Squid Classic
the first strategy manual

One rule change turns standard Hold'em on its head.

Squid Classic is 6-max No-Limit Hold'em — standard blinds, 100bb stacks, same positions, same deck. Everything you know about the game still applies. Except one thing: at the end of the game, the only player who never won a pot pays everyone else.

Here is the rule. The winner of each main pot receives a "squid" — a win token. Each player can hold at most one. In a 6-player game, there are exactly 5 squids to award. The game ends the moment 5 of 6 players each hold a squid. The remaining player — the one who never won a main pot — is the loser. They pay 5 × val big blinds, split evenly among the 5 holders (each holder receives val BB).

The val parameter controls how much the penalty is worth. The model was trained on five discrete settings: val = 1, 2, 3, 5, and 10 BB. At val = 3, the loser pays 15 BB. At val = 10, the loser pays 50 BB.

Two edge cases to know: split pots do not award a squid (no clear winner, no token), and a player who already holds a squid gains nothing from winning another pot (binary — you either have one or you don't).

That's the entire rule change.

The terminology you need

Two labels come up constantly in this book:

• Safe — a player who already holds a squid. They cannot be the game-end loser. Their risk is zero.
• Desperate — a player with no squid. They are still at risk of paying the full penalty.

These labels follow directly from the win-token rule. If you have a squid, you are safe. If you don't, you are desperate. The labels describe game-mechanical status, not emotional state — a desperate player with AA under the gun is in fine shape this hand, but they still carry forward-looking risk until they win a pot.

Why this rule reshapes everything

In standard Cash, every hand is independent. You fold 8♠7♠ on the button when the raise is too large, and nothing carries over to the next deal. The decision is pure chip-EV: what's the expected value of calling, raising, or folding given the current pot and the ranges involved?

In Squid Classic, folding has a hidden cost. Every hand you don't play is a hand you can't win — and every hand you can't win is one fewer chance to escape the penalty. This creates a second EV dimension layered on top of chip-EV: squid equity, the probability-weighted change in your risk of being the game-end loser.

Here is what that looks like in practice. You are on the button with 8♠7♠. CO opens. In Cash, this is a marginal call — sometimes correct, sometimes a fold, depending on opener tendencies and stack depth. In Squid Classic at val = 3, the chip-EV of calling might be slightly negative. But the squid-equity gain from entering the pot — a small increase in your chance of winning this hand and becoming safe — pushes the total EV positive. You call hands in Squid that you would fold in Cash, not because you are being loose, but because the math changed.

That single mechanism — squid equity turning marginally-negative chip-EV hands into overall +EV entries — cascades through every decision in the game:

• Every preflop range widens. Hands that are unprofitable to play in Cash become profitable once squid equity is added. The effect scales with val.
• Limping returns as a legitimate strategy. Limping is the minimum-chip-cost way to enter a pot and take a shot at winning a squid. For hands too weak to raise but still worth playing, limping is the equilibrium action — not a leak.
• The position gradient amplifies. Later positions already had higher chip-EV in Cash. Adding squid equity on top of an already-favorable baseline widens the gap. BTN and SB widen the most; UTG widens the least.
• Strategy becomes state-dependent. A safe player's squid-equity term drops to zero — they already have their token. A desperate player's term is positive and grows as more opponents become safe. Your range depends on your own state AND on each opponent's state.
• Some Cash theories reverse. BB overdefends rather than underdefending the minimum defense frequency (MDF — the fold rate that makes the opponent's bluffs break even). Protection betting on dry boards becomes correct where Cash said to check. Blocker logic on A-high boards flattens.
• Late streets revert toward Cash. The squid-equity term is forward-looking and settles at the pot level, not per-street. By the turn and river, the range filter from earlier streets has already done its work, and decisions return to near-Cash logic.

What "compounds" and what doesn't

A common misreading of the Squid mechanic: "every fold costs you a penalty, and the penalty compounds hand over hand." This is wrong in two ways.

First, folding does not incur a penalty. The penalty is assessed once, at game end, to the single player who never won a main pot. Folding a hand keeps your chip stack intact and your squid count unchanged. There is no per-fold cost.

Second, nothing compounds in Classic mode. Each player holds at most one squid — binary, 0 or 1. Winning a second pot after you are already safe adds nothing to your squid count and nothing to your payout. The moment you win your first main pot, your squid-equity term drops to zero and stays there. "Once safe, done" is a Classic-only property, and it is absolute.

The correct mental model: Squid Classic adds a single forward-looking term to every decision. That term is the change in your probability of being the game-end loser, weighted by the penalty size. It is largest when you have no squid and shrinks to zero the instant you get one.

A word on the label "desperate"

"Desperate" sounds dramatic. In Squid Classic, it simply means "does not yet hold a squid." At the start of a fresh game, every player is desperate — including the chip leader, the best player at the table, and the person with aces in the hole.

The label matters because desperate players behave differently from safe ones. They defend wider, fold less often, and take marginal spots that safe players skip. When you see "desperate" in this book, read it as a game-state descriptor: this player still needs to win a pot.

Where the rules come from

Every rule stated in this part traces to the ground-truth rules reference verified against both the training code and the independent product specification. The two sources match on every Classic-mode rule: total squids = N − 1, binary cap, main-pot-winner-only awarding, no squid on split pots, and the penalty formula (N − 1) × val.

The strategic findings in the rest of this book are the model's learned response to these exact rules — not to a simplified approximation, and not to a per-fold penalty that does not exist.

The preflop tree is where Squid Classic hits hardest. Every decision you make before the flop — open, call, raise, limp, fold — shifts under the penalty, and the shifts are large enough to see in a single session. This part covers the five preflop findings: range widening, limping re-emergence, the hero-safe tightening effect, full state dynamics, and how BB reads the opener's squid state.

Measurement conditions: fresh state (all players start with zero squids). Mid-game adjustments: §2.4.

2.1 — Every position plays wider, and the gap between positions grows

The headline finding is simple: every position opens wider in Squid than in Cash. The effect scales monotonically with val — the higher the game-end penalty, the wider the ranges.

Preflop VPIP by position and val. Fresh state · all players start with zero squids · val sweeps columns · 6-max · 100bb effective

Source: squid-deltas.md Table 1 lines 62–70

Two things stand out.

First, the position gradient is preserved. Cash runs UTG 17.2% → BTN 43.3% → SB 57.9%. Squid val=3 runs UTG 25.6% → BTN 67.1% → SB 99.6%. Later positions were already wider in Cash; they get even wider in Squid.

Second, the gradient itself grows. UTG adds +8.4pp from Cash to val=3. BTN adds +23.8pp. SB adds +41.7pp. The widening effect amplifies with position — later positions gain more because they already had higher baseline pot-winning edges in Cash.

SB is the extreme case: at val=3 it enters 99.6% of hands. At val=5 and above, SB plays literally every hand dealt.

Why does the gap grow?

What this means in practice: At val=3, add roughly +8pp to UTG/MP, +15pp to CO, +24pp to BTN, and treat SB as "play everything." The adjustment scales from there — higher val means wider still, lower val means closer to Cash.

2.2 — Limping comes back

In modern Cash NLHE, solvers don't limp. Limping is strictly dominated by raising or folding. In Squid, limping returns as a legitimate strategy.

Preflop limp % by position and val. Fresh state · all players start with zero squids · val sweeps columns · 6-max · 100bb effective

Source: squid-deltas.md Publisher-gap lift table (limp % × position × val), lines 315–319

At val=3, BTN limps 30.2% of the time and SB limps 98.3%. That is not a model bug. At val=10, CO limps 75.5% — three out of four entered hands are limps.

The mechanism is straightforward. In Squid, folding costs you something: you give up the chance to win this pot and collect a squid. Limping is the cheapest way to stay in the hand. For hands too weak to profitably raise — where the extra chips committed don't generate enough fold equity — limping invests the minimum and still keeps your shot at the pot alive.

SB is the most extreme limper because SB has the smallest entry cost and the worst fold equity. SB already posted half a big blind; completing costs only half a big blind more. Meanwhile, BB has the best possible pot odds to defend any raise, so SB's fold equity from raising is near-zero. The math favors limping for nearly SB's entire range.

What this means in practice: If you see a BTN limp in Squid, don't assume it's a weak player. It's the equilibrium strategy for the middle of their range. Counter by raising from BB with a wider 3-bet range to punish the limped ranges.

2.3 — When hero is safe, ranges tighten toward Cash

Here's what happens when the widening incentive disappears. A player who already holds a squid is safe from being the game-end loser. Their forward-looking squid-equity incentive drops — in Classic mode's binary system, winning another pot can't add a second squid — so their range collapses back toward Cash.

The clearest measurement: CO at val=3 with a squid and zero no-squid opponents plays 26.7% VPIP. Cash CO is 28.1%. The two are within 1.4pp.

