Blood Battle

Part 1 — What is Blood Battle

What this book covers

This book is a strategy manual for Blood Battle — one of four variants in the Squid family of NLHE-with-tokens poker games. Blood Battle is the variant trained on the QuintAce model under the codename SquidType::BLOOD_BATTLE. This primer establishes the ruleset; the rest of the book is what the trained model has learned about playing it.

Where Blood Battle sits in the Squid family

Four variants share the Squid backbone: every main pot winner collects a "squid" token, and at game end, players without squids pay a chip penalty. The variants differ in how a squid count translates into chip payout:

In the canonical Squid-family pedagogical order — Stand-up → Hunt Regular → Hunt Progressive → Blood Battle — this book is the most strategically rich variant. Each step adds one new structural axis on top of the previous: binary → linear accumulation → tiered cliffs → smooth quadratic ramp. For a deeper comparison of all four shapes and the engineering path to the missing one, see the Squid Family Variants Primer.

The Blood Battle ruleset

Blood Battle is 6-max NLHE with two rules layered on.

Rule 1 — Squids accumulate. Every time you win a main pot, you collect a squid (a win token). There's no per-player cap. A player who wins five pots holds five squids.

Rule 2 — Squids translate to chips through a quadratic multiplier curve at game end. The weight function is weight(s) = min(5, s) × s. Up through your fifth squid, weight grows quadratically — each new squid is worth more than the last. After the fifth, weight grows linearly with slope 5 — every additional squid is a flat +5.

The 4→5 jump is +9 weight units — the biggest single jump in the table. The intuition this curve invites is "race to five — the next squid is always more valuable until you cap out at five." The math is correct. But the strategy doesn't follow the math the way you'd expect — players actually play tighter as they approach the s = 5 peak, not wider. The chapters in this book will show why — preview: the shrinking downside as you accumulate matters more than the growing upside.

What's the same as Stand-up Game

The basic frame carries over. You're playing 6-max NLHE with 100bb stacks, standard blinds, all the usual positions. Squids are awarded only to the main pot winner — split pots and side pots award no squid. The val parameter scales how much each squid is worth in chips, trained on five settings: 1, 2, 3, 5, and 10 bb. The reward formula is still chip-EV plus the change in your forward-looking squid value, zero-sum at settlement.

If you've read Stand-up Book 2, the rule frame is familiar. The strategy is not.

What's different from Stand-up — three rule changes

1. No per-player cap. Stand-up caps you at 1 squid. Blood Battle lets squids stack. A player who wins five pots has five squids.
2. More squids in the pool. Total squids handed out per game is N + 4 — that's 10 in 6-max (Stand-up has N − 1 = 5). The pool is bigger to allow accumulation.
3. A quadratic multiplier on the squid count. Stand-up's weight is binary (0 or 1). Blood Battle's weight is min(5, s) × s — the curve in the table above.

How games end

The game ends at Z = 1 — the moment only one player has zero squids. That player pays the penalty to all the holders, and the game stops. By the time Z = 1 fires, no further play happens.

This means you'll always be playing in a state where at least two players still have zero squids (Z ≥ 2). The strategic question is how many — and where in the gradient from "everyone still desperate" (Z = 6, fresh state) to "only two left" (Z = 2, the cliff before the game ends) the table currently sits.

The trained model reflects this: it has only learned to play states with Z ≥ 2. It was never trained on Z = 1 (the terminal state) or Z = 0 (which never arises, because the game ends before it can). When this book talks about strategy at "the start of the game" or "near the end," it means the gradient from Z = 6 down to Z = 2.

What's at stake — the payout math

At settlement, each holder receives val × weight(s) × Z (Z = the number of zero-squid players, which by construction is exactly 1 at game-end since Z = 1 is the trigger). Each loser pays val × sum_of_holder_weights.

Worked example, val = 3. Game ends at Z = 1 with one player at 5 squids, four players at 1 squid each, one player at 0 (the lone loser).

• Sum of holder weights: 25 + 1 + 1 + 1 + 1 = 29
• Loser pays: 3 × 29 = 87 bb
• Holder at 5 squids gets: 3 × 25 × 1 = 75 bb
• Each holder at 1 squid gets: 3 × 1 × 1 = 3 bb (12 bb total to the four)
• Sums to zero: 75 + 12 − 87 = 0 ✓

Compare to Stand-up at val = 3: the loser pays a fixed 5 × 3 = 15 bb. Blood Battle's loser in the same setup pays 87 bb — nearly 6× more. The big payout comes from the one player who concentrated 5 squids. Concentration creates outsized stakes.

