 2 (flag): EQR is not directly queryable from the strategy_grid API. Theory is retained in the catalog for completeness, but Artifact 2 cannot verify it directly. Per b1-field-usability-matrix.B.md, equity is "likely safe but not B1-tested" — so even indirect EQR inference is limited.

Compare fold-to-c-bet rate for the same hand from BB vs from IP defender (SB open → BTN 3bet cold call scenario). If BB folds more and wins less showdown, EQR inference holds directionally.

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• LIT-8 (Protection): "Thin value hands can bet 'for protection' when they simultaneously: (a) extract value from worse hands AND (b) fold out competing equity" [PRT-8]; "Bets and raises derive EV from inducing low-equity hands to call AND high-equity hands to fold" [PRT-12]; "Primary goal of value betting is extracting calls from near-dead equity, not pricing in draws" [PRT-14]
• LIT-8: AA on 8h6d4h example — "Betting 75% pot loses approximately 7% of the pot in expectation vs checking" [PRT-1, PRT-4]; "C-betting AA on 8h6d2c is more acceptable than on 8h6d4h" [PRT-6]
• Model: EV-magnitude claims here require the ev field in an unsafe way per b1-field-usability-matrix.B.md — KI-1 blocks absolute EV, KI-4 blocks per-hand EV comparisons.

C-MED (1 lit source with multiple corroborating claims; Model does NOT count because EV is KI-1/KI-4 qualified)

LIT CORR EV-QUALIFIED-KI-1 EV-QUALIFIED-KI-4

Frequency of "bet with thin-value hands" (e.g., K8 on K72r) vs bluff-catching check frequency by board class — wet boards should show a higher bet-for-protection frequency than dry boards for the same hand class. This is the frequency-layer shadow of the EV claim.

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• LIT-7 (Equity Realization): "ALL hands have lower EQR when playing out of position" [EQR-3]; "BB's Ad2d realizes <2% equity on JhTd9h; HJ's Ad2d realizes ~100% equity on the same board" [EQR-4]
• LIT-7: range composition × position effects [EQR-5, EQR-7]
• Model (B1 A1 Position → Range Width): PASS on Cash — position effect is structurally present in the frequency layer (IP players play wider, consistent with better EQR)

C-HIGH (1 lit with many supporting claims + B1 A1 PASS = 3 sources counting position-claim multiplicity) Caveat: For Squid B1 shows H1 FAIL ("position may not improve EV with desperate opponents"). On Cash, H1 PASSES, so this theory is C-HIGH for Cash only. In Squid it is known to break down; not this document's scope but worth noting.

LIT CORR

For the same hand (e.g., Ad2d), compare BB's fold-to-33%-c-bet rate vs BTN cold-caller's fold-to-c-bet rate on the same flop — BTN should fold less due to better EQR.

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• LIT-1 (MDF and Alpha): formula definitions [MDF-3, MDF-4]; 37.5% / 62.5% worked example [MDF-6]; 125% pot overbet EV worked example [MDF-8]; pure bluff EV formula [MDF-5]
• LIT-1: definitional framing [MDF-18, MDF-19] (marked definitional in extracts)

C-HIGH — LIT-1 + LIT-11 (BLK-4,5) + LIT-13 (IND-2,3) via IA-3 + LIT-22 (RCP-2..5, Red Chip Poker) via IA-3 cross-family search + B1 D1 PASS = 5 sources across 2 source families (GTO Wizard + Red Chip Poker). RCP-2..5 independently state the alpha formula at 25/33/40/50% with matching numbers — first true cross-family corroboration in the corpus.

LIT CORR

Average BB fold-to-c-bet% across a wide board sample for a 33% pot bet, compared to the MDF = 25% prediction.

• LIT-1 (MDF): "BB is consistently overfolding to all bet sizes on the flop vs. MDF predictions" [MDF-14]; "Defender with position calls much closer to MDF on average" [MDF-15]; QQ3r example 75% MDF vs 50% solver [MDF-16]; JhTd7c 43% MDF vs 53% solver [MDF-17]; four-condition under-MDF list [MDF-9]; four-condition over-MDF list [MDF-10]
• Model (B1 A1 PASS + B1 D1 Value-Bluff Balance PASS): both support frequencies deviating from pure MDF in direction consistent with range composition

C-HIGH (1 lit with 6 direct claims + 2 B1 PASSes = 3+ sources)

LIT CORR

For BB vs CO 33% c-bet, fold rate on K72r (dry) vs 765 (wet). Predict: K72r > 25% (over-fold), 765 < 25% (under-fold).

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• LIT-1 (MDF and Alpha): "When bluffs have equity as a checkback, the goal is to make bluffs indifferent between betting and checking (not between betting and folding)" [MDF-11]; "A villain's 20% equity checkback bluff requires only 40% call frequency" [MDF-12]; "A 20% equity draw bluff requires approximately 57% call frequency" [MDF-13]
• LIT-6 (River Play): "A well-constructed polarized betting range makes opponent roughly indifferent to calling with medium-strength hands" [RVR-7]
• Model: Intra-spot EV-equality at mixed strategies — B1 I2 (Mixing Implies Indifference) PASS on Cash. This validates the mechanism (mixed actions have ~equal EV), but MDF-12 and MDF-13 specifically need per-action EV magnitudes (blocked by KI-1).

C-HIGH (GTO Wizard) — LIT-1 + LIT-6 + LIT-13 (IND-1..7, full dedicated article) via IA-3 + B1 I2 PASS = 4 sources. Quantitative sub-claims (MDF-12/13 specific percentages) remain capped at C-MED by KI-1 block. Mechanism layer is C-HIGH. Note: all GTO Wizard source family.

LIT CORR EV-QUALIFIED-KI-1 for the quantitative sub-claims

Mixing proportions at the bettor side — on boards where the bettor has high-equity semi-bluffs (flush draws, straight draws), the bet-frequency should be higher and the defender fold-frequency should also be higher relative to boards where the bettor has dry no-equity bluff candidates only.

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• LIT-1 (MDF/Alpha): Alpha formula defines bluff-to-value ratio requirement [MDF-1]; pure bluff EV formula [MDF-5]
• LIT-6 (River Play): "Bluff availability constrains value bet sizing: if you don't have enough bluffs to balance, you cannot bet as large with strongest hands" [RVR-6]; "A well-constructed polarized betting range makes opponent roughly indifferent to calling with medium-strength hands" [RVR-7]
• Model (B1 D1 Value-Bluff Balance): PASS on Cash

C-HIGH (2 lit + B1 D1 PASS = 3 sources)

LIT CORR

On boards where the bettor has few natural bluff candidates (e.g., BTN c-bet on QQ3r monotone where BTN's range is weighted toward made hands), average bet size should be smaller than on boards rich in bluff candidates (e.g., BTN c-bet on K94ss with many flush-draw combos).