This specific measurement is directionally supportive, not a clean experimental control — see the Research notes at the end of this part for why.

2.4 — Your strategy depends on who has a squid

The widening and tightening effects from §2.1–§2.3 aren't fixed — they depend on the table's squid distribution. Squid Classic is a state-dependent game. Before every decision, you need to know two things: Am I safe? and How many of my opponents are safe?

Here's what the data looks like from CO at val=3.

Table A — Hero is desperate (no squid)

Hero VPIP when hero does NOT hold a squid. val=3 · CO · 6-max · states vary by row

Source: squid-deltas.md lines 150–160

Table B — Hero is safe (holds a squid)

Hero VPIP when hero holds a squid. val=3 · CO · 6-max · states vary by row

Source: squid-deltas.md lines 379–384

The spread between extremes is 75.9pp — from 12.9% (hero safe, three desperate opponents) to 88.8% (hero desperate, all opponents safe). That is an enormous range for the same position at the same stack depth.

The two tables tell a consistent story. Each opponent's squid state determines whether they provide fold equity.

• Safe opponents (have a squid) can afford to fold. They have no forward-looking squid-equity reason to call. Aggression against them works — so hero widens.
• Desperate opponents (no squid) won't fold easily. They need this pot. Fold equity evaporates — so hero tightens and plays value-only.

Note on Table B: the "0 no-squid opponents" row requires hero (1 squid) plus all five opponents (5 squids) = 6 total squids, but Classic mode caps total squids at 5 (one fewer than the number of players). This state cannot occur in actual play. The measurement is still informative as a directional signal — see Research notes for the full explanation.

What this means in practice: Count the squids before every decision. Hero desperate + many safe opponents = widen aggressively (you have fold equity AND squid-equity upside). Hero safe + many desperate opponents = tighten hard (no fold equity, no squid-equity upside). The 75.9pp spread between these extremes dwarfs most preflop adjustments you'll ever make.

2.5 — BB reads the opener's state too

The state-dependence goes both ways. BB adjusts its defense based on whether the opener has a squid.

BB defense vs CO open (2.5bb), val=3. val=3 · fresh CO (no squid) vs squid-holding CO · states named in rows

Source: squid-deltas.md lines 328–331

BB correctly recognizes that a squid-holding opener has a stronger range. Why? A safe opener has no squid-equity pressure to enter marginal pots — they're already safe, so they only open with hands that are profitable on chip-EV alone. That makes their opening range tighter and stronger.

BB responds by defending less aggressively against the tighter range. The 3-bet drop (−23.9pp) is larger than the defense drop (−14.7pp) because 3-betting was the most profitable exploit against the fresh opener's wider range. Against a squid-holder's stronger range, 3-betting loses fold equity and runs into more value.

What this means in practice: From the BB, watch the opener's squid state. A fresh opener has a wider, weaker range — 3-bet them aggressively. A squid-holding opener has a stronger range closer to Cash — tighten your 3-bets and defend more passively.

The three findings at a glance

The preflop picture in Squid Classic reduces to three forces pulling in different directions:

1. Widening. Every position plays wider than Cash. The effect scales with val and amplifies with position.
2. Limping. Hands too weak to raise but too valuable to fold enter by limping. SB limps 98.3% at val=3.
3. State-dependence. Safe heroes tighten toward Cash. Desperate heroes widen further when facing safe opponents. BB reads the opener's state and adjusts.

These three forces interact at every preflop decision. A desperate hero on the button facing two safe opponents and one desperate opponent is in a different strategic universe from a safe hero under the gun facing four desperate opponents — even though both are playing the same game at the same val.

The val parameter is a dial, not a switch

A common question: how much does val matter? Here's CO VPIP across all six trained val levels. The scaling is smooth and monotonic — there's no "cliff" where strategy changes suddenly.

CO preflop VPIP across all trained val levels. Fresh state · all players start with zero squids · CO · 6-max · 100bb effective

Source: squid-deltas.md Table 1 lines 62–70

At val=1 the shift from Cash is modest (+3.4pp). At val=3 it's substantial (+14.8pp). At val=10 CO plays three out of four hands dealt. Think of val as a dial that smoothly turns up the squid-equity pressure — the higher it goes, the wider everything gets.

BB's defense expansion is one of the largest strategy shifts in Squid Classic. The data shows three things, and they build on each other:

1. BB defends almost every hand.
2. The hands BB adds are almost all offsuit junk.
3. BB overdefends minimum defense frequency (MDF — the chip-EV floor for how often to call to stop auto-profitable bluffs) by a massive margin, flipping a well-known Cash pattern.

Each finding sets up the next. The wide defense feeds into every flop mechanism covered in Part 4 — you cannot understand why c-bet frequencies shift in Squid without first understanding what BB is actually defending with.

Measurement conditions: fresh state (all players start with zero squids). For the impact of opener squid-status on these numbers see §2.5.

3.1 — BB defends almost every hand

BB's defense rate versus a 44-combo standard open across four opener positions and six val levels:

BB defense rate vs opener position × val. Fresh state · all players start with zero squids · 2.5bb open · BB vs opener · 6-max · 100bb effective

Source: squid-deltas.md Table 2 lines 78–86. MP data partially sampled — dashes indicate untested val levels.

The headline number: BB vs CO at val=3 defends 95.8%, up from 51.8% in Cash. That is a +44.0pp shift. Against UTG — the tightest opener — BB still defends 84.6% at val=3, nearly double the Cash rate of 36.5%.

Two patterns stand out.

First, the Cash→v1 jump is enormous. Against CO it is almost +30pp. Against BTN it is +26.5pp. This first step — turning on the Squid overlay at its minimum penalty level — produces most of the defense expansion. Additional val increments push the rate higher but more gradually.

Second, by val=5 defense is near-saturated against every opener. Against CO and BTN it is already 99%+. Against UTG it is 95.9%. At val=10 every opener approaches 100%. BB is defending literally everything.

Why it is that extreme. BB faces the same squid-equity math as an opener. Folding forgoes the chance to win this hand's squid. In Cash, BB folds a marginal hand because the chip cost of calling exceeds the expected value of seeing the flop. In Squid, calling also preserves the chance to win a squid — a forward-looking equity component that pushes marginal hands past the break-even point. BB already has the best pot odds at the table because the blind is already committed, so the extra chip cost to continue is small. The squid-equity benefit only needs to outweigh a small chip gap to push the defend rate up.

The val-scaling is monotonic because that squid-equity component grows linearly with val. Higher val means bigger game-end stakes, which means the squid-equity benefit of staying in the hand grows, which means more hands clear the threshold.

What this means in practice: In Squid at val=3, you should almost never fold the big blind to a single raise — not against UTG, not against anyone. This is not loose play. The math says defend.

3.2 — What BB adds is offsuit junk

Where do all those extra defending hands come from? The composition table tells the story.

BB defense composition by hand category across val — BB vs CO 2.5bb open. Reach measured in combos out of 1,326 total. Fresh state · all players start with zero squids · BB vs CO 2.5bb open · val sweeps columns

Source: squid-deltas.md Table 9 lines 432–449.

The first six categories — everything from premiums through suited broadway — are at maximum in Cash already. Every AA, every KQs, every medium pair: already defending at 100%. The growth from Cash to Squid adds zero combos in those rows.

The expansion comes from three places, and one of them does essentially all the work.

Cash→v1 growth (total +441 combos):

• Offsuit junk: +361 combos (82% of the added hands)
• Suited junk: +74 combos (17%)
• Suited connectors: +6 combos (1%)

Cash→v3 growth (total +716 combos):

• Offsuit junk: +628 combos (88% of the added hands)
• Suited junk: +82 combos (11%)
• Suited connectors: +6 combos (1%)

At val=10, offsuit junk accounts for 815 of 816 possible combos defending — essentially the entire category.

What this means in practice: The hands BB adds in Squid — K4o, J6o, 83o, T2o — are the weakest part of the deck. They are correct to defend preflop. But they are terrible on most flop textures, which is why the opener gets to c-bet so aggressively on the flop.

3.3 — BB overdefends MDF — a Cash theory reversal

In Cash, BB systematically underfolds relative to MDF. This is the well-documented "BB overfolds" finding: against standard raise sizes, BB defends 7–13pp below the theoretical MDF threshold. In Squid, the direction flips.

MDF is the chip-EV floor for how often you need to call to prevent your opponent's bluffs from being automatically profitable. It is calculated purely from the bet size — it does not account for squid equity or any non-chip consideration.

BB defense vs MDF deviation by raise size — Cash and Squid v3, CO opener. Fresh state · val=3 · raise sizes 2.0–5.0bb

Source: squid-deltas.md Table 18 lines 693–712. Squid v3 data at 4.0bb and 5.0bb not tested — dashes indicate missing data.

In Cash, BB is 7–13pp below MDF at every tested raise size. In Squid v3, BB is 39–44pp above MDF at the three tested sizes. The direction is completely reversed.