Two strategic axes

Strategy in Blood Battle depends on two axes — both well-tested across the in-distribution Z = 2 to Z = 6 range.

Axis 1 — The co-desperate count (Z). How many players still have zero squids? Z = 6 means everyone (fresh state at the start of a game). Z = 2 means only two — the game is one squid from ending. As Z decreases (the table moves from fresh state toward game-end), strategy shifts gradually: hero plays modestly wider and more limp-heavy, opponents tighten in some ways and widen in others. The shifts are continuous, not stepped — the model treats the gradient smoothly across Z = 2 through Z = 6.

Axis 2 — Hero's own squid count (three regimes). Where hero sits on the multiplier curve creates three play styles:

• Desperate (s = 0). Hero has no squid. The lone-loser threat is real. Strategy: take any pot. Maximum participation, even at terrible chip-EV, because the downside of being the lone loser dominates the chip math.
• Accumulating (s = 1 to 4). Hero has at least one squid — safe from being the lone loser. But the multiplier curve still rewards stacking more. Strategy: tighter than desperate, still aggressive on positive-chip-EV spots. The forward-looking jackpot at s = 5 is real but moderated by the fact that hero is no longer fighting for survival.
• Past-peak (s ≥ 5). Hero has captured the multiplier peak. Each additional squid is worth a flat +5 — a moderate fixed bonus per future pot won. Strategy: most selective. Hero plays close to chip-EV-only with a small accumulation bonus.

The two axes interact: a desperate (s = 0) hero plays differently when six players are still desperate (fresh state) versus when only two are (one squid from game-end). The chapters of this book walk through the interaction across spots — preflop opens, BB defense, flop c-bet, etc.

Terminology for Blood Battle

Language to avoid:

• "Hero-has" without a count — ambiguous in Blood Battle.
• "Once safe, done" — wrong in Blood Battle; the multiplier curve still pulls players to accumulate after safe.
• Treating Blood Battle as "Stand-up but bigger numbers" — the marginal structure is qualitatively different.

Two known implementation gaps

The AceSense product spec defines two extras for Blood Battle that the trained model does not know about. Any solver-backed work has to scope around them.

• Super Squid — a randomly selected pot during the game gives a 2× squid (counts as 2 instead of 1). Declared in code, not implemented in training.
• First-hand double squid — the winner of the first hand of every game gets 2 squids immediately (split pots void). Declared, not implemented.

Future research needs the engineering team to extend training to close these gaps. Both are tracked as open ENG items.

What this primer does NOT cover

• Strategic findings — those are the rest of the book. This primer just establishes the rules and frames.
• Squid Hunt Regular — sibling Squid-family variant with linear weight = s. Not yet trained on the model. Engineering ticket pending. Will get its own book once trained.
• Squid Hunt Progressive — the tiered/cliff variant of the Squid family (1× / 2× / 4× multipliers at s = 3 and s = 5). Currently labeled SquidType::DOUBLE in code, trained, but a separate scope and a separate book.
• Super Squid + first-hand double squid behavior — not implemented in training.
• Z = 0 or Z = 1 strategic states — out of scope. Z = 1 is the game's terminal state; Z = 0 never arises during play. The training sampler enforces Z ≥ 2 by construction.

Where the rules come from

The rules and multiplier table trace to the engineering team's ground-truth reference at engineering-department/gameplay-ai/projects/llm-verifier-game-expansion/squid-blood-battle/GAME-RULES.md. The folder name and the code identifier SquidType::BLOOD_BATTLE use the variant's literal name — Blood Battle is the canonical product name we use throughout this book. Rules cross-checked against the AceSense product spec §II ("Bloody Mode"). Core mechanics match; two product features (Super Squid, first-hand double squid) are spec'd in product but not yet trained.

The strategic findings in the rest of this book are the model's learned response to these rules, queried only at in-distribution states (Z ≥ 2) per meta_seed_sampler.h:628.

Draft · Blood Battle Part 1 primer · revised 2026-05-01 (renamed from "Squid Hunt Progressive")

Part 2 — The co-desperate gradient: how strategy shifts as the game approaches its end

The single biggest read in Blood Battle

The game ends when only one player remains without a squid. That moment is fixed — Z=1 is the game-end trigger. Everything before that moment, though, exists on a gradient. Z, the number of players currently at zero squids, runs from 6 (fresh state, nobody has won yet) down to 2 (one squid from the game ending). As Z decreases, the table is moving toward its end-state, and the model's strategy shifts.

The shift is gentle, not dramatic. About a 10-percentage-point swing in opening frequency between Z=5 and Z=2 at val=3 — meaningful, but not a regime cliff. Reading where the table sits on this gradient is the single biggest read in Blood Battle — but the read is "how far along is the game," not "is the squid game on or off."