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• LIT-2 (Probe Betting): "BB's check-raise bluffs are all draws" [PRB-13]; "AK8 flop: BB pure checks and folds worst hands, but checks some strong hands (sets, two pairs, AJ, AQ)" [PRB-14]
• LIT-4 (Donk Betting): "Betting so many medium-strength hands incentivizes opponent to raise; BB balances with nut hands and strong draws (sets, straights, 75, 65, 54) to make UTG indifferent" [DNK-18]
• LIT-5 (Turn Strategy): "Draws have the trickiest decisions and often end up indifferent at equilibrium" [TRN-6]; "Flush draws with a pair or Ace have showdown value and thus less incentive to semi-bluff" [TRN-16]
• Model (B1 D1 Value-Bluff Balance + B1 D4 Blocker Logic): both PASS on Cash

C-HIGH (3 lit + 2 B1 PASSes = 5 sources)

LIT CORR

On 654r at BB (after BB donk/probe), BB's bet range should contain sets (66/55/44) AND straights (75/53) at high frequency, AND strong draws as balance. Compare the combo composition at the fraction-of-range level.

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• LIT-2 (Probe Betting): IP raiser has much stronger range than BB caller [PRB-1]
• LIT-4 (Donk Betting): "654r at 100bb: BB donk bets much less often vs BTN opener than vs UTG opener" [DNK-29] — implicitly, BTN's opening range at 100bb is wider with more straight/two-pair combos
• Model (B1 A1 Position → Range Width): PASS on Cash

C-HIGH (2 lit + B1 A1 PASS = 3 sources)

LIT CORR

Preflop VPIP by position on Cash 100bb — should grow monotonically from UTG → MP → CO → BTN.

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• LIT-1 (MDF): "You should defend LESS than MDF when: (a) you are out of position" [MDF-9]; "SB vs BB (SB in position) — Defender with position calls much closer to MDF on average" [MDF-15]
• LIT-7 (Equity Realization): "ALL hands have lower EQR when playing out of position" [EQR-3]; BB Ad2d vs HJ Ad2d example [EQR-4]
• Model (B1 A1 PASS) — structural

C-HIGH (2 lit + B1 = 3 sources)

LIT CORR

Same as A7 (identical manifestation).

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• LIT-4 (Donk Betting): "654r at 100bb vs UTG: UTG has very few combos of 87, 65, 54, and 32; does not have 44 at full frequency" [DNK-30]; "BB donk bets much less often vs BTN opener than vs UTG opener" [DNK-29]
• Model batch: cross_opener (8 boards 2026-04-12) + C3 extension (987r/J87r/T76r 2026-04-14)

C-HIGH (GTO Wizard) — LIT-4 + LIT-9 (FHI-17..20) + LIT-10 (CBS-2..9) + LIT-21 (MON-2) via IA-3 + B1 A10 PASS = 5 sources. All GTO Wizard source family.

LIT CORR [MODEL-BATCH] Scope (batch-confirmed): C3 holds on sequential T-9-8 and 9-8-7 boards; flat on J-8-7 and all dry/paired boards; reverses on T-7-6, 6-5-4, A-high boards. Extension panel (987r +9.2pp, J87r flat, T76r −11.8pp) confirms the boundary: UTG advantage requires both sequential AND mid-range (7-10) cards. ---

• LIT-1 (MDF): "SB vs BB (SB in position) — Defender with position calls much closer to MDF on average" [MDF-15]
• LIT-13 (Indifference): IND-2..4 — range-structure implications for blind-vs-blind spots
• LIT-12 (Range management): RMO-4..5 — range composition effects in SB position
• Model batch: cash/data/batches_cash_sb_postflop/R_cash_sb_postflop.json — SB postflop cbet on 6 boards: K72r 65.4%, A94r 61.6%, KK5 79.4%, T98 25.6%, 654 3.9%, K94ss 9.8%. Confirms SB uniquely constrained: barely cbets low-connected/monotone boards (vs CO's 56.4% and 32.2% on same boards). CONFIRMED 2026-04-12.

C-HIGH (upgraded from C-MED 2026-04-14: 3 LIT source-articles + MODEL-BATCH = 4 sources across 2 source families [LIT + MODEL-BATCH]. Upgrade was pending documentation — SB postflop batch already existed and directly addressed this theory.)

LIT [MODEL-BATCH]

SB postflop cbet on low-connected boards vs CO cbet — expected SB dramatically lower (positional disadvantage forces passivity on texture where CO would cbet). Observed: SB 3.9% vs CO 56.4% on 654; SB 9.8% vs CO 32.2% on K94ss. Passes.

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• LIT-2 (Probe Betting): AK8 LJ 65% equity → "bets ~90% of range" at small size [PRB-5, DCB-6]
• LIT-4 (Donk Betting): "654r flop (20bb, UTG vs BB): Equities are almost exactly 50/50" [DNK-5]; "Only very specific low/medium-connected flops bring BB close to 50% equity" [DNK-8]
• LIT-7: position × range composition mechanics [EQR-4]
• Model (B1 A1 PASS + B1 D2 Nut Advantage PASS): both support frequency response to equity + nuts split
• Model batch: cross_opener CO row + surviving batches (2026-04-12) — 11 cells confirmed

C-HIGH (3 lit + 2 B1 PASSes + 11-cell batch confirmation = 5+ sources)

LIT CORR [MODEL-BATCH]

• LIT-5 (Turn Strategy): "Strong hands (two pair, sets) almost exclusively bet the turn; they have only one more street to grow the pot" [TRN-4]
• LIT-6 (River Play): "UTG splits sets between 275% pot shove and 85% pot bet based on blockers" [RVR-13]
• Model (B1 D2 Nut Advantage → Betting): PASS on Cash
• Model (B1 S4 Board Texture → Sizing): PASS on Cash

C-HIGH (2 lit + 2 B1 PASSes = 4 sources)

LIT CORR

Average bet size across strong hands (sets, two-pair) vs medium hands (top pair) on K72r vs 765 — expect nuttier boards to push strong-hand sizing higher.

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• LIT-8 (Protection): "Thin value hands can bet 'for protection' when they simultaneously: (a) extract value from worse hands AND (b) fold out competing equity" [PRT-8]; "As8h2d rainbow: 8x bets at 70% frequency with 33% pot sizing; forcing 75% sizing loses ~6bb/100 EV" [PRT-9]; "Upsizing thin value bets isolates against a stronger range when called" [PRT-10]
• Model (B1 D3 Hand Strength Gradient + D4 Blocker Logic): both PASS
• EV-specific claim ([PRT-9] -6bb/100) is blocked-KI-1/KI-2 in extracts — blocked at the quantitative level.

C-HIGH (GTO Wizard) — LIT-8 + LIT-9 (FHI-12..14) + LIT-10 (CBS-7,8,16) + LIT-14 (OVB-6) via IA-3 + B1 D3/D4 PASS = 5 sources. Quantitative EV sub-claim (PRT-9 -6bb/100) remains EV-QUALIFIED-KI-1. All GTO Wizard source family.