What this means in practice: Do not apply the Cash MDF formula in Squid. At val=3 the correct defense is 40pp above what MDF says. If you are defending at MDF or below, you are folding far too much.

The position-dependent caveat: Cash "BB overfolds" is narrow-opener-only

The Cash underfold finding needs a refinement. When the opener is wide — specifically, when BB faces an SB open — the Cash pattern already flips.

BB defense vs SB open × val, 2.5bb. Cash and Squid v3 · BB vs SB open · wide-opener condition

Source: squid-deltas.md Table 22 lines 797–820.

In Cash, BB already overdefends MDF by +20.9pp when facing SB — a wide opener. Compare to the −10.4pp underdefense against CO at the same raise size. The crossover between underdefense and overdefense happens somewhere between BTN-as-opener and SB-as-opener in Cash.

The actual pattern across both modes:

• Cash: BB overfolds against narrow openers (UTG, MP, CO). BB overdefends against wide openers (SB). The narrow-opener MDF underdefense is what the literature documents. The wide-opener overdefense is less discussed.
• Squid v3+: BB overdefends against every opener, regardless of width. The squid-equity cost of folding overwhelms the chip-EV considerations that kept Cash BB below MDF against narrow openers.

So the "reversal" from Part 3 of the Cash literature is real but more nuanced than "BB always overfolds in Cash, always overdefends in Squid." The correct statement is: Squid collapses the position-dependent split. Against every opener, at every tested raise size, BB defends well above MDF.

The flop is where the biggest Squid-specific deltas live. This part walks through seven findings, organized by board texture: what the solver does on each texture family, why, and where it breaks from Cash theory.

Measurement conditions: fresh state (all players start with zero squids), CO vs BB SRP, 100bb effective.

4.1 Dry rainbow, A-high, and paired boards: bet almost everything

On boards where BB's added junk has no equity, CO's c-bet frequency jumps to 91–99% in Squid.

CO flop c-bet frequency on six board textures where the fold-equity amplification effect dominates. Fresh state · CO vs BB SRP · 100bb effective · val=3, Cash and v3 shown

Source: squid-deltas.md Table 3 lines 92–108

The largest delta is A94r at +33.5pp. That board starts at only 64.9% in Cash — plenty of headroom for the Squid overlay to push the frequency up. The dry rainbow boards (K72r, J72r, Q83r) start higher in Cash, so the Squid boost is smaller in absolute terms, but they all land at 96–99%.

The pattern is the same across all six textures: BB's wider Squid range is loaded with offsuit junk that has no equity on these boards. The compositional data confirms it — 82% of the hands BB adds to its defense when switching from Cash to Squid are offsuit junk. On a K♠7♣2♦ rainbow, those hands have no pair, no draw, no backdoor. They fold to a c-bet.

4.2 The mid-connected exception: 654, 765, 876r

Three boards break the pattern. CO c-bets less in Squid than in Cash on 654, 765, and 876r.

CO flop c-bet frequency on the three boards where the range-advantage reversal applies. Fresh state · CO vs BB SRP · val=1 · SRP only — 3BP direction reverses

Source: squid-deltas.md Table 27 lines 942–951. The direction — all three boards bet less in Squid — is stable across training runs. The exact magnitudes vary; cite the pattern, not the specific numbers.

Every other board in our test set shows a positive Cash→Squid delta. These three are the only negatives. The full val trajectory confirms all three stay negative through val=10.

Why do these boards reverse? The hands BB adds in Squid — the 54s, 65s, 76s, 87s, small pocket pairs — hit 654/765/876 hard. Straights, two pair, sets, strong draws. CO's high-card opening range (AK, AQ, KQ, broadway) misses these boards entirely. Range advantage flips to BB, and CO correctly checks back.

Even premium hands slow down. On 765 specifically, the premium (AA–JJ) hand category bet frequency drops from 36% (Cash) to 20% (val=1). CO's strongest hands slow-play because BB's range is too strong to extract value from betting.

Scope bounds — this is narrow. The reversal applies to exactly three boards: 654, 765, 876r. Other connected boards do not reverse:

• 543 (+2.4pp) and 432r (+12.6pp) — too low. BB's added connectors don't line up as cleanly.
• 987r (+3.9pp) and T98 (+20.1pp) — too high. CO has JT/QJ/T9 coverage on these boards.

And in 3-bet pots, the entire pattern flips. On 765 in 3BP, Cash→v3 is +17.5pp — the board goes from worst for CO in SRP to one of the best in 3BP. BB's 3-bet range is tight and polarized (AA–TT, AK, AQs). It does not contain the low connectors and small pairs that drive the reversal. With those hands filtered out, 765 reverts to a CO-favorable texture.

4.3 Monotone boards: bet aggressively despite the intuition

The counterintuitive headline: monotone boards show the largest positive c-bet deltas in the entire dataset.

CO flop c-bet frequency on monotone boards across the full val range. Fresh state · CO vs BB SRP · 100bb effective · val sweeps columns

Source: squid-deltas.md Table 3 lines 106–107

K94ss goes from 32% to 87% — a +54.7pp swing. That's the largest positive delta in the preflop-to-flop tree, bigger than any dry or paired board.

The intuition says "monotone boards are dangerous for CO because BB has flush draws." The data says the opposite. Here is why.

BB's Squid-added defense range on monotone boards is 82–87% offsuit junk with no spade. The flush-carrying hands (Axs, suited broadways, suited connectors with the board suit) were already defending in Cash. They didn't grow. What grew is the junk — K4o, J6o, 93o — hands with zero flush potential. When CO c-bets K♠9♠4♠, those offsuit hands have no pair, no draw, nothing. They fold.

The naive "flush draws protect BB" story is wrong for the range BB is actually defending with. The flush-draw hands are a small, fixed portion. The overwhelming majority of the added defense is junk that collapses to a c-bet on a monotone texture.

4.4 Cash slow-play theory splits by texture

In Cash, the solver slow-plays certain premium hands on wet and monotone boards. In Squid, some of those slow-plays survive and some collapse. The dividing line: why the slow-play existed in the first place.

Premium hand slow-play behavior in Cash vs Squid — structural slow-plays survive, pot-control slow-plays collapse. Fresh state · CO vs BB · val=3

Source: squid-deltas.md lines 615–623

The pattern is clean. Slow-plays motivated by structural range danger — a board where your hand is genuinely vulnerable — hold up even under Squid's penalty pressure. Slow-plays motivated by generic pot control — "I'm ahead, let me keep the pot small" — collapse because the squid-equity cost of letting opponents see free cards now outweighs the pot-control benefit.

4.5 Protection betting AA on 8h6d4h: the Cash rule reverses

In Cash, the solver says betting AA on 8♥6♦4♥ is overvalued — checking is higher EV. In Squid, the theory reverses cleanly.

AA bet frequency on 8h6d4h across the val range. Fresh state · CO vs BB SRP · 100bb effective · val sweeps rows

Source: squid-deltas.md lines 589–596

Cash 0.3% → val=10 98.9%. Three things shift in Squid that make protection betting correct:

1. BB's wider range has more non-draw junk. In Cash, BB's calling range on 864 is draw-heavy (65s, 75s, 97s, suited connectors). In Squid, BB's range also includes a lot of offsuit trash that will fold to pressure. CO's c-bet gets folds it wouldn't get in Cash.
2. Free cards hurt more. Checking gives BB's draws a free look at the turn. In Cash, the cost of giving a free card is purely in chip equity. In Squid, there's a second cost — if a draw gets there and BB wins the pot, CO loses the squid-equity upside of winning that hand.
3. Protection becomes positive-EV. The combination of more fold equity and higher cost of free cards tips the scale. The chip-negative line in Cash becomes overall-positive in Squid once the squid-equity term is added.

4.6 Pocket pairs on A-high: the Cash non-monotonicity flattens

In Cash, pocket pairs on A-high boards show a non-monotonic pattern driven by blocker logic. KK checks almost always (the Ace blocks your range advantage). 99 bets almost always (set). Pairs in between follow complicated blocker reasoning, not raw hand strength.

In Squid, all of that flattens.

Pocket pair bet frequency on an A-high board, Cash vs Squid v3. Fresh state · CO vs BB SRP · A-high board · 100bb effective · val=3

Source: squid-deltas.md lines 705–716

Look at the Cash column. KK checks 98%. QQ checks 90%. Then JJ bets 39%, TT 74%, 99 (set) 98% — a jump. Then 88 drops to 16% and 77 to 24%. That pattern makes sense only through blocker logic: KK blocks top pair on an A-high board, 99 flopped a set, 88/77 are weak underpairs without useful blockers.

Now look at the Squid column. Everything is 70–100%. The non-monotonicity vanishes. KK goes from a pure check (2.1%) to betting 70% of the time. 88 goes from checking 84% to betting 96%.