What the gradient looks like — preflop opens

CO opens at val=3, with hero at s=3 (mid-accumulation), as Z decreases:

VPIP rises ~10 percentage points (76% → 86%) from Z=5 to Z=2. Limp rises ~15 points (48% → 63%). The raise rate stays roughly stable in the 24–32% band. The closer the game is to ending, the more pots hero plays, and the more cheaply hero plays them — limp-heavy participation as the squid stakes per pot get more concentrated and the game-end becomes imminent.

What the gradient looks like — BB defense

BB defense vs CO open at val=3, hero (BB) at s=3:

BB defends 100% across every Z value — folding doesn't return at any point. The shift is internal: as Z decreases, call rate climbs ~16 points (28.7% → 45.1%) and raise rate falls a similar amount. BB flats more as the game gets closer to ending, and the reason is structural: when fewer co-desperates remain, the desperate opp's chance of winning the next pot is more concentrated, so BB doesn't want to bloat the pot with a 3-bet that prices opponents out — better to flat, see the flop, and let chip-EV decide.

Note: this is a smaller effect than headline framings might suggest. A 16pp call rate shift across the gradient is real but doesn't constitute a "BB defense regime change."

Postflop: frequency saturates, sizing barely moves

CO c-betting on a dry A-high (Ah9c4d) at val=3, hero=s=3:

C-bet frequency is essentially constant. Sizing varies by 0.6bb — basically noise. On dry boards, the co-desperate gradient does not significantly affect c-bet frequency or sizing. The pressure that distinguishes Z=2 from Z=5 expresses preflop in opening shape and BB defense mix; postflop on dry textures, the model has converged.

On a wet board (Ts9h8h), the picture is similar: c-bet ranges from 78.6% (Z=2) to 82.0% (Z=5), sizing 13.38–13.59bb. Modest gradient on frequency, near-flat on sizing.

This is an important calibration: postflop in Blood Battle looks much closer to NLHE than the preflop expansion suggests. The squid mechanic affects entry, not the size of the bet you make once you've decided to play.

What the gradient does NOT look like

Earlier framings of this book (and earlier Phase 2 pulls) compared four_at_1 (one opp left desperate, Z=1) to all_at_1 (no opps desperate, Z=0) and found a 62-percentage-point VPIP collapse. Both of those states are out-of-distribution. The training sampler at meta_seed_sampler.h:628 enforces Z ≥ 2 by construction — Z=1 is the terminal state where the game ends, and Z=0 never arises. Querying the model at Z=1 or Z=0 returns OOD output, not learned strategy.

So the dramatic "two regimes" claim from earlier framings is invalidated. The real gradient — the one the model is trained on — is the smooth Z=5 → Z=2 shift documented above. About 10pp of VPIP gradient, 16pp of call/raise mix shift, near-zero sizing variation. Real, but a gradient, not a cliff.

How val interacts with the gradient

The val parameter scales the squid pressure. At val=3, the gradient is roughly ~10pp VPIP across Z=5→Z=2. At val=1 (small squid bonus per pot), the gradient is similar in shape but smaller in magnitude. At val=10 (huge squid bonus), the gradient is reversed and dampened — at high val, hero plays close to NLHE-shaped strategy across all Z values because chip stakes per pot dominate the squid bonus until stack depth exceeds 200bb (see Part 8).

For practical reads at val=3 (the canonical anchor), the Z=5→Z=2 gradient is the right rule of thumb. At val=10, Z matters less.

What this means for the rest of the book

The chapters that follow each pick up one of the spots where the gradient shows up:

• Part 3 — Preflop Opens — per-position widening + how the Z gradient interacts with hero count
• Part 4 — BB Defense — the call-vs-raise mix as the dominant lever, and how Z shifts it
• Part 5 — Flop C-Bet — why postflop on dry boards barely moves with Z
• Part 6 — Per-Squid-Count Strategy — the orthogonal axis: hero's own count produces three play regimes
• Part 7 — Stack Depth, Val Asymmetry, and Limits — when the Z gradient amplifies (deep stacks, low val) and when it dampens (val=10 chip-dominated)
• Part 8 — Open Questions and Actionables — what the framework doesn't cover, and the practical reads to walk away with

If you remember nothing else from this chapter: the closer the game is to its end, the more hero plays — modestly wider, modestly more limp-heavy. Reading where Z sits is your first table read. But it's a gentle gradient, not a switch.