LIT CORR EV-QUALIFIED-KI-1 for the quantitative sub-claim

Bet-sizing distribution for top pair on A94r — expect strong concentration at 33% sizing, not 75%.

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• LIT-5 (Turn Strategy): "Lower betting frequencies and bigger bet sizes indicate more polar ranges" [TRN-9]; "K84 flop then Q turn: UTG bets barely 40% of range, always for an amount larger than the pot (overbet)" [TRN-7]
• LIT-5: stack-depth interaction [TRN-10 through TRN-14]
• Model (B1 A5 Own Bet Sizing Polarization + S4 Board Texture → Sizing): both PASS

C-HIGH (GTO Wizard) — LIT-5 + LIT-9 (FHI-6,19) + LIT-10 (CBS-3,11) + LIT-12 (RMO-1,6) + LIT-14 (OVB-4) via IA-3 + B1 A5/S4 PASS = 7 sources. All GTO Wizard source family.

LIT CORR

Turn barrel rate and turn bet size on K72r turn cards following flop c-bet + BB call. Compare to flop c-bet rate and size — expect turn rate < flop rate, turn avg size > flop avg size.

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• LIT-5 (Turn Strategy): KK/QQ on K84Q block villain's paying-off combos → exception to "always bet strong hands" [TRN-15]
• LIT-6 (River Play): "UTG splits sets between 275% pot shove and 85% pot bet based on blockers" [RVR-13]; "Holding a single card on paired/flushed boards can dramatically reduce opponent's calling frequency, incentivizing smaller bets" [RVR-9]
• Model (B1 D4 Blocker Logic): PASS on Cash

C-HIGH (2 lit + B1 D4 PASS = 3 sources)

LIT CORR

Per-combo bet-size distribution for AK on an Ace-high flop — KhAh blocks heart flush combos; its bet size distribution should differ from non-suited AK. (Connects to KI-7, which flagged KhAh anomaly on 8h6d4h.)

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• LIT-4 (Donk Betting): "764r (20bb): Donk bet size is small — 33% pot; only other size is all-in" [DNK-15]; "Donk betting frequency drops by nearly two-thirds from 20bb to 100bb" [DNK-21]; stack-depth reversal effect [DNK-27, DNK-28]
• LIT-5 (Turn Strategy): "At 20bb: UTG's most common bet size is 50% pot rather than an overbet" [TRN-10]; "At 20bb: Top pair bets more often" [TRN-11]; "At 20bb: Draws bet less often" [TRN-12]
• Model: B1 S5 (SPR → Sizing Concentration) FAIL at 20bb (1 violation — edge case). Cannot cite Model for 20bb claims; for 100bb claims, S4 PASSES.

C-HIGH (2 lit source-articles [LIT-4 + LIT-5] + CORR [B1 S4 PASS] = 3 sources across 2 source families at 100bb core level. Upgraded from C-MED 2026-04-14.) Scope caveat: 20bb-specific sub-claims are C-LOW — B1 S5 FAILs at shallow stacks (1 violation), so 20bb sizing claims cannot be model-corroborated. The theory is C-HIGH for 100bb-focused sizing claims only. Analogous to G1's treatment (Cash C-HIGH; Squid scope caveat).

LIT CORR — 20bb sub-claims [UNCORR at model level] due to S5 failure

Average donk size on 654r at 20bb vs 100bb — expect reduction in sizing-diversity at 20bb (concentrated at 33% + shove) but this is at the boundary of B1-trusted territory.

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• LIT-6 (River Play): "Holding a single card on paired/flushed boards can dramatically reduce opponent's calling frequency, incentivizing smaller bets" [RVR-9]
• LIT-5 (Turn Strategy): KK/QQ block AA/KK paying combos [TRN-15]
• CORR (B1 D4 Blocker Logic): PASSes at the frequency layer — blocker structure affects action distributions
• MODEL-BATCH: cash/data/batches_cash_blocker_sizing/R_cash_d6_blocker.json — per-combo suit filtering on T98ss (Ts9s8c) and A94ss (As9s4c), 2026-04-14. AA on T98ss: with A♠ cbet=90.8% vs without A♠ cbet=33.6% (Δ=+57.2pp frequency effect). QQ on T98ss: with Q♠ → bet1.8=84.4% (smaller); without Q♠ → bet2.8=70.4% (larger). JJ on T98ss: with J♠ → bet1.8=52.5%/bet2.8=47.4%; without J♠ → bet1.8=7.5%/bet2.8=92.1%. Direction: WITH blocker → smaller sizes; WITHOUT blocker → larger sizes.

C-HIGH (2 LIT sources [LIT-6 RVR-9 + LIT-5 TRN-15] + CORR [B1 D4 PASS] + MODEL-BATCH [blocker sizing batch, direction confirmed] = 4 sources across 3 source families. Upgraded from C-MED 2026-04-14. Quantitative EV layer [exact bb improvement per combo] remains capped by KI-4.)

LIT CORR [MODEL-BATCH] EV-QUALIFIED-KI-4 for quantitative per-combo EV sub-claims Batch ref: cash/data/batches_cash_blocker_sizing/d6-analysis.md (2026-04-14)

• LIT-58 (Play Optimal Poker 2 — Brokos): "Bet sizing must be consistent across value and bluff hands; using different sizes for value vs bluffs (larger with weak hands to get folds, smaller with strong hands to get calls) is a major exploitable leak" [POP-1-9]
• Model batch: cash/data/batches_cash_sizing_per_combo/ — per-hand sizing via extract_per_hand_class() on 6 boards (K72r, T98, A94r, AK6r, KK5, 772), 2026-04-14
• Model (B1 D1 Value-Bluff Balance): PASS on Cash — the ratio of bluffs to value at each bet size is balanced; this structurally implies no systematic size divergence

C-HIGH (LIT-58 POP-1-9 cross-family [Play Optimal Poker 2] + 6-board model batch + B1 D1 PASS = 3 sources across 2 source families. Upgraded from C-MED 2026-04-14 upon discovery of POP-1-9 as direct LIT corroboration.)

LIT [MODEL-BATCH] CORR Batch ref: cash/data/batches_cash_sizing_per_combo/d7-analysis.md (2026-04-14) Key per-hand examples: - K72r: KK (top set = nuts) uses bet1.8 89%; QJs/JTs/QTs (bluffs) use bet2.8 97-99%. Nuts is SMALLER. - A94r: AA (nut set) uses bet1.8 99%; QJs/JTs (bluffs) use bet2.8 90-93%. Nuts is SMALLER. - AK6r: QJs/QTs (bluffs) use bet8.2 (overbet) at 63%/52%; AA uses bet1.8 96%. Bluffs are BIGGER. - KK5: 55 (set) and QJs/JTs/T9s (bluffs) all use bet1.8 95-99%. Identical. - 772: KK/22 (value) and QJs/AQs (bluffs) all use bet1.8 74-83%. Identical. - T98: 88/99 (value) and AQs/AJs/KQs (bluffs) all use bet2.8 92-100%. Identical.