Squid pressure overrides blocker logic. When BB's defense range is wide and junk-heavy, the question simplifies: "Does this hand have enough equity against BB's calling range to profitably bet?" For every pocket pair on an A-high board, the answer in Squid is yes.

4.7 Overbet usage grows

In Cash, the solver almost never overbets the flop — 0.09% of bets. In Squid v3, overbet usage rises to roughly 5% of bets on dry rainbow and monotone boards. That is approximately 50–60× more frequent than Cash.

Squid creates more "extreme nut advantage" spots. On K72r, CO's range has massive equity advantage over BB's junk-heavy defense. On K94ss, the same story plays out with the added wrinkle that BB's non-flush junk has almost zero equity. In both cases, CO can profitably size up to 150%+ pot for fold equity against a range that has no defense.

How three Cash theories shift on the flop

The flop findings above break three Cash NLHE theories. Here is the summary.

The flop is where Squid's biggest deltas live. But the flop is not the whole story. What happens after the c-bet gets called? After CO checks? After both players limp in and see a flop?

The short version: Squid's wider flop ranges do not carry forward at full strength. Turn barrels decrease, probes decrease, limped-pot aggression drops. The one exception — delayed c-bets after a flop check — increases sharply, and it confirms exactly why the rest decreases. The river, meanwhile, becomes a polarized battlefield.

Measurement conditions: all findings below use val=3 on 100bb effective 6-max unless otherwise noted. Scope caveats per subsection are called out in the body.

5.1 Turn barrels decrease despite wider flop ranges

This is the finding that surprises most players when they first see it.

CO c-bets wider on the flop in Squid — we covered that in Part 4. The natural assumption is that wider flop aggression leads to wider turn aggression. It does not. CO barrels the turn less frequently in Squid than in Cash.

Here is the turn barrel breakdown on K72r by turn card:

CO turn barrel frequency after c-betting K72r flop. CO vs BB · SRP · K72r flop · 6-max · 100bb effective · val=3 · turn card sweeps rows

Source: squid-deltas.md lines 338–342

Three of the four turn cards show CO barreling less in Squid. The Ace turn has the biggest drop — 543 — never mind, let me state this plainly. On a blank turn the barrel rate falls by 9.2pp. On an Ace turn it falls by 13.4pp. On the turn that pairs the seven, the effect is small (−2.0pp).

The one exception is the King turn, which pairs the board. When the turn pairs, CO actually barrels more in Squid (+9.3pp). That exception is instructive — we will come back to it.

Why does a wider flop range produce fewer turn barrels? The answer is about what happens to the hands CO added to its flop c-bet.

In Cash, CO c-bets K72r at 83.6%. In Squid v3, CO c-bets at 98.1%. That extra 14.5pp of flop c-bets includes hands that Cash CO would never have bet — marginal bluffs with no turn equity. CO bet them in Squid because the squid-equity overlay made the flop c-bet profitable on the whole.

But on the turn, that squid-equity overlay does not generate a new per-street bonus. The decision to enter the pot already captured the forward-looking squid equity. Turn decisions revert to chip-EV math. And chip-EV says: the marginal bluffs that CO only c-bet in Squid have nothing on the turn. They give up.

The hands that do barrel the turn — the value hands, the strong draws — are roughly the same hands that would have barreled in Cash. But the measured turn barrel rate averages over a wider population that now includes all the Squid extras who gave up. More hands facing the decision, same hands actually firing. The rate drops.

The King-turn exception confirms this. When the turn pairs the board, CO's range gains new equity (trips, full houses). Those are real value hands that barrel. The addition of equity on a paired turn flips the pattern — CO's range got stronger on that specific card, not weaker.

The causal story here — wider flop ranges filter on the turn so that measured barrel rates drop — is directionally confirmed across multiple spot types but has not been tested against a competing poker-theory alternative that predicts the same direction via a different mechanism. The finding carries a scope caveat; see Research notes.

5.2 Delayed c-bets increase when you check the flop

The flip side of §5.1. If CO checks the flop instead of c-betting, the turn bet frequency rises sharply in Squid.

• K72r + blank turn: Cash 65.9% → Squid v3 82.7% (+16.8pp)
• T98 + blank turn: Cash 42.7% → Squid v3 55.2% (+12.5pp)

Source: squid-deltas.md lines 349–351

This is the mechanism from §5.1 working in reverse. When CO c-bets the flop, BB's calling range gets filtered — the junk folds. The remaining BB range on the turn has real hands. But when CO checks the flop, BB's range does not get filtered. All that Squid-defense junk BB added (82% offsuit junk — see Part 3) is still in BB's turn range, unimproved.

A turn bet from CO now catches that unimproved junk. The fold equity is higher than in Cash because BB's turn range is bloated with hands that never faced a flop c-bet.

5.3 BB probes less after IP checks back

When CO checks the flop and BB leads into the turn, that probe is less profitable in Squid than in Cash.

BB probe frequency after IP check-back. val=3 · 6-max · 100bb effective · probe spots: IP checks flop, OOP probes turn · boards and positions sweep rows

Source: squid-deltas.md lines 344–347

In Cash, an IP check-back is a strong tell. When CO c-bets 83.6% of the time on K72r, the 16.4% that checks is a relatively well-defined weak range. BB can probe into that weakness profitably.

In Squid, CO c-bets 98.1% on K72r. The check-back range is only 1.9% of hands — and it is not necessarily weak. CO might be trapping with a monster, or making a pot-control play with a hand that Cash CO would have bet. The check-back no longer screams "I have nothing."

BB's probe loses fold equity because it is no longer targeting a predictably weak range. The signal from the check-back is weaker.

Notice the position gradient: the probe drop is 7.8pp vs CO but only 2.1pp vs BTN. BTN already c-bets at near-saturation in Cash, so the Cash-to-Squid expansion is smaller. BTN's check-back was already less informative in Cash. CO's check-back got much less informative in Squid, so the probe delta is larger.

5.4 Limped pot aggression drops

Once both players limp into a pot, postflop aggression drops sharply relative to Cash.

BB bet frequency after SB limp, flop. BB vs SB · limped pot · 6-max · 100bb effective · val=3 · board sweeps rows

Source: squid-deltas.md lines 353–356

After a limp-limp, neither player has a clearly stronger range. In a raised pot, the raiser's range is tighter and more defined — there is a natural aggression dynamic. In a limped pot, both ranges are wide and weak. Value betting is less profitable because the opponent's range is amorphous. Fold equity is lower because neither player committed enough to have "nothing" in their range — both players entered cheaply with marginal holdings.

The drops are large: 18pp on K72r, 20pp on T98, 14pp on 543. T98 shows the biggest absolute drop, ending at just 37.8% BB bet frequency in Squid. On 543, BB barely bets at all — 9.0% in Squid, down from 23.1% in Cash.

This finding is from single-street BB-bet-after-SB-limp data only (BB's flop bet frequency on K72r, T98, 543). Turn, river, and multi-street post-limp dynamics are untested. Apply this to the flop decision in limped pots; do not extrapolate to later streets or complex post-limp lines.

5.5 Facing a check-raise, CO folds more and re-raises less

When BB check-raises CO's c-bet on K72r, the action distribution shifts dramatically in Squid.

CO response to BB check-raise on K72r. CO vs BB · K72r · val=3 · 6-max · 100bb effective · fresh state · Cash vs Squid v3

Source: squid-deltas.md lines 367–370

Cash CO re-raises 42.5% of the time facing a check-raise on K72r. Squid CO re-raises 5.6%. That is a collapse of nearly 37pp. Meanwhile, folding jumps by 19pp.

The logic follows directly from the flop c-bet composition. CO's Squid c-bet range on K72r is 98.1% of hands — it includes a massive bluff portion. When BB check-raises, those bluffs have nothing to continue with. They fold. And the value hands that would have re-raised in Cash take a more cautious line: they flat-call more and re-raise less, because BB's check-raise range in Squid is also expanded (more flush draws, more semi-bluffs — see Part 4's note on BB's check-raise range expansion).

The finding generalizes beyond K72r. Cross-texture testing on five boards (K72r, K94ss, A94r, T98, 543) at CO confirms the fold-up, re-raise-down direction on all five textures.

Position matters. CO and BTN show the pattern universally across all tested textures. UTG and MP show a texture-conditional split:

• On connected boards like T98, UTG and MP do fold more in Squid facing a check-raise — the mechanism holds.
• On high-card dry boards (K72r, A94r, and Q72r), UTG and MP fold less in Squid and call more. Early-position ranges on high-card boards are A-heavy (AK, AQ, AJ, AT all hit A94r), so in Squid those hands call the check-raise to preserve squid equity rather than folding.

Val scope. The fold-heavy pattern is certified at val=3. At val=5, the fold/call balance inverts — CO calls more and folds less as the squid stake in the pot grows large enough to incentivize staying in.