Draft · Blood Battle Part 2 (revised) · 2026-04-28 · renamed 2026-05-01

Part 3 — Preflop Opens

Every position widens

The first place Blood Battle bites is the open frequency. Every position opens substantially wider than the same position in NLHE — and wider than in Stand-up Game too. Here's what fresh-state opens look like at val=3, with each position's VPIP shown for NLHE Cash, Stand-up Game, and Blood Battle:

Blood Battle widens every seat by 42 to 56 percentage points relative to NLHE. The absolute VPIPs are striking — UTG plays 66% of hands, MP plays 75%, BTN plays 95%. Compared to Stand-up Game, Blood Battle widens roughly another 30 percentage points across positions; the no-cap accumulation plus the multiplier curve make every starting hand more valuable than its Stand-up equivalent.

The position gradient is preserved. UTG is still the tightest seat; BTN the widest. But the absolute frequencies are pulled upward by the squid bonus on every pot, regardless of where you're sitting.

The val=3 peak

Naïvely, you'd expect Blood Battle opens to widen monotonically with val: bigger penalty per game-end → wider opens → more pots played to chase squids. The data says otherwise.

Watch UTG across the val ladder:

UTG VPIP peaks at val=3 and then narrows at val=5 and val=10. The same shape shows up at MP, CO, BTN — every position peaks at val=3 (or close to it) and gets tighter at higher val.

Why? At val=10 the squid bonus is huge, but each individual pot is also more valuable individually. The model becomes more selective per pot — picking spots where chips actually accumulate, not just spots where it can enter cheaply. At val=3, the bonus is large enough to widen ranges substantially, but small enough that any pot is worth playing. Val=3 sits in a sweet spot for "play almost everything."

Practical: when you sit down at a Blood Battle table, val matters in shape, not just magnitude. Val=3 is the canonical anchor — most aggressive widening. Val=10 narrows back partway, even though the chip stakes are bigger.

The shape inversion as hero accumulates

Across the same chair, the same position, hero plays differently depending on hero's own squid count. At CO val=3 with all opponents fresh:

VPIP narrows by 12 percentage points (84.5% → 72.7%) as hero accumulates from 0 to 5 squids. But the bigger story is the shape inversion: at s=0, hero limps 77.6% and raises 6.9%. At s=5, hero limps 33.5% and raises 39.2%. The limp share of VPIP collapses from 92% to 46%. Limp-heavy when desperate; raise-heavy when accumulated.

Why? Two forces, going opposite directions:

When hero has zero squids, the lone-loser threat is real. Hero needs to win at least one pot before the game ends. Limp is the cheapest way to be in a pot — minimum chip commitment, maximum participation. So hero plays almost everything, but cheaply.

When hero is at five squids — past the multiplier peak — hero is guaranteed safe and has captured the major reward. The next squid is worth a flat +5 (much less than the +9 jackpot at the s=4→5 transition). Hero plays fewer hands, but commits more when playing them, because there's no urgency to enter every pot.

The sweet spot in the middle (s=3, s=4) is where the multiplier is still pulling — the next squid is worth +7 or +9 weight units. Hero plays narrower than desperate, more aggressive than past-peak, with a balanced limp/raise mix.

The same shape shows up at UTG and BTN with smaller magnitude. BTN at val=3 hero-count s=0 limps 85.1% raise 10.2%; at s=5 limps 35.6% raise 48.9%. UTG at val=3 hero-count s=0 limps 63.4% raise 3.0%; at s=5 limps 29.9% raise 31.0%. Position scales the magnitude; the inversion shape is universal.

"Race to 5" is the wrong intuition

The math says the next squid is worth more as you approach s=5. Marginal weight goes +1, +3, +5, +7, +9 across s=1 through s=5. So you'd expect the most aggressive play right before the peak — at s=4, racing toward the +9 jackpot.

The data says no. At s=4 hero plays 73.6% VPIP — tighter than s=0's 84.5%. At s=4 hero limps 38.5% — much less than s=0's 77.6%. The model is not pushing harder as it approaches the peak. It's playing more selectively.

The reason is structural. The forward-looking multiplier curve creates an upside, but the lone-loser threat creates a downside. At s=0, the downside is enormous — hero is at risk of paying the full penalty. As hero accumulates, the downside shrinks — at s=1 hero is safe, at s=5 hero has captured the peak reward. The shrinking downside drops faster than the growing upside rises.

So strategy doesn't follow the multiplier curve directly. It follows the net of "what happens if I play this pot" minus "what happens if I don't" — and the lone-loser fear weighs heavier than the jackpot draw, throughout the gradient.