• LIT-2 (Probe Betting): "AK8 flop (AdKh8h): LJ has 65% equity; LJ checking range is about 10% of hands" [PRB-5]
• LIT-3 (Delayed C-Betting): "AK8 flop: LJ has 65% equity and bets ~90% of range" [DCB-6]
• Model (B1 A1 PASS + B1 S4 Board Texture → Sizing PASS)

C-HIGH (2 lit + 2 B1 PASSes = 4 sources)

LIT CORR

CO c-bet% and avg size on A94r, K72r — expect 80-95% bet frequency at ~33% pot.

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• LIT-1 (MDF/Alpha): "QQ3r flop: CO bets 33% pot; MDF suggests 75% defense but solver recommends defending only ~50% due to bluff equity" [MDF-16]
• LIT-24 (Playing Calls from the Button): "When there are two cards below a Ten on the flop, UTG checks with very high frequency because BTN holds all low pocket pairs" [BTN-6] — corroborates reduced defense on boards where BTN's range hits hard
• LIT-27 (IP 4-Betting Deep-Stacked): "Medium-connected flops are the worst for IP c-betting in 4-bet pots" [I4B-5] — inverse confirms OOP range disadvantage on medium-connected/paired boards
• LIT-28 (OOP 4-Betting Deep-Stacked): "Medium, connected flops are the worst for OOP c-betting" [O4B-6] — same pattern in OOP 4BP confirms board-class defense-width principle
• Model (B1 A10 Opener Strength → Defender Width PASS)

C-HIGH — LIT-1 + LIT-24 (BTN-6) + LIT-27 (I4B-5) + LIT-28 (O4B-6) + B1 A10 PASS = 5 sources. Upgraded from C-MED with v1.3.0 literature expansion (LIT-23..49 batch). All GTO Wizard source family.

LIT CORR

BB fold-to-33%-c-bet on QQ3r vs on K94ss — expect QQ3r fold% significantly higher.

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• LIT-2 (Probe Betting): "654 flop (6h5d4d): Equity is split almost exactly 50-50 between LJ and BB" [PRB-9]; "654 flop: LJ rarely continuation bets; BB enjoys nuts advantage" [PRB-10]
• LIT-4 (Donk Betting): "Low-connected boards are among the worst for the preflop raiser to continuation bet" [DNK-4]; "Low card flops (6-high, 5-high) show the most significant donk betting as part of BB's strategy" [DNK-3]
• Model (B1 A1 + D2 PASS)

C-HIGH (2 lit + 2 B1 PASSes = 4 sources)

LIT CORR

CO c-bet% on 654r vs A94r — expect 654r significantly lower (by 30+pp).

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• LIT-3 (Delayed C-Betting): "7h6h is never checked (flush draw); 7d6d is rarely checked (flush draw protection)" [DCB-8] — implicit confirmation of suit-informative logic
• Model (B1 C1 Suit Isomorphism): PASS on Cash
• Model batch: cash/data/batches_cash_isomorphism/R_cash_isomorphism.json — K72 in 4 suit rotations (Kh7d2c, Ks7h2d, Kd7c2h, Kc7s2h): CO cbet identical at 83.6% across all 4 rotations. Zero spread. STRONGLY CONFIRMED 2026-04-12.

C-HIGH (upgraded from C-MED 2026-04-14: 3 sources across 3 source families — LIT [LIT-3 DCB-8] + CORR [B1 C1 PASS] + MODEL-BATCH [isomorphism batch zero-spread confirmation]. Upgrade was pending documentation — batch already existed.)

LIT CORR [MODEL-BATCH]

Strategy comparison between two suit-isomorphic boards (no flush draws present) — should match within noise. Observed: 83.6% vs 83.6% vs 83.6% vs 83.6% — bit-identical across 4 rotations.

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• LIT-3 (Delayed C-Betting): "AK8 flop: 7h6h is never checked (flush draw); 7d6d is rarely checked (flush draw protection)" [DCB-8] → E5(CONF)
• LIT-5 (Turn Strategy): "Flush draws with a pair or Ace have showdown value and thus less incentive to semi-bluff" [TRN-16] → E5(CONF-NUANCED) (flush draw alone checks; flush draw + board equity bets — refines the LIT claim)
• Model (B1 D4 Blocker Logic PASS — suit-specific combo behavior)
• Model batch: draw_mixing (K94ss/T98ss/876hh per-class) + two_tone (K72r/K74ss, A94r/A94ss, T98/T98ss) — 2026-04-14

C-HIGH (LIT-3 DCB-8 + LIT-5 TRN-16 + batch; 3 boards; +13.1pp/+8.2pp >> 5pp threshold; consistent direction).

LIT CORR [MODEL-BATCH] Batch ref: cash/data/batches_cash_draw_mixing/e5-analysis.md Scope revision: The conditional is important — flush draw alone is insufficient. Hands bet aggressively when they carry flush draw AND have secondary equity (pair, straight draws). Pure flush draws without board equity check. This refines LIT-3 DCB-8's framing ("flush draws never/rarely checked") to: "flush draws with board equity never/rarely checked; flush draws alone usually checked." ---

• LIT-2 (Probe Betting): "654 flop: When small cards turn, BB enjoys significant range advantage; when big cards turn, LJ's equity improves" [PRB-15]; "654 flop: BB's strategy depends heavily on turn card — far more so than on the static AK8 flop" [PRB-16]
• LIT-3 (Delayed C-Betting): "Strong turn cards (A, K on AK8 board) don't significantly increase LJ aggression because BB's range already accounts for these cards" [DCB-9]
• LIT-5 (Turn Strategy): "On 986 flop, an offsuit 7 is worst turn for UTG because BB has more 7x and 5x" [TRN-20]; "Ace and King turns help UTG more than BB on 986" [TRN-21]
• Model (B1 A9 Street → Range Narrowing PASS)

C-HIGH (3 lit + B1 A9 PASS = 4 sources)

LIT CORR

CO turn barrel rate by turn card on 654r flop — expect high variance across turn cards; same metric on A94r should show lower variance.

---

• LIT-4 (Donk Betting): "Low card flops (6-high, 5-high) show the most significant donk betting as part of BB's strategy" [DNK-3]; "Low-connected boards are among the worst for the preflop raiser to continuation bet" [DNK-4]; "654r flop (20bb, UTG vs BB): Equities are almost exactly 50/50" [DNK-5]; "On the average flop, the preflop raiser has a significant equity advantage; only very specific low/medium-connected flops bring BB close to 50% equity" [DNK-8]
• Model (B1 A1 PASS + B1 D2 Nut Advantage → Betting PASS)

C-HIGH (1 lit with 4 direct claims + 2 B1 PASSes = 3+ sources)

LIT CORR

BB donk% on 654r vs on A94r at Cash 100bb — expect 654r much higher.