The fold-up direction cited above is from v1.0 certification values. Subsequent checkpoint retesting found the fold direction does not reproduce on the current model — CO folds less, not more, with the volume shifting to calls. Only the re-raise suppression direction is stable across checkpoints. See Research notes for the full retesting history. The re-raise advice (narrow your re-raise range sharply) holds on both the published and current checkpoints.

5.6 River play: more active, larger sizes

The Squid river on dry board blank runouts is a different street from the Cash river.

CO bet frequency and average sizing across streets on K72r + blank turn + blank river. CO vs BB · K72r + blank turn + blank river · 6-max · 100bb effective · val=3 · street sweeps rows

Source: squid-deltas.md lines 631–638

Look at the river row. Cash CO bets the river 6.2% of the time for an average of 16.5bb. Squid CO bets the river 57.1% of the time for an average of 35.1bb. Frequency goes up nearly tenfold. Size more than doubles.

By the river on a K72r blank runout, both ranges have been filtered through the entire hand. CO's continuing range is narrow but value-heavy — CO bet the flop, barreled or checked the turn, and arrived at the river with hands that survived multiple decision points. BB's continuing range is slightly wider in Squid (because BB defended wider throughout the hand), and it includes more bluff-catchers — middling hands that called the flop c-bet in Squid that Cash BB would have folded.

The result is a polarized dynamic. CO can overbet for value against BB's bluff-catchers. BB knows CO can value-bet, so CO's bluffs at large sizes also get respected. The equilibrium is: bet the river on more hands, at bigger sizes, in a sharply polarized structure.

River data is from blank runouts on K72r only (K72r + 3d + 3s). Scare card runouts (flush completions, straight completions, paired runouts), state-conditional river behavior (hero-desperate vs hero-safe at river), and other board textures are untested. This is a directional finding on dry-board blank runouts — treat river strategy on other runout types as Cash-theory defaults until data exists.

Hero-last is the sharpest state in Squid Classic. You are the only player without a squid. Everyone else is safe. If the game ends now, you pay the full penalty.

The solver's response is not "play wide and hope." It is polarized aggression: raise almost everything, limp almost nothing, fold what cannot survive a call.

Measurement conditions: hero-last state (hero is the only no-squid player; all opponents hold a squid). Val=3 for the pair threshold table; direction holds at val=1 and val=10 with the threshold shifting accordingly.

The headline numbers

At val=3, hero-last CO opens 5% of hands. Of those, only 2.4% are limps. The rest — roughly 97% of entered pots — are raises.

Compare that to the fresh state (nobody holds a squid yet), where CO opens 42.9%. Or the hero-has state with three no-squid opponents, where CO opens just 12.9%. Hero-last is an entirely different mode of play.

Where the threshold sits: the pocket-pair raise-vs-limp table

The polarization is not random widening. There is a clean equity floor — a specific pair rank below which the solver stops raising and starts limping or folding.

CO c-bet strategy for BB-last pocket pairs at val=3. BB-last hero-last state · val=3 · 6-max · 100bb effective · pocket-pair hands sweep rows · preflop raise-vs-limp

Source: batches_m8_bb_last_defense/M8-BB-last-defense-results.md (v1.6.0 refresh)

The threshold sits between 88 and 77. At 88, the solver still raises three-quarters of the time. At 77, the solver limps three-quarters of the time. That is a cliff, not a gradual slope.

Above the threshold, you commit. Below it, you enter cheaply or fold. The solver does not try to trap with the top of its range — AA through TT are pure raises, no exceptions.

The threshold shifts with val

At val=1 and val=10, the same polarization structure exists, but the specific pair-rank floor moves. At val=1 the threshold is closer to 99/88. At val=10 it shifts back toward the same neighborhood — different equity floors for different stakes.

The direction — raise strong hands, fold or limp weak ones — holds at every tested val. The exact pair where the cliff appears is what changes.

Why the solver raises instead of limping

Safe opponents can afford to fold — they already hold a squid and have no forward-looking incentive to defend marginal hands. Raising forces them into a decision, and many of them will fold. Limping gives them a cheap look at a flop, which is the opposite of what hero-last wants.

The solver's logic: if a hand has enough showdown equity to survive a call, raise it and generate fold equity. If it does not, fold. Limping is the worst of both worlds for hero-last — it invests chips without generating fold equity and lets safe opponents realize their positional advantage cheaply.

What this means in practice: If you are the last player without a squid, your preflop strategy is binary. Raise 88 and above, raise all Ax, raise suited broadway. Below that, fold or limp — do not invest chips aggressively in hands that cannot win a called pot. And do not slow-play the top of your range. AA through TT are pure raises. No trapping, no deception, no limping big pairs "to see a cheap flop." The math says raise or fold.

The specific 88/77 threshold at val=3 is empirically observed from one BB-last preflop batch. A follow-up resolution attempt confirmed the broad M8 direction postflop — hero-last fires c-bets at 97%/96%/82% across K72r/K94ss/T98 — but per-pair postflop extraction returned no data (the API does not expose per-combo postflop frequencies). Treat the 88/77 boundary as approximate: somewhere in that neighborhood, not a hard rule. See Part 8 §8.2 for the full scope discussion.

Everything in Parts 4 and 5 assumed a single-raised pot. CO opens, BB calls, flop comes, CO decides whether to c-bet. The mechanisms that drive Squid's flop behavior — wider BB defense creating fold equity, range advantage reversing on mid-connected boards, monotone non-flush junk folding — all depend on BB's defending range being loose and junk-heavy.

In a 3-bet pot, that assumption breaks.

Measurement conditions: all findings in this part use val=3 on 100bb effective 6-max. SRP = single-raised pot (CO opens, BB calls). 3BP = 3-bet pot (BB 3-bets CO's open, CO calls). Fresh state (all players start with zero squids).

BB's 3-bet range is tight and polarized: AA–TT, AK, AQs, KQs, plus a handful of suited connectors as bluffs. It does not contain offsuit junk. It does not contain small pocket pairs. It does not contain the low connectors that define the SRP exception boards. When BB's range changes that dramatically, the flop mechanisms change too — some amplify, some reverse, and one nearly disappears.

7.1 The SRP exception boards flip in 3-bet pots

This is the single most actionable 3BP finding. The three boards where CO checks back more in Squid SRP — 654, 765, 876r — go from worst to best for CO in 3-bet pots.

Here is the clearest example: 765.

CO vs BB c-bet frequency on 765, SRP vs 3BP. CO vs BB · SRP and 3BP · 765 board · 6-max · 100bb effective · val=3 · pot type sweeps columns

Source: squid-deltas.md lines 862–889 (Table 25, R18 3BP data); squid-deltas.md Table 3 lines 100–101 (SRP data)

In the single-raised pot, 765 is the classic exception: CO c-bets less in Squid than in Cash (−7.6pp). BB's wider SRP defense range is loaded with connectors — 76s, 65s, 54s, 87s, small pairs — that crush this board. CO's high-card–heavy opening range mostly misses. Range advantage flips to BB, and CO correctly checks back.

In the 3-bet pot, every one of those connector hands is gone. BB's 3-bet range is AA–TT, AK, AQs, KQs, with suited connectors only as occasional bluffs. No 76o, no 65s in quantity, no 77, no 66. Without those hands, 765 is no longer a BB-favorable texture — it is CO-favorable. CO's 3BP calling range has TT through QQ as overpairs that dominate BB's 3-bet range on this board.

The result: 765 flips from one of CO's worst c-bet boards in SRP to one of the best in 3BP. Cash 3BP c-bet is already 70.5%, and Squid v3 adds a hair more at 71.4%.

What this means in practice: If you are in a 3-bet pot and the flop comes 765, 654, or 876r, c-bet aggressively. The SRP advice ("check back more, including your premiums") does not carry over. BB's range is tight enough that CO's overpairs and high cards are ahead again.

7.2 Dry boards get an even bigger lift in 3-bet pots

On dry rainbow and paired boards, the Squid c-bet amplification is stronger in 3BP than in SRP. The reason is headroom: CO's 3BP baseline is lower than SRP (CO is more selective when ranges are tighter), so there is more room for the penalty pressure to push c-bet frequency up.

Cash→v3 c-bet delta, SRP vs 3BP on dry boards. CO vs BB · SRP and 3BP · dry-rainbow boards · 6-max · 100bb effective · val=3 · board sweeps rows · Cash→v3 delta

Source: squid-classic-theory.md §7.2; squid-deltas.md Appendix A (SRP deltas); squid-deltas.md Table 25 lines 862–889 (3BP data)

K72r in SRP already jumped from 83.6% to 98.1% — a big move, but most of the frequency ceiling was already eaten in Cash. In 3BP, Cash starts at 65.7% (CO is more disciplined when ranges are tighter), and Squid v3 pushes it to 93.7%. That is a +28.0pp lift — nearly double the SRP delta.