The co-desperate gradient

The other axis: how many opponents are still desperate. As Z (the count of zero-squid players) decreases, the table is moving closer to its end-state. Phase 2.5 measured the gradient at hero=s=3 CO val=3:

VPIP rises ~10 percentage points as Z falls from 5 to 2. Limp rises ~15 points. The gradient is consistent: closer to the game's end-state → more participation → more limp-heavy.

This is a much smaller gradient than earlier framings suggested — about a 10pp swing across the in-distribution range, not a 60pp cliff. There's no binary "regime shift." Strategy slides smoothly across the gradient as Z decreases.

When Z is high (game is far from ending), hero plays the chip-EV-shaped game with squid bonus added. When Z is low (game is close to ending), hero participates more — every pot is one of the last chances to be in the game. The shift is real, but a coach teaching this shouldn't sell it as a binary read.

Hero-count × Z interaction

The two axes (hero count, Z) compound when hero is desperate. Phase 2.5 measured the gradient at hero=s=0, varying co-desperates:

When hero is desperate, the fewer co-desperates exist, the more hero plays. Z=2 (one other desperate) reaches 94.3% VPIP. The reason is intuitive: when many players share the desperation, the lone-loser fate is diluted across them, and any one player has a smaller share of the threat. When few share, hero is closer to "the one who will lose" — so hero scrambles harder.

Combine with the safe-hero gradient: at hero=s=3 the gradient is ~10pp (76% → 86%); at hero=s=0 it's ~10pp (84% → 94%). Both axes are real but modest. The big picture: the closer the game gets to ending AND the fewer co-desperates hero has, the wider hero plays.

Practical reads at the table

The reads stack:

1. Count zeros. That's Z. Tells you where on the gradient the table sits.
2. Read your own count. That's the hero-count regime — desperate, accumulating, or past-peak.
3. Pick the corner of the table. Hero count × Z gives you four regions: (desperate × high Z), (desperate × low Z), (safe × high Z), (safe × low Z). Each plays slightly differently — gradient, not switch.
4. Account for val. Val=3 is the canonical sweet spot. Val=1 dampens everything. Val=10 narrows back from peak (you become more selective).
5. Don't overweight position. Position still matters — UTG is tighter than BTN — but the squid bonus pulls every position so far above NLHE baseline that the position gradient matters less than NLHE habits suggest.

The single biggest preflop adjustment from NLHE: stop folding marginal hands. Squid pressure makes almost every hand worth playing in some form. If a hand was a marginal call in NLHE, it's a comfortable limp in Blood Battle. If it was a fold in NLHE, it's a marginal limp.

If you remember nothing else from this chapter: at val=3, every seat's open range expands by 40-50 percentage points vs NLHE. Limp returns. Fold becomes rare. The exact widening varies with hero count and Z, but the directional shift is universal.

Draft · Blood Battle Part 3 · 2026-04-28 · renamed 2026-05-01

Parts 3–8 — Content Outlines (revised post Phase 2.5)

These outlines reflect the in-distribution mechanism catalog (6 mechanisms, down from 9). The dropped chapters — Hero-Last (was Part 7) and the binary Two-Regimes thesis — rested on OOD model output (Z=1 hero alone; Z=0 all safe). The book is now 8 parts instead of 9.

The two unifying threads:

• The co-desperate gradient (Part 2 thesis). Z=2 to Z=6 produces a gentle 10-pp VPIP swing — real, gradual, not a cliff.
• The hero-count regimes (orthogonal axis). Desperate / accumulating / past-peak. Driven by shrinking-downside, not "race to 5."

Revised structure

(The old "Part 7 — Hero-Last and Lone-Desperate" chapter has been dropped. Its data anchors were all Z=1 OOD. The strategic concept — what hero does when alone-desperate — isn't a state the model is trained for.)

Part 3 — Preflop Opens

Mechanisms: M1 (per-position widening), M2 (hero-count regime), M3 (co-desperate gradient), M4 (val pressure) Length target: ~1,800 words Theory lens: classical NLHE opening tree (chip-EV per position) + squid-bonus overlay. The chapter walks how the squid bonus widens every position vs the NLHE baseline, then how the widening varies with hero count and Z.