---

• LIT-5 (Turn Strategy): "On 986 flop, an offsuit 7 is worst turn for UTG because BB has more 7x and 5x" [TRN-20]; "Ace and King turns help UTG more than BB on 986" [TRN-21] — consistent with E8 (on connected 986/654, pure-overcard high cards help CO; connecting low cards hurt)
• LIT-3 (Delayed C-Betting): "Strong turn cards (A, K on AK8 board) don't significantly increase LJ aggression" [DCB-9] — on CO-favored AK8, board-pairing high cards suppress CO's barrel (consistent with E8's AK8r prediction)
• Model batch: cash/data/batches_cash_turn_cards/R_cash_turn_cards.json — 13 turn ranks × 2 flops (654, AK8r), 2026-04-12
• Model batch (E8 ext): cash/data/batches_cash_turn_cards/R_cash_e8_turn_ext.json — 13 turn ranks × T98, 2026-04-14. K inversion confirmed: K=64.7% on T98 vs 38.0% on AK8r. A inversion confirmed: A=72.9% on T98 vs 51.5% on AK8r. Q exception on T98 (34.6%) reveals mechanism: Q completes Q-J-T-9-8 straight, consistent with draw-completing suppression pattern.

C-HIGH (upgraded from C-MED 2026-04-14: 3 flops tested — 654, AK8r, T98 — showing consistent inversion for pure-overcard and blank turns. K-inversion confirmed across all 3 boards. 2 LIT sources [TRN-20/21 + DCB-9] + MODEL-BATCH = 3 sources across 2 source families. Prior upgrade blocker was 2-flop scope; resolved by E8 extension batch.)

LIT [MODEL-BATCH] Batch refs: - cash/data/batches_cash_turn_cards/turn_cards-analysis.md (2026-04-12) — original batch - cash/data/batches_cash_turn_cards/e8_turn_ext-analysis.md (2026-04-14) — E8 extension: T98 3rd flop Key data: On 654 (BB-favored low-connected): - DRAW-NEUTRAL high cards: 9s=86.9%, Ks=86.2%, Ts=83.5%, Js=78.6%, Qs=76.9% — all ≥77% - DRAW-COMPLETING: 7s=45.7% (completes 4-5-6-7 for BB), As=44.1% (wheel draw: A-2-3-4-5) On AK8r (CO-favored): - BLANK turns: 9s=89.5%, 6s=88.6%, 4s=87.9%, 7s=87.1%, 2s=86.8%, 5s=86.4%, 3s=86.6% — all ≥86% - BOARD-PAIRING turns: Ks=38.0%, Js=50.5%, As=51.5%, Ts=51.5%, Qs=56.3% — all ≤57% On T98 (BB-favored mid-connected) [new 2026-04-14]: - DRAW-NEUTRAL turns: As=72.9%, 4s=68.8%, 3s=69.2%, 2s=69.1%, 6s=67.1%, Ks=64.7%, 5s=59.9% — all ≥60% - DRAW-COMPLETING: Qs=34.6% (Q-J-T-9-8 straight), 7s=46.4% (T-9-8-7 OESD completing) — lowest K-turn cross-board (clearest inversion signal): - AK8r: 38.0% (K pairs top pair — strong suppressor on CO-favored) - T98: 64.7% (K = pure overcard — boosts on BB-favored) - 654: 86.2% (K = pure overcard — strongest booster on BB-favored)

• LIT-2 (Probe Betting): "On favorable flops for the raiser, a check typically indicates a medium hand (not weak) that did not benefit much from betting" [PRB-2]; PRB-4 condensing [PRB-4]; PRB-6 AK8 BB nut advantage after LJ checks [PRB-6]
• LIT-3 (Delayed C-Betting): "After opponent checks the flop following aggressor's check, the aggressor can value bet more thinly than on the flop" [DCB-2]
• Model (B1 A9 Street → Range Narrowing PASS)

C-HIGH (2 lit + B1 PASS = 3 sources)

LIT CORR

CO turn bet rate and value-to-bluff ratio on K72r after CO checks flop vs after CO bets flop — expect different sizing/frequency patterns on the delayed-c-bet line.

---

• LIT-3 (Delayed C-Betting): "Medium-strength hands benefit most from checking back and gaining information (e.g., A2, K6, JJ)" [DCB-4]; "After flop check, IP player mostly plays a bluff-catching game on later streets" [DCB-15]; "Raises after flop check are almost exclusively slowplayed monsters" [DCB-17]; 9s turn on AK8 [DCB-10]
• LIT-5 (Turn Strategy): "Medium-strength hands (third pair, second pair, most top pairs) have more incentive to check for cheap showdown on the turn" [TRN-3]; "Weak hands face binary choice on the turn" [TRN-5]
• Model (B1 A1 PASS + B1 F4 Check EV ≥ Fold EV PASS — structural support for medium-hand checking)

C-HIGH (2 lit + 2 B1 PASSes = 4 sources)

LIT CORR

Check frequency for medium-strength hand class (e.g., A2/K6/JJ on K72r) by CO after preflop raise — expect ≥50% check rate.

---

• LIT-4 (Donk Betting): "BB should almost never donk bet unless with clear exploitative purpose" [DNK-2]; "JT9r flop: BB never donk bets despite same UTG vs BB configuration" [DNK-7]; "A simple rule of never donk betting will rarely lead you astray" [DNK-34]; position scaling [DNK-1]; low-board exceptions [DNK-3]; SPR scaling [DNK-19]
• Model (B1 A1 PASS for default action distribution)

C-HIGH (GTO Wizard) — LIT-4 + LIT-18 (EQD-6) + LIT-21 (MON-8) via IA-3 + B1 A1 PASS = 4 sources. All GTO Wizard source family.

LIT CORR

BB donk% across a wide board sample at Cash 100bb — expect aggregate below 10%, with exceptions concentrated on low-connected boards.

---

• LIT-5 (Turn Strategy): TRN-3 medium hands check; TRN-4 strong hands bet; TRN-5 weak hands binary (big bluff or give up); TRN-7 K84Q UTG 40% bet freq, overbet size; TRN-9 lower freq + bigger size = polar
• Model (B1 A5 Own Bet Sizing Polarization + B1 S4 Board Texture → Sizing): both PASS

C-HIGH (1 lit with 5 direct claims + 2 B1 PASSes = 3+ sources)

LIT CORR

Sizing distribution entropy on flop vs turn c-bet on K72r — expect turn to be more concentrated at larger sizes, flop more dispersed.

• LIT-6 (River Play): "Value bets must expect to win >50% of the time when called to be profitable" [RVR-1]; "OOP players can sometimes value bet with hands that win somewhat less than 50%" [RVR-2]; "Smaller bets incentivize opponent to call with weaker hands" [RVR-4]; "Relative nuts advantage determines how thinly a player can value bet" [RVR-3]
• Model: EV-based claim — requires per-combo absolute EV comparisons across actions (ev(bet) > ev(check) for the value hand). This uses the ev field in a way that B1's F6/F7 failures (KI-1) block for absolute magnitudes. Intra-spot direction IS safe (F4/F5 PASS, I1/I2 PASS), but the ">50% when called" claim requires cross-hand EV ordering which is KI-4a / KI-4b blocked.