KK5 shows the same pattern: SRP +18.3pp, 3BP +32.3pp.

What this means in practice: In 3-bet pots on dry rainbow or paired boards, c-bet almost everything. If you thought SRP c-bets were automatic in Squid, 3BP c-bets are even more so. K72r and KK5 are essentially pure-bet boards in Squid 3BP.

7.3 A-high boards in 3BP: the one texture where the lift shrinks

A94r is the outlier — the board where 3BP reduces the Squid amplification rather than increasing it.

CO c-bet on A94r, SRP vs 3BP. CO vs BB · A94r board · 6-max · 100bb effective · val=3 · SRP and 3BP both shown

Source: squid-classic-theory.md §7.3; squid-deltas.md Table 25 lines 862–889 (3BP data); squid-deltas.md Table 3 line 98 and Appendix A (SRP data)

The SRP delta is massive: +33.5pp, driven by BB's wide junk-heavy range folding to any c-bet on an ace-high board. In 3BP, the delta is still positive (+15.7pp) but the overall frequency drops from 98.4% to 62.4%.

The reason is BB's 3-bet range composition. BB 3-bets with AK, AQ, AJs — hands that all make top pair on A94r. Roughly a third of BB's 3-bet range connects hard with this board. CO is c-betting into a range where top-pair-or-better is common, not rare. Fold equity collapses, and the Squid widening effect cannot fully compensate.

What this means in practice: On A-high boards in 3-bet pots, slow down. BB's 3-bet range actually connects with A-high boards more than the SRP range does. A c-bet frequency around 62% is correct — not the 98% you might default to from SRP experience.

Putting it together: the 3BP texture map

The three findings tell a clean story. In a 3-bet pot, BB's range is fundamentally different from SRP: tight, polarized, no junk. That changes the flop c-bet calculus in texture-specific ways.

How 3BP changes the Squid c-bet lift, by texture category. CO vs BB · representative boards per category · val=3 · 6-max · 100bb effective · SRP vs 3BP direction

Source: squid-classic-theory.md §7.1–7.3; squid-deltas.md Table 25 lines 862–889

The pattern is consistent: wherever BB's SRP range had specific hands that drove a mechanism (connectors on 654/765/876r, junk on dry boards, A-x on A-high), the 3BP range either removes them or keeps them, and the mechanism responds accordingly.

Measurement conditions: Part 8 is a meta-chapter summarizing what the research does and does not cover. Findings are Classic mode only, 6-max, 100bb effective. Multiway findings are at val=3 only.

Part 8 is not about how to play. It is the explicit map of what this research covers, what it does not, and where the confidence boundaries are. If you take one thing away from this section, it should be this: every actionable in Parts 2–7 is the intersection of Classic mode, 6-max, 100bb effective, trained val levels, and the specific positions and boards we tested. Step outside that intersection, and you are extrapolating without solver backing.

8.1 What we know well

The research identified ten mechanisms that characterize how Squid Classic strategy differs from Cash. Here is where they stand.

Seven mechanisms are at full confidence — primary explanation confirmed, at least two alternative causal stories contradicted:

• M1 — Squid equity maximization. The root mechanism. Every position widens because each hand is a chance to win a squid. Confirmed by the hero-has control (safe hero returns to near-Cash), the val-scaling gradient, and the per-seat state data.
• M2 — Limping as low-cost pot entry. Upgraded from tentative to full confidence after the v1.3.0 resolution batch contradicted the fold-equity-saturation alternative. CO limp at val=5 is 43.3%; at val=10 it is 75.5% — still rising, not saturating.
• M3 — Fold equity amplification on the flop. BB's widened defense is 82% offsuit junk. On boards where that junk has no equity, CO's c-bet captures huge fold equity.
• M4 — Range advantage reversal (SRP-only, 654/765/876r). BB's added connectors hit mid-connected boards hard, flipping range advantage. Confirmed by the 3-bet pot reversal: when BB's range is tight (3BP), the same boards become CO-favorable.
• M5 — Monotone non-flush fold equity (heads-up only). The hands BB adds on monotone boards are almost entirely offsuit junk with zero flush potential. CO exploits this to produce the largest positive c-bet deltas in the dataset.
• M6 — State-dependent range adaptation. The model reads each opponent's squid state and adjusts. Hero widens when opponents are safe (they fold); hero tightens when opponents are desperate (they do not fold).
• M8 — Desperation polarization (hero-last). When hero is the only player without a squid, strategy polarizes to near-pure raising. Hand-level data shows a clean raise-vs-limp threshold between pocket eights and pocket sevens at val=3.

Two additional mechanisms are at full confidence with narrower scope:

• M-Probe — Passive signal weakening. BB's probe rate after an IP check-back decreases in Squid. Confirmed with a position-differential test (the effect is larger vs CO than vs BTN, matching the prediction). Scope is non-A-high boards — A-high boards often show the opposite direction.
• M-XR — Aggression signal collapse (reraise-suppression only). When facing a check-raise, CO re-raises far less in Squid than in Cash. The reraise-suppression half holds across multiple boards and positions. The original "CO folds more" claim does not reproduce on the current checkpoint and has been retracted — 24 out of 24 board × position × size test cells show CO folding less, with the volume shifting to calls. Scope: CO+BTN universal for reraise suppression; UTG+MP texture-dependent (connected boards hold, high-card dry boards reverse).

One mechanism is tentative:

• M7 — Wider range weakens later streets. Directionally confirmed across multiple spot types (turn barrel, probe, delayed c-bet, limped-pot bet). However, the methodology requires at least one adversarial alternative to be contradicted, and the only tested alternative (a Cash-theory "range filter" story) was not contradicted — it predicts the same direction through a related mechanism. That makes M7 underdetermined, not wrong. Resolution path is described in §8.2.

One sub-claim is ambiguous:

• M8's specific pair-rank threshold (88/77 at val=3) is empirically observed but not independently confirmed at the postflop level. The API does not expose per-combo postflop data. Aggregate hero-last c-bet rates confirm the broad polarization direction; the exact threshold pair is approximate.

8.2 What remains uncertain

Three items are not at full confidence. Here is what each needs and where it stands.

M7 — tentative (adversarial alternative not tested)

The primary finding is that wider preflop ranges leave fewer high-equity bluffs for later streets, so turn barrel rates drop while delayed c-bet rates rise. The data is consistent and covers multiple spot types. The problem is Alt-A: a standard Cash-theory explanation ("later-street aggression declines from general range-filter effects regardless of squid equity") predicts the same direction. The two stories are hard to separate because both involve the same filter mechanism — just with different attributions for why the filter matters more in Squid.

The resolution path is a targeted probe test. On M4-scope boards (765 or 654), CO c-bets less in Squid than in Cash, so CO's check-back range on those boards contains more genuine weakness. M7's population-shift story predicts BB probe should increase on M4 boards (more real weakness to attack). Alt-A predicts probe should still decrease (filter ran regardless). The differentiating prediction runs BB probe rate on 765 or 654 after CO check-back at val=3. The test was run in v1.5.0; the result was FAIL — probe decreased on both M4 boards, so Alt-A was not contradicted. M7 stays tentative until a new differentiating prediction is found or the M4-board probe is repeated under different conditions. The directional advice in Part 5 ("barrel less on turn after a Squid flop c-bet") is still reliable — both M7 and Alt-A agree on the direction. What is uncertain is the mechanism, not the pattern.

M2 upgrade to full confidence (v1.3.0) — a success case

M2 was initially tentative because one alternative — that limping at extreme val is driven by fold-equity saturation, not by the cost-minimization mechanism — could not be ruled out. The discriminating query was straightforward: CO limp% at val=5 vs val=10. If fold-equity saturation were the driver, limping should plateau between val=5 and val=10 (BB already defends 99%+ at val=5, so there is no marginal fold-equity loss from val=5 to val=10). If cost-minimization were the driver, limping should keep rising because the squid-equity component grows with val.

Result: CO limp at val=5 is 43.3%, at val=10 is 75.5%. Still rising sharply. Saturation contradicted. M2 upgraded to full confidence across the entire trained val range.

This is the template for how T-status updates should work: state the alternative, find a discriminating prediction, run the query, update the grade. M7 needs the same treatment.

M-XR scope (reraise-suppression only, v1.6.0 downgrade)

M-XR was originally certified as a two-part finding: CO folds more and re-raises less when facing a check-raise in Squid. The v1.6.0 and v1.6.1 fresh-server re-runs retracted the fold-direction half entirely. Across five textures at CO, nine bet-size combinations on K72r, four positions on K72r, and six board × position combinations at UTG/MP — 24 cells total — every single one shows CO folding less in Squid, not more. The volume that leaves the fold bucket goes to calls, not re-raises.