Key data anchors: - Pull 1 — per-position × val (NLHE / Stand-up / BB baselines, 5 positions × 4 val tiers) — in-dist - Pull 2 + 3a — per-hero-squid-count at fresh state CO/UTG/BTN — in-dist - Phase 2.5 Axis A — Z gradient at hero=s=3, CO val=3 — in-dist - Phase 2.5 Axis B — Z × val ladder — in-dist

Sections:

• 3.1 The widening — Blood Battle vs NLHE. Per-position table at fresh state val=3 (UTG +27 to BTN +56pp wider). Single biggest preflop effect: every position widens substantially.
• 3.2 The val=3 peak. Counter-intuitive: VPIP doesn't grow monotonically with val at fresh state. UTG: 44.9% (v=1) → 66.4% (v=3) → 55.9% (v=5) → 60.7% (v=10). Hypothesis: at high val, the model becomes more selective per pot because each individual pot is more valuable.
• 3.3 The shape inversion: limp-heavy when desperate, raise-heavy when accumulated. Pull 2 (CO at val=3, opps fresh): s=0 limp 77.6% raise 6.9% → s=5 limp 33.5% raise 39.2%. The 91.8% → 46.0% limp-share inversion. Explained via shrinking-downside: you participate cheaply when you NEED a pot; you commit selectively when you don't.
• 3.4 The co-desperate gradient on opens. Phase 2.5 Axis A: as Z decreases (game closer to end), VPIP rises ~10pp and limp climbs ~15pp. Modest gradient. Read where the table sits, but don't expect dramatic regime shifts.
• 3.5 Hero-count × Z interaction. Phase 2.5 Axis H (hero=s=0, vary co-desperates): the desperate-hero gradient. As fewer opps share the desperation, hero plays wider — Z=2 VPIP 94.3%, Z=6 VPIP 84.5%. Co-desperates dilute the lone-loser threat for any one of them.
• 3.6 Practical reads for the seat. A short rule list: count zeros first, identify your own count, then play the regime + gradient.

Theory-vs-data combination point: Part 3 is where the chip-EV opening tree gets two new dimensions stacked on it — hero count and Z. Both are gentler than the OOD comparisons earlier suggested. The chapter walks the math of why.

Part 4 — Preflop Defense (BB)

Mechanisms: M2, M3, M4 Length target: ~1,400 words Theory lens: NLHE BB defense is governed by pot odds + realization equity (MDF). Blood Battle saturates defense at 100% — fold-rate is essentially zero across in-distribution states. The interesting axis is call vs 3-bet, not defend vs fold.

Key data anchors: - Pull 6 sweep A — per-BB-squid-count at fresh-state opps — in-dist - Phase 2.5 Axis CD — BB defense × Z × val — in-dist

Sections:

• 4.1 BB folds 0% across all in-distribution states. Across hero squid count {0..5} at val=3 with Z=5: fold rate 0.0%. Across val=1/3/5/10 with Z=2/3/5 hero=s=3: fold rate 0.0% (with one tiny exception at val=1 Z=2 of 0.2%). MDF essentially vanishes — BB always defends.
• 4.2 The call-vs-raise inversion as hero accumulates. Sweep A: at s=0, raise 85.1% / call 14.9%. At s=5, raise 67.6% / call 32.4%. Symmetric inverse of opens (which shifted limp→raise). At opens, accumulation reduces commitment; at defense, accumulation reduces aggression.
• 4.3 The Z gradient on defense. Phase 2.5 Axis CD at val=3 hero=s=3: as Z decreases, call rate rises ~16pp (28.7% → 45.1%), raise rate drops by similar. BB flats more as the game gets closer to its end — bloat-the-pot logic reverses when the desperate opp benefits from multiway pots.
• 4.4 Val asymmetry: BB peaks at val=1. CD data: at val=1 Z=2, BB calls 81.3%; at val=3 Z=2, 45.1%; at val=5/10 Z=2, ~47%. Why does defense peak at low val? Hypothesis: BB has 1bb already committed (smaller chip-baseline); even small squid pressure tips toward minimum-commitment defense.
• 4.5 Hero-count × Z interaction. Combine sweep A and Axis CD: the four-way table of (hero count × Z) defense behavior. Practical: figure out which corner you're in.
• 4.6 Practical: 3-bet vs flat decision tree. Rule list. Default to flat in low-Z states. 3-bet in high-Z states with high-equity hands. The fold range is essentially empty.

Theory-vs-data combination point: MDF as a frame breaks down. The pot-size management decision (call vs 3-bet) replaces it as the strategic axis. The chapter argues this directly: in Blood Battle, BB defense isn't a fold-or-defend question; it's a flat-or-3bet question.

Part 5 — Flop C-Bet — Frequency and Sizing

Mechanisms: M3, M6 Length target: ~1,400 words (was 1,800; the chapter is shorter without the OOD sizing claims) Theory lens: classical c-bet theory — frequency tracks range advantage, sizing tracks nut advantage. Blood Battle: in-distribution states show postflop has converged. Both axes are largely insensitive to the Z gradient.