C-MED (1 lit with 4 direct claims; Model does NOT count because EV pathway for quantitative threshold is blocked by KI-1/KI-4)

LIT CORR EV-QUALIFIED-KI-1 EV-QUALIFIED-KI-4

Distribution of which hands value-bet the river after turn check-through — hands ranked by equity-when-called should show a cutoff near the expected threshold. This is a frequency-layer shadow.

---

• LIT-2 (Probe Betting): "654 flop: BB's strategy depends heavily on turn card" [PRB-16]
• LIT-4 (Donk Betting): multi-street planning example [DNK-17]
• LIT-5 (Turn Strategy): flop check-call BB range strengthens for turn [TRN-18]; BB condensed range limits UTG turn bet [TRN-19]; "The same turn principles apply even after a lower flop betting frequency" [TRN-22]
• LIT-8 (Protection): wet board draws turn AA into "zero-EV bluff catcher" on turn/river [PRT-13]
• Model (B1 A9 Street → Range Narrowing PASS)

C-HIGH (4 lit + B1 A9 PASS = 5 sources)

LIT CORR

Same-hand (e.g., QQ on K72r flop) check vs bet behavior by planned-turn-response — solver decisions branch on anticipated turn barreling/check-back, measurable as mixed strategy on flop.

---

• LIT-3 (Delayed C-Betting): "Gutshot hands (7s6s with 4 outs) call turn overbets profitably, relying on river bluffs for EV" [DCB-18]
• LIT-4 (Donk Betting): "ATo and KTo are not pure bluffs but 'clean up equity' — set up to bet for value when turning a T, or check-induce when turning A/K" [DNK-17]
• LIT-5 (Turn Strategy): "Draws have the trickiest decisions and often end up indifferent at equilibrium" [TRN-6]; "Flush draws with a pair or Ace have showdown value and thus less incentive to semi-bluff" [TRN-16]
• Model (B1 I2 Mixing Implies Indifference): PASS on Cash

C-HIGH (3 lit + B1 I2 PASS = 4 sources)

LIT CORR

Per-combo mixed probabilities for flush draws on flop — expect broad mixing (not pure) between bet and check.

---

• LIT-8 (Protection): PRT-13 "wet board draws turn strong IP hands into zero-EV bluff catchers on turn/river" — mechanism support: flush draws in BB's checking range reduce CO's turn-barrel EV
• LIT-3 (Delayed C-Betting): DCB-2 "after check, IP value bets thinner" — general F1 framework; DCB-11 was flagged board-not-queried in the original audit (K94ss not in original batch); F8 fills this gap
• Model batch: cash/data/batches_cash_delayed_cbet/R_cash_delayed_cbet.json — K94ss 11.0% vs 7 rainbow boards 36-76%; batches_cash_two_tone/R_cash_two_tone.json — two-tone boards suppress initial cbet 8-14pp (consistent direction, smaller magnitude than monotone)
• Model batch (F8 ext): cash/data/batches_cash_delayed_cbet/R_cash_f8_monotone_ext.json — T98mono 4.2% and A94mono 21.1% (2026-04-14); 3 monotone boards now tested, all 4–21% vs rainbow minimum of 36.3%
• Model (B1 A1 Position → Range Width PASS): structural support — board wetness reduces IP's effective range advantage

C-HIGH (upgraded from C-MED 2026-04-14: 3 monotone boards tested at delayed-cbet level — K94ss 11.0%, T98mono 4.2%, A94mono 21.1% — establishing this as a board-class phenomenon, not a single-board artifact. 2 LIT sources [PRT-13 + DCB framework] + MODEL-BATCH = 3 sources across 2 source families. Original single-board scope was the upgrade blocker; resolved by F8 extension batch.)

LIT [MODEL-BATCH] Key data: | Board | Type | Initial cbet% | Delayed cbet% | vs Rainbow suppression | |-------|------|--------------|---------------|------------------------| | K72r | Rainbow dry | 83.6 | 72.6 | — (baseline) | | A94r | Rainbow A-high | 64.9 | 59.1 | — (baseline) | | Q83r | Rainbow semi-dry | 74.2 | 75.9 | — (baseline) | | KK5 | Paired | 79.3 | 45.3 | — | | T98r | Connected rainbow | 59.6 | 36.3 | — (baseline) | | 654 | Low-connected | 56.4 | 74.4 | — | | 883 | Paired low | 69.6 | 56.5 | — | | K94ss | Monotone | 32.2 | 11.0 | −61.6pp vs K72r | | T98mono | Monotone connected | — | 4.2% | −32.1pp vs T98r | | A94mono | Monotone A-high | — | 21.1% | −38.0pp vs A94r |

CO delayed c-bet rate on monotone boards after flop check-back, brick turn. Threshold: <25% on monotone (all 3 boards confirmed: 4–21%), vs rainbow minimum 36.3% on T98r. Gap ≥ 15pp confirmed on all 3 boards.

Batch refs:

• cash/data/batches_cash_delayed_cbet/delayed_cbet-analysis.md (2026-04-12) — original batch
• cash/data/batches_cash_delayed_cbet/f8_monotone_ext-analysis.md (2026-04-14) — F8 extension: T98mono + A94mono

• LIT-4 (Donk Betting): "Shallower stacks make donk betting more feasible; getting raised holding T7 is not scary with SPR of 3" [DNK-19]; "At 20bb, Good Hands are good enough to treat as the nuts" [DNK-20]; DNK-21 donk frequency drops 66% from 20bb → 100bb; DNK-27/DNK-28 reversal of individual hand treatment
• LIT-5 (Turn Strategy): TRN-10/11/12 stack-depth-specific behaviors; "At 20bb: Top set slow-plays more often because it blocks the hands most likely to pay off" [TRN-13]
• Model (B1 A6 Stack Depth → Range Width PASS on Cash); (B1 A7 Stack Depth → All-in Freq PASS); (B1 H2 Stack Depth Widens EV PASS)

C-HIGH (2 lit + 3 B1 PASSes = 5 sources)

LIT CORR Scope caveat: A6 FAILS on Squid (per B1 results) — this theory is C-HIGH for Cash only.

Same spot (CO open, BB defends, 654r flop) compared at 20bb vs 100bb effective — expect BB donk% and sizing distribution to differ qualitatively.

---

• LIT-4 (Donk Betting): ICM claims DNK-31, DNK-32, DNK-33 marked N/A for cash — but the general "multiway tightens" mechanism is well-established.
• LIT-20 (MWY-1..10): dedicated multiway article, 10 direct claims on 3-way+ tightening via IA-3
• LIT-37 (Cold-Calling in Straddle+Ante Games): "Cold-calling range in straddle+ante should emphasize multiway-viable hands: pocket pairs, suited connectors, suited broadways, suited aces" [STRD-5] — direct confirmation that multiway pot likelihood shapes hand selection
• Model (B1 A8 Num Players → Range Tightness): PASS on Cash
• Model batch: multiway_4way (K72r/T98/654, 2026-04-12) + g2_multiway_4way_ext (A94r/K94ss/543/876, 2026-04-14)

C-HIGH (LIT-20 + LIT-37 STRD-5 + B1 A8 PASS + batch; 3-way 5/5; 4-way 6/7 with T98 scope-qualified).