The reraise-suppression half holds. At CO and BTN, reraise frequency drops sharply on every tested board. At UTG and MP, reraise-suppression is present on connected boards (T98) but reverses on high-card dry boards (K72r, A94r, Q72r). The mechanism is position × texture dependent: UTG/MP ranges are dominated by high-card hands that hit high-card boards, so on those boards their Squid-added hands are strong enough to call or re-raise rather than fold.

Scope summary: CO+BTN reraise-suppression is universal. UTG+MP reraise-suppression holds on connected boards only. The "fold more" direction is retracted globally on the current checkpoint.

M8-Threshold (ambiguous — API extraction gap)

The broad hero-last polarization direction is firmly confirmed. The specific pair-rank floor (the 88/77 boundary at val=3) is empirically observed from one BB-last preflop batch. The v1.3.0 resolution attempt ran per-pair postflop queries — TT, 99, 88, 77, 66, 55 in hero-last state at val=3 — but the API does not expose per-combo postflop data. Every per-pair extraction returned "not found." Aggregate data from the same batch confirms hero-last fires aggressively postflop (97% on K72r, 96% on K94ss, 82% on T98), supporting the broad direction. The per-pair threshold question is unresolvable with the current API surface. Treat the 88/77 floor as approximate — somewhere in that neighborhood, not a hard rule.

8.3 What we don't have data for

Four regions have zero or thin coverage. If you are applying a finding from Parts 2–7 to one of these spots, you are outside the tested scope.

• MP postflop. The research has preflop data for all five positions (UTG, MP, CO, BTN, SB), but postflop testing was concentrated on CO. MP postflop behavior under Squid has not been characterized.
• Limped pot postflop (multi-street). BB's flop aggression after SB limp is tested (Part 5.4). Deeper post-limp dynamics — turn and river lines, hand-level breakdowns — are largely absent. This is a zero-data region.
• Multiway postflop at val ≠ 3. Multiway c-bets were tested at val=3 only. Whether the 3-way and 4-way findings scale with val is unknown.
• River SPR dynamics under state conditions. River play is characterized on blank runouts only (K72r + blank turn + blank river). Scare cards, flush completions, and paired runouts have not been tested in state-dependent configurations (hero-desperate vs hero-safe at river).

8.4 Known model issues

Three documented issues in the project's issue register affect EV-field usage. None of them affect the findings in this book, because all findings in Parts 2–7 are policy/frequency-based, not EV-based. The issues are listed here for completeness.

• KI-1 (raw vs fold-anchored EV). The strategy server returns raw EV, not fold-anchored. Three Cash trust-gate properties (F3, F6, F7) were not cleanly testable because the raw-EV offset makes their pass/fail criteria ambiguous. No Squid-specific findings are affected.
• KI-2 (Squid regression smoothing). Some EV values in Squid show smoothing artifacts at the boundary of the regression model. This is under investigation by the training team. Again, no policy/frequency claims are affected.
• KI-4 (model EV behavior concerns). Four trust-gate properties (G1, G2, G3, G4) showed model-behavior-level failures in the EV field rather than measurement issues. These concern whether the model's internal EV representation is faithful, not whether its policy outputs are. All mechanism findings in this book are derived from policy/frequency outputs and are independent of the EV field.

8.5 Mode scope

All findings in this book are for Classic mode only.

Squid is a family of three modes. Blood Battle (mode=2, accumulating squids with a quadratic weight function, total squids = N+4) and Double (mode=3, accumulating with a tiered 1×/2×/4× multiplier) are defined in the training code but not tested. Extrapolating Classic findings to the other modes would be unsound — accumulating squids fundamentally changes the incentive structure because winning pots beyond the first squid now has value, so the "once safe, done" logic that underpins M6 and M8 does not apply.

Here is the per-mechanism transfer status. These are theory-level predictions derived from the rules, not empirical findings.

Mechanism transfer status from Classic to Blood Battle / Double. Classic mode findings · transfer predictions to Blood Battle and Double · mechanism sweeps rows · transfer labels from source

Source: hypotheses-and-mechanisms.md per-mechanism Scope fields

Until Blood Battle and Double data exists, treat every actionable in Parts 2–7 as Classic-only.

8.6 Multiway scope findings (v1.3.0)

All flop c-bet data in Parts 4 and 7 is heads-up (CO vs BB, single-raised pot). The v1.3.0 batch extended testing to multiway configurations: 3-way (CO-BTN-BB), 4-way (CO-BTN-SB-BB), and 5-way (CO-BTN-SB-BB + MP limp-call).

CO flop c-bet Cash→v3 delta by player count. CO vs BB, CO vs BB+callers · flop c-bet · val=3 · 6-max · 100bb effective · player count sweeps columns · Cash→v3 delta

Source: squid-deltas.md publisher-gap lift tables (CO cbet T98 × player count) and squid-classic-theory.md §8.6

The pattern is not monotone with player count.

At 3-way, direction holds on both boards but magnitude shrinks to roughly half of the heads-up delta.

At 4-way on K72r, direction reverses. Cash 4-way c-bet is 55.6% while Squid v3 4-way is 47.7% — the squid incentive is no longer enough to overcome the fold-equity loss of three callers behind.

At 5-way on K72r, direction rebounds strongly. Cash 5-way c-bet collapses to 22.0% (five callers makes blasting nearly unprofitable), while Squid v3 sustains at 46.7%. The squid motivation overrides the fold-equity math at the extreme because Cash's baseline drops so fast that even a modest Squid incentive produces a large positive delta.

The reversal at 4-way and recovery at 5-way happens because Cash baseline collapses faster than Squid motivation with additional players. Do not treat this as a simple "Squid delta shrinks with more players" rule. Instead, treat the multiway findings as directionally informative at each specific player count.

Texture within multiway. The 4-way cross-texture testing showed the same texture split as heads-up. Dry rainbow boards (K72r, K94ss) and connected boards (T98, 543) follow their respective HU directions at reduced magnitude. M4 exception boards (654, 765) show further negative deltas in multiway, consistent with the BB-range-advantage story getting amplified when additional defenders also carry Squid-widened connector hands.

BTN-opens-SB-calls (BTN-SB-BB 3-way). This configuration was previously excluded from coverage as "non-typical equilibria" in v1.2.2. The v1.3.0 revisit found a clean position × texture split — not anomalous behavior. On K72r, BTN 3-way delta is +24.1pp (larger than CO HU, consistent with BTN's stronger positional fold equity as the last in-position player). On T98, BTN 3-way delta is −14.0pp (reverses, larger magnitude than CO HU). BTN as the in-position opener amplifies both directions relative to CO sandwiched between BTN and BB.

Scope note. Multiway postflop c-bet behavior at val ≠ 3 is not tested. The 4-way and 5-way findings are at val=3 only. Do not extrapolate player-count patterns to other val levels.

What's next

Three research priorities would close the largest remaining gaps:

• Resolve M7's adversarial alternative via a new differentiating prediction. The M4-board probe test (v1.5.0) did not separate M7 from Alt-A. A different test is needed — possibly comparing turn barrel populations at the hand-level to isolate the "extras give up" signal directly.
• Expand MP postflop coverage. MP is the largest positional gap. A targeted MP c-bet sweep across the same board panel used for CO would close it.
• Blood Battle and Double mode pilots. Even a small-scale query set (preflop VPIP × position × val for Blood Battle) would test the M1 transfer prediction and reveal whether the accumulating-squid incentive structure produces qualitatively different behavior.

Every actionable from Parts 2–7, compressed into a single reference sheet. Each one traces back to the mechanism and data in its parent section — follow the cross-references if you want the full reasoning, the tables, or the caveats.

Measurement conditions: all findings are Classic mode, fresh state (all players start with zero squids), 100bb effective, heads-up CO vs BB unless noted. State-dependent adjustments: §2.3–§2.5.

Preflop (Part 2)

1. Every position opens wider in Squid — and the widening amplifies toward late position. At val=3, roughly add +8pp for UTG/MP, +15pp for CO, +24pp for BTN. SB saturates near 100%. At higher val, every position moves further wide. See §2.1.

2. Limping is not a leak. BTN limps 1% — wait, let me re-check. BTN limps 30.2% at val=3. CO limps 15.5%. SB limps 98.3%. These are equilibrium frequencies, not mistakes. Counter by raising from BB with a wider 3-bet range. See §2.2.

3. If you already hold a squid, play closer to Cash. Your squid-equity term drops to zero once you're safe — your range is driven entirely by chip EV. Tighten further when more opponents are no-squid (they defend wide, so your fold equity shrinks). The specific "safe hero at 0 desperate opponents plays 26.7% (≈ Cash 28.1%)" measurement is directionally supportive, but the exact magnitude has a caveat — see Part 2 §2.3.

4. Count the squids before every decision. The spread between hero's widest and tightest VPIP — desperate with 3 safe opponents (88.8%) vs safe with 3 desperate opponents (12.9%) — is 75.9 percentage points. Nothing else in poker theory produces that kind of strategic swing from a single game-state variable. Ask two questions: "Am I safe?" and "How many safe opponents do I face?" The answers set whether you widen or tighten. See §2.4.