Key data anchors: - Phase 2.5 Axis E — c-bet on dry A94r × Z gradient — in-dist - Phase 2.5 Axis F — c-bet on wet T98ss × Z gradient — in-dist

Sections:

• 5.1 Postflop has converged. On dry A94r at val=3 hero=s=3: c-bet 97.9–98.6% across Z=2 to Z=5; sizing 11.56–12.14bb. On wet T98ss: c-bet 78.6–82.0%; sizing 13.38–13.59bb. Both axes barely move. The major postflop variation captured in the OOD comparisons earlier was an artifact.
• 5.2 The squid pressure expresses preflop, not postflop. A short structural argument: by the time the flop is dealt, the range is fixed; the chip cost of the c-bet decision is governed by chip-EV math (range advantage, board structure). The squid bonus per pot won is now baked in to all the hand classes that reached the flop. So sizing on dry boards converges to the chip-EV optimum.
• 5.3 Why dry boards saturate at ~98%. Range advantage on dry A-high in 3bp (CO opener with 3-bettor BB — wait, this is the SRP version). Actually for SRP CO-vs-BB on A94r, CO has the wider opening range so BB's check generally yields a wide CO c-bet. The squid pressure compounds — even cheaper c-bets are attractive — but the frequency saturates at near-maximum either way.
• 5.4 Wet boards — frequency varies more. On T98ss, c-bet drops to 78–82% (vs 98% dry). The lower frequency reflects ranges that don't dominate as cleanly. The Z gradient effect is small even here — ~3pp swing.
• 5.5 Sizing — two findings (one positive, one null). Positive: sizing is much larger than NLHE. The 11–13bb avg bets are overbets relative to pot — driven by squid bonus in the chip-equivalent. Null: sizing barely moves with Z within the in-distribution range. The "bet bigger when desperates abound" thesis from earlier framings was the OOD artifact — in-distribution, hero just bets big regardless.
• 5.6 Practical: read the regime, not the postflop board. The chapter inverts conventional wisdom slightly: postflop in Blood Battle is closer to NLHE than the preflop expansion suggests. The c-bet decision tree is dominated by board structure, not table state.

Theory-vs-data combination point: This chapter acknowledges what doesn't change as much as we initially thought. It's a careful chapter — needs the corrections from Phase 2.5 to be honest.

Part 6 — Per-Squid-Count Strategy

Mechanisms: M2 (consolidated) Length target: ~1,400 words Theory lens: marginal utility of next squid (forward-looking), set against the marginal cost of being the lone loser (downside). The chapter argues — counter to "race to 5" — that the SHRINKING DOWNSIDE dominates the GROWING UPSIDE. As you accumulate, you're more "safe-from-lone-loser" than "racing-toward-jackpot."

Key data anchors: - Pull 2 — per-hero-squid-count at CO val=3, opps fresh — in-dist - Pull 3a — replication at UTG and BTN — in-dist - Pull 6 sweep A — BB defense per hero count, opps fresh — in-dist

Sections:

• 6.1 Three regimes: desperate / accumulating / past-peak. Define s=0, s=1-4, s≥5. Each plays differently. The chapter walks each.
• 6.2 Desperate (s=0). Maximum participation. Limp-heavy at opens (77.6% at CO val=3), raise-heavy at defense (85.1% raise). The "I must play this hand" state. Why: lone-loser threat dominates chip-EV.
• 6.3 Accumulating (s=1-4). Tighter than desperate, more aggressive than past-peak. The value of the next squid grows (+3 → +5 → +7 → +9 weight units), but the lone-loser threat is gone. So aggression on positive-chip-EV spots; pass on truly junk-tier spots.
• 6.4 The "race to 5" hypothesis falsified. Naïve theory: as you approach s=5, marginal value peaks at +9, so play widest at s=4. Data says no: s=4 VPIP 73.6% (CO val=3, opps at 0) — TIGHTER than s=0's 84.5%. Walk why: shrinking downside dominates growing upside.
• 6.5 Past-peak (s≥5). Selective. Marginal squid value is flat +5. Hero plays close to chip-EV-only with a small fixed bonus per pot won. The "off-mode for me individually" state.
• 6.6 Practical: read your own count first, then opponent state. Two reads stacked: hero-count regime, Z value. The product gives you the right play.

Theory-vs-data combination point: Part 6 is where Blood Battle's "race to 5" naïve interpretation gets pushed back on. The quadratic multiplier exists in the math (+9 at s=5), but the model's behavior shows the dominant force is downside-shrinkage.