LIT CORR [MODEL-BATCH] Scope qualification: G2 universally holds at 3-way. At 4-way, T98 reverses (+11.1pp) — a T98-specific player-count-level anomaly, not a general texture pattern (876 same category is flat). All other tested boards tighten or stay flat. Batch ref: cash/data/batches_cash_g2_multiway_4way_ext/g2-analysis.md (2026-04-14)

• LIT-3 (Delayed C-Betting): "Against 130% pot overbet, call with Aces (blocks many value hands); lower pairs are indifferent or fold" [DCB-16]
• LIT-5 (Turn Strategy): TRN-15 KK/QQ block AA/KK; TRN-17 straight draws blocking folding range
• LIT-6 (River Play): "BB sometimes folds top pair despite sometimes calling with second pair — these decisions are based on blockers" [RVR-8]; "Holding a single card on paired/flushed boards" [RVR-9]
• LIT-8 (Protection): overcard prevalence & blocker effects on BB range [PRT-11]
• Model (B1 D4 Blocker Logic): PASS on Cash

C-HIGH (4 lit + B1 D4 PASS = 5 sources)

LIT CORR

Per-combo call/fold decisions for top pair hands on high-action rivers — compare suit-specific combos to verify blocker differentiation.

---

• LIT-4 (Donk Betting): "Under ICM, both players have less incentive to grow the pot" [DNK-31]; covered vs covering asymmetry [DNK-32, DNK-33]

N/A — NOT APPLICABLE to Cash NLHE. Retained in catalog for completeness.

LIT CORR — applicable to MTT/Squid/Bomb-Pot variants only.

N/A for Cash.

---

• LIT-1 (MDF/Alpha): QQ3r and JhTd7c solver-deviates-from-MDF examples [MDF-16, MDF-17]
• LIT-4 (Donk Betting): "764r (20bb): 85 (nuts) mostly checks; 53 mostly bets" [DNK-14] — counterintuitive
• LIT-5 (Turn Strategy): KK/QQ exception to "always bet strong hands" [TRN-15]
• Model batch: systematic scan via extract_per_hand_class on K72r/T98/BB-vs-K72r (2026-04-14) — 285+ mixed hands across 3 board/position combinations

C-HIGH (LIT-1 + LIT-4 + LIT-5 + LIT-10 CBS-13/14 + LIT-13 IND-7 + 285+ batch confirmations).

LIT CORR [MODEL-BATCH]

• LIT-5 (Turn Strategy): "Hand values are more static on the turn than on the flop" [TRN-1]; "Hand values are more dynamic on the turn than on the river" [TRN-2]; TRN-3 medium-hands-check on turn (cheap showdown motivation)
• Model (B1 A9 Street → Range Narrowing): PASS — structurally consistent with value becoming more static
• Model batch: cash/data/batches_cash_mixed_strategy_fraction/R_cash_mixed_strategy_fraction.json — Pure-strategy fraction by street: K72r-2d-5h: flop 15.4% → turn 27.2% → river 38.5% (+23pp); A94r-4c-8d: flop 7.7% → turn 22.5% → river 31.4% (+23.7pp). STRONGLY CONFIRMED 2026-04-12. Magnitude (~23pp lift) consistent across both runouts.

C-HIGH (upgraded from C-MED 2026-04-14: 3 sources across 3 source families — LIT [LIT-5 TRN-1/2/3] + CORR [B1 A9 PASS] + MODEL-BATCH [mixed_strategy_fraction batch ×2 runouts]. Upgrade was pending documentation — batch already existed and directly addressed this theory.)

LIT CORR [MODEL-BATCH]

Fraction of mixed-strategy combos by street on a given line — expect decreasing mixed-strategy fraction as streets progress. Observed: pure fraction rises monotonically by 23pp (K72r) and 23.7pp (A94r) from flop to river. Passes.

---

• LIT-3 (Delayed C-Betting): "AK8 flop: LJ checks medium pairs (A2, K6, JJ), weak hands with no improvement potential (7s6s), and some monsters with blocking effects (AA)" [DCB-7]; DCB-13 unfavorable flop, "continuation betting is limited primarily to sets and straights" — opposite pattern for balance
• LIT-4 (Donk Betting): "764r (20bb): 85 (nuts) mostly checks; 53 mostly bets" [DNK-14]
• LIT-5 (Turn Strategy): TRN-13 "At 20bb: Top set slow-plays more often because it blocks the hands most likely to pay off"; TRN-15 KK/QQ block
• Model (B1 D2 Nut Advantage → Betting PASS — the exception to the rule is what this theory is about)

C-HIGH (3 lit + B1 support = 4 sources)

LIT CORR

Per-combo betting frequency for top-of-range hands (AA, KK, sets) on various boards — expect non-zero check frequency on some boards (especially 20bb or when blocker structure creates exception).

---

• LIT-8 (Protection): "AA on 8h6d4h: Betting 75% pot loses approximately 7% of the pot in expectation vs checking" [PRT-1]; "GTO strategy captures 2.77bb on 8h6d4h; protection-focused strategy captures 2.7bb" [PRT-4]; "Checking entire range on 8h6d4h captures 2.75bb — much closer to GTO than protection strategy" [PRT-5]; PRT-8 the two-condition rule; PRT-10 upsizing isolates against stronger range; PRT-14 "Primary goal of value betting is extracting calls from near-dead equity, not pricing in draws"
• CORR (B1 frequency layer PASS): structural support for frequency-layer claims
• MODEL-BATCH: cash/data/batches_cash_protection/R_cash_g8_protection.json — AA cbet on 8h6d4h=0.3% vs 8h6d2c=84.0% (Δ=−83.7pp). Full overpair hierarchy on wet board: AA=0.3%, KK=27.8%, QQ=51.3%, JJ=93.9%, TT=99.5% — inverted rank ordering. CONFIRMED 2026-04-14.

C-HIGH (LIT-8 [PRT-1/PRT-4/PRT-8] + CORR [B1 frequency PASS] + MODEL-BATCH [protection freq batch, Δ=−83.7pp] = 3 sources across 3 source families. Upgraded from C-MED 2026-04-14. EV-magnitude sub-claims [7% of pot, 2.77bb vs 2.7bb] remain blocked by KI-1/KI-4.)