Part 7 — Stack Depth, Val Asymmetry, and Limits of the Framework

Mechanisms: M4, M5 Length target: ~1,500 words Theory lens: the squid game pressure is a function of two ratios — (squid_value × stack_depth) / chip_pressure. The framework's strength scales with that ratio, not with val alone.

Key data anchors: - Phase 2.5 Axis G — stack-depth at val=10, Z=2 — in-dist - Pull 4 + Phase 2.5 Axis B — val ladder for opens - Pull 7 + Phase 2.5 Axis CD — val ladder for defense

Sections:

• 7.1 The val=10 puzzle. At val=10 and 100bb stacks, the squid mechanic's grip looks loose — hero plays close to NLHE-shaped strategy. Counter-intuitive: bigger penalty should mean bigger squid game pressure, not smaller.
• 7.2 Resolution: stack depth. Phase 2.5 Axis G — at val=10 Z=2:
• 50bb: limp 20.8%, raise 65.2% (chips dominate, raise-heavy)
• 100bb: limp 23.4% (chips still dominate)
• 200bb: limp 41.6% (squid mechanic returns)
• 400bb: limp 70.5% (squid mechanic dominates)
• The val=10 reversal at 100bb is a chip-stake artifact, not a permanent feature.
• 7.3 The unifying frame. M-Z-IMMINENT strength ∝ (squid_pressure × stack_depth) / chip_pressure. When chips are larger relative to squid, chip-EV dominates. When squid pressure is larger relative to chips, squid-EV dominates.
• 7.4 Position asymmetry: val peak by chair. CO opens peak at val=3. BB defense peaks at val=1. Why? Hypothesis: BB has 1bb committed (smaller chip-baseline → smaller val needed to tip). CO has 0bb committed (needs more val to tip).
• 7.5 What the framework doesn't cover. Limits: above 400bb stacks (untested), antes/straddles, 7-max+ tables, MTT-format adjustments.
• 7.6 Practical: when to trust the prescription. Default trust at val ∈ {1,2,3,5,10} × stacks ∈ {100, 200} × 6-max × CO/BB × Z ∈ {2-6}. Outside that, the model's prescription becomes extrapolation.

Theory-vs-data combination point: Part 7 consolidates val + stacks into a unified pressure ratio. Theory: (squid × depth) / chips. Data: Phase 2.5 Axis G stack ladder + val ladders.

Part 8 — Open Questions, Scope Limits, and Actionables

Mechanisms: none — synthesis Length target: ~1,500 words Theory lens: consolidation of what the book did claim, what it didn't, and the practical implications.

Sections:

• 8.1 The 6 mechanisms, recap. M1 per-position widening. M2 hero-count regimes. M3 co-desperate gradient. M4 val pressure. M5 stack-depth amplification. M6 cross-street consistency. One sentence each.
• 8.2 The two reads that matter most. Count zeros (Z value). Read your own count (hero-tier). Everything else falls out.
• 8.3 What this book did NOT cover. Hero-last / lone-desperate states (Z=1, OOD). All-safe scenarios (Z=0, OOD). Squid Hunt Regular variant (engineering-pending, untrained). Squid Hunt Progressive variant (the cliff-tier SquidType::DOUBLE, separate scope). Antes / straddles in Blood Battle. Higher table sizes.
• 8.4 Open questions for future research rounds.
• Does the gradient hold in 8-max, 9-max?
• How do antes interact with the squid mechanic (stack baseline shifts)?
• Is the val=3 peak position-dependent across all positions?
• Does the postflop convergence hold on river?
• What's the strategy at concentrated accumulation (one player at 5+, others spread)?
• 8.5 Engineering blockers / hand-offs. ENG ticket pending: parametrize DOUBLE for Hunt Regular + custom progressive curves. Companion: Variants Primer at /blood-battle-preview/squid-family-primer.html.
• 8.6 Cheatsheet (the actionable list). Six rules: (1) count zeros to find the gradient position. (2) hero-count tiers (desperate / accumulating / past-peak). (3) limp at opens when desperate. (4) flat at defense when Z is low. (5) bet big on dry boards regardless of Z. (6) read the squid pressure × stack depth ratio at high val.

What I'd want from you on review

1. Overall structure: is the 8-part flow tight enough? Should anything else be merged or cut?
2. The dropped Hero-Last chapter: comfortable losing it entirely? It was the most dramatic chapter in the original outline; the data behind it was OOD.
3. Length: total target now ~12K words across 8 parts (vs 13–15K across 9). Right size?
4. Theory-lens balance: enough classical scaffolding (chip-EV, MDF, range/nut advantage) on the in-distribution mechanisms?

Once approved, I draft Parts 3–8 in full prose against these outlines.