LIT CORR [MODEL-BATCH] EV-QUALIFIED-KI-1 EV-QUALIFIED-KI-4 for EV-magnitude sub-claims Batch ref: cash/data/batches_cash_protection/g8-analysis.md (2026-04-14) Inverted hierarchy finding (new): On 8h6d4h, the GTO rank ordering of cbet frequency is: TT (99.5%) > JJ (93.9%) > QQ (51.3%) > KK (27.8%) > AA (0.3%). Stronger overpairs check MORE, not less. Mechanism: AA/KK face near-zero overcard risk on 8h6d4h — their equity lead is so wide that flush draws are the dominant threat, and AA needs to allow those draws to continue (they lose to AA regardless). TT/JJ are genuinely threatened by overcards (Q, K, A falling on the turn) — they need to make those draws pay or fold. The two-condition rule (PRT-8) explains: protection is warranted only where the bet folds out hands with genuine live equity against the bettor's specific holding. Verdict: CONFIRMED (frequency layer: AA cbet Δ=−83.7pp wet vs drier; inverted hierarchy confirmed. EV-magnitude pending KI-1/KI-4 resolution.) ---

• LIT-53 (C-Betting OOP in 3-Bet Pots): O3B-7 "Near-zero checking range at low SPR (40bb) on most non-connected textures"; O3B-10 "At 100bb, checking frequency rises sharply even with equity advantage"
• Model (batch test cash/data/batches_cash_h8_oop_3bp_40bb/R_cash_h8_oop_3bp_40bb.json): 7 boards × 2 depths (40bb vs 100bb), avg delta +37.7pp on low-card boards (654r, 543r, 765r). BATCH-CONFIRMED 2026-04-14. Exceptions: T98 delta = −5.1pp (range miss dominates SPR effect); K72r inverts direction (more betting at 100bb, not less).

C-HIGH (LIT-53 O3B-7/O3B-10 = GTO Wizard article; model batch confirmation at frequency layer = passes B1 framework for policy claims; books LIT-53 original source is GTO Wizard; plus batch direct verification). One model, 14 data points, +37.7pp average delta on 5 non-exception boards.

LIT MODEL CORR

BB check% on 654r at 40bb vs 100bb (BTN opens 2.5bb, BB 3-bets to 7.5bb/9bb, BTN calls → BB first to act on flop). Threshold: check@40bb < 20% AND check@100bb > 35% AND delta > 20pp.

• LIT-56 (Overcalling from the BB): OVL-7 "Disconnected offsuit hands (A8o, Q7o, K4o) leave BB calling range when overcalling; lack of straight/flush potential is the driver"; OVL-9 "74o calls but Q7o and K4o fold — connectivity and draw potential required, not raw card strength"; OVL-10 "In 3-way overcall scenario, every BB call has two-card straight or flush potential; A9o exception" [A9o exception is CONTRADICTED by model data]
• Model (batch test cash/data/batches_cash_h9_bb_overcall/R_cash_h9_bb_overcall.json): 2 scenarios (UTG raises + BTN calls; CO raises + BTN calls). 7/7 tested disconnected offsuit hands fold 100%. Suited connectors 54s/65s/76s call 99–100% in both scenarios. Delta suited-connector vs disconnected: +74.6pp (UTG) / +90.7pp (CO). BATCH-CONFIRMED 2026-04-14.

C-HIGH (LIT-56 OVL-7/OVL-9 + model batch confirmation; 2 scenarios; delta >> 30pp threshold).

LIT MODEL CORR — A9o sub-claim: LIT [CONTRADICTED by MODEL]

BB call% on 54s vs K4o facing UTG+BTN-call, 100bb. Expect 54s ≥ 90%, K4o ≤ 5%.

• LIT-53 (C-Betting OOP in 3-Bet Pots): O3B-7 "Near-zero checking range on non-connected textures at low SPR" — establishes 3BP cbet is board-texture extreme; IP 3-bettor follows symmetric pattern
• LIT-3 (Delayed C-Betting): DCB-6 "favorable flop for the raiser" — in 3BP, raiser's range advantage on high-card textures is more absolute (tighter range = more board-specific concentration)
• Model batch (Scenario B): cash/data/batches_cash_3bet_pot/R_cash_3bet_pot.json BTN 3-bet vs CO cold-call, 6 boards 2026-04-12. BATCH-CONFIRMED.
• Model batch (Scenario C): cash/data/batches_cash_3bet_pot/R_cash_h10_3bp_ext.json BTN 3-bet vs UTG cold-call (tighter range), 6 boards 2026-04-14. High-board poles identical; connected boards 20-37% (bimodal LOW pole confirmed, magnitude-higher due to UTG range being capped). BATCH-CONFIRMED.

C-HIGH (upgraded from C-MED 2026-04-14: 2 position pairs tested — BTN vs CO and BTN vs UTG cold-call — bimodality confirmed in both. High-card poles invariant; connected-board poles vary by opponent range tightness. 2 LIT sources [LIT-53 + LIT-3] + 2 MODEL-BATCH runs = 4 sources across 2 source families. Original upgrade blocker was 1-position-pair scope; resolved by Scenario C.)

LIT [MODEL-BATCH] Key data: Scenario B (BTN 3-bets, CO cold-calls): | Board | BTN cbet% | CO SRP cbet% (ref) | 3BP−SRP gap | Note | |-------|----------|--------------------|-------------|------| | K72r | 100.0 | 83.6 | +16.4 | High-dry — full merge | | KK5 | 99.9 | 79.3 | +20.6 | Paired high — full merge | | A94r | 74.3 | 64.9 | +9.4 | A-high — strong merge | | K94ss | 85.8 | 32.2 | +53.6 | Monotone: blocker effect inverts suppression | | T98 | 7.5 | 59.6 | −52.1 | Connected — range miss, near-zero | | 654 | 13.2 | 56.4 | −43.2 | Low-connected — range miss, near-zero | Scenario C (BTN 3-bets, UTG cold-calls — 2026-04-14): | Board | BTN cbet% | vs Scenario B | Note | |-------|-----------|---------------|------| | K72r | 100.0 | 0.0pp | High pole invariant | | KK5 | 99.9 | 0.0pp | High pole invariant | | A94r | 73.3 | −1.0pp | Essentially identical | | K94ss | 81.1 | −4.7pp | Blocker effect persists | | T98 | 20.0 | +12.5pp | Connected LOW pole — higher (UTG range capped) | | 654 | 36.5 | +23.3pp | Low-connected LOW pole — higher (same reason) | Bimodal gap: Scenario B K72r(100) vs T98(7.5) = 92.5pp; Scenario C K72r(100) vs 654(36.5) = 63.5pp. Both dramatically exceed SRP gap (24pp).

BTN 3BP cbet on K72r vs T98 — threshold K72r ≥ 95%, T98 < 30%. Observed: Sc-B 100%/7.5%; Sc-C 100%/20.0%. Both exceed threshold.

Batch refs:

• cash/data/batches_cash_3bet_pot/R_cash_3bet_pot.json (2026-04-12) Scenario B
• cash/data/batches_cash_3bet_pot/R_cash_h10_3bp_ext.json (2026-04-14) Scenario C