5. Read the opener's squid state from the BB. A squid-holding opener has a stronger range than a fresh one — they have no penalty pressure to open marginal hands. Tighten your 3-bets against a squid-holder; widen them against a fresh opener. BB defense vs a has-squid CO drops 14.7pp; the 3-bet rate drops 23.9pp. See §2.5.

BB Defense (Part 3)

6. Defend almost everything from the BB. At val=3 vs a CO 2.5bb open, BB defends 95.8%. At val=10, it's 100%. Bluff-catch hands that would be auto-folds in Cash — K4o, J6o, low offsuit gappers — become mandatory calls. See §3.1.

7. BB's added defenders are junk. 82% of the hands BB adds to its Cash→v1 defense range are offsuit junk. 17% are suited junk. 1% are suited connectors. Premium and strong categories were already defending 100% in Cash — they don't grow. This compositional fact drives the flop c-bet mechanisms. See §3.2.

8. MDF does not apply in Squid. In Cash, BB systematically underdefends MDF by 7–13pp against narrow openers. In Squid at val=3, BB overdefends by +39.2pp vs a CO 2bb open. The squid-equity cost of folding pushes defense well above the Cash break-even threshold. Against wide openers like SB, BB overdefends MDF even in Cash — so the actual pattern is that Squid makes BB overdefend against every opener. See §3.3.

Flop C-Bet (Part 4)

9. Dry rainbow, paired, and A-high boards: c-bet almost everything. Cash frequencies of 65–86% rise to 91–99% in Squid at val=3. BB's defending range is loaded with offsuit junk that has no equity on these textures. Use sizes in the 2.5–3.5bb range. See §4.1.

10. The mid-connected exception: 654, 765, 876r. These three boards — and only these three — show negative c-bet deltas in Squid single-raised pots. CO c-bets less than in Cash because BB's added defenders (low connectors, small pocket pairs) actually hit these boards hard. Range advantage flips to BB. Check back more, including your premiums. The direction is negative at every tested val; the strength ranking among the three boards is val-dependent — cite the direction, not a specific ordering. The exception does not apply to 543, 432r, 987r, or T98. See §4.2.

11. Monotone boards: bet aggressively. The intuition says "monotone protects BB via flush draws." The data says the opposite. K94ss goes from 32.2% → 86.9% (+54.7pp). 652ss goes from 47.5% → 93.2% (+45.7pp). BB's Squid-added range on monotone boards is 82–87% offsuit junk with zero flush potential — the flush-carrying hands were already defending in Cash. The c-bet catches unimprovable junk. See §4.3.

12. Slow-play for structural reasons, not for pot control. A slow-play motivated by structural range danger — KK on K94ss where KK has no spade blocker, or AA on 765/876r where range advantage flips to BB — survives into Squid. A slow-play motivated by generic pot control — AA on T98, AA with the ace of spades on K94ss — collapses. Cash: AA bets T98 62%. Squid: 89%. See §4.4.

13. The Cash "protection betting is overvalued on 864" theory reverses cleanly. AA on 8h6d4h: Cash bets 0.3%. Squid at val=3 bets 47.4%. At val=10, 98.9%. BB's wider range has more non-draw junk that folds, and the penalty cost of surrendering equity through free cards compounds. Bet AA on low/middle-connected dry boards in Squid. See §4.5.

14. The Cash non-monotonic blocker logic (KK 2%, 99 98%, 88 16%) flattens out. In Cash on A-high boards, pocket pair bet frequencies are all over the map — KK checks because it blocks top pair, 99 bets because it's a set, 88/77 check because they're weak underpairs. In Squid at val=3, every pocket pair from KK to 77 bets between 70% and 100%. Penalty pressure overrides blocker reasoning. See §4.6.

15. Overbet usage grows from near-zero to about 5% of flop bets. Cash overbets the flop 0.09% of the time. Squid at val=3 overbets roughly 50–60× more often on dry rainbow and monotone boards. About 5% of your c-bets on K72r/K94ss should be overbets. See §4.7.

Later Streets (Part 5)

16. Barrel less on the turn after a flop c-bet gets called. Despite wider flop c-betting, CO fires the turn less in Squid. On K72r + blank turn: Cash 58.2% → Squid 49.0% (−9.2pp). On K72r + ace turn: Cash 74.5% → Squid 61.1% (−13.4pp). The one exception is when the turn pairs the board — K72r + king turn goes from 22.2% → 31.5% (+9.3pp). Give up more bluffs on the turn; keep the value barrels. See §5.1.

17. Delayed c-bet more after checking the flop. When CO checks the flop, BB's range doesn't get filtered by a c-bet — it's still bloated with Squid-defense junk. A turn bet catches that junk unimproved. K72r + blank turn after a flop check: Cash 65.9% → Squid 82.7% (+16.8pp). T98 + blank turn: Cash 42.7% → Squid 55.2% (+12.5pp). See §5.2.

18. Probe less after IP check-backs. BB probe after CO checks flop on K72r + blank: Cash 35.4% → Squid 27.6% (−7.8pp). T98 + blank: Cash 55.7% → Squid 49.3% (−6.4pp). The directional finding — probe drops in Squid — is reliable. The independent mechanistic story behind it is less certain and may simply be the wider-range effect from the flop. See §5.3.

19. Limped pots: play cautiously postflop. Once both players limp, neither has a clearly stronger range. BB bet frequency drops sharply — K72r: Cash 69.6% → Squid 51.4% (−18.2pp). T98: Cash 58.1% → Squid 37.8% (−20.3pp). 543: Cash 23.1% → Squid 9.0% (−14.1pp). See §5.4.

20. Facing a check-raise: re-raise less, flat more. CO's re-raise frequency on K72r facing BB's check-raise drops from 42.5% in Cash to 5.6% in Squid (−36.9pp). Flat the marginal value; only re-raise the top of your range. Note: the older "fold more" direction does not hold on the current model — CO actually folds less in Squid, shifting volume to call. See §5.5.

21. River play is polarized — overbets for value, fewer but bigger bluffs. On K72r + blank turn + blank river: Cash fires 6.2% at 16.5bb avg. Squid fires 57.1% at 35.1bb avg. CO's continuing range is narrow and value-heavy; BB's is wider and bluff-catcher-heavy. Use overbets on dry-board blank runouts. See §5.6.

Hero-Last and Desperation Polarization (Part 6)

22. Hero-last: raise big pairs, fold small pairs, and don't limp. Hero-last enters 88.8% of hands but limps only 2.4% — the solver raises almost everything playable. There's a sharp raise-vs-limp threshold in the pocket pairs: raise the big pairs, fold the small ones. On the current model, the threshold sits around 88/77 at val=3. Full details in Part 6.

3-Bet Pots (Part 7)

23. The mid-connected exception reverses in 3-bet pots — c-bet 765/654/876r aggressively. The SRP "check back" advice on these boards does not apply in 3BP. BB's 3-bet range is AA–TT, AK, AQs, KQs — it doesn't contain 54o, 65o, 76o, or small pairs. Without those hands, 765 no longer has a BB range advantage. CO's 3BP calling range has TT–QQ as overpairs that dominate. SRP 765 Cash→v3: −7.6pp. 3BP 765 Cash→v3: +0.9pp. See §7.1.

24. 3BP c-bets on dry boards are even more automatic than SRP c-bets. CO's Cash baseline in 3BP is lower (more selective), so there's more headroom for penalty pressure. K72r Cash→v3 in SRP: +14.5pp. In 3BP: +28.0pp. KK5 SRP: +18.3pp. 3BP: +32.3pp. See §7.2.

25. On A-high boards in 3-bet pots, c-bet less. BB's 3-bet range actually connects with A-high boards — roughly 35% of 3-bet hands hit top pair or better on A94r. Fold equity collapses. A94r Cash→v3 in SRP: +33.5pp. In 3BP: only +15.7pp. Overall bet frequency drops from 98.4% (SRP) to 62.4% (3BP). See §7.3.

How to use this page

• Takeaway 10 (mid-connected exception) has strict scope bounds. It applies to 654, 765, and 876r in single-raised pots only. It does not apply to 543 (+2.4pp), T98 (+25.5pp), 432r (+12.6pp), or 987r (+3.9pp) — those boards all show positive deltas. And it reverses in 3-bet pots — c-bet aggressively on these three boards in 3BP (Takeaway 23).
• Takeaway 4 (count the squids) is the prerequisite for everything else. Every finding in Parts 2–7 is measured in fresh state. When hero is safe or opponents are safe/desperate, ranges shift dramatically — up to 75.9pp of VPIP swing. Apply the state-awareness adjustment from §2.3–§2.5 before applying any other takeaway.
• Takeaway 16 (barrel less on the turn) has a king-card exception. When the turn pairs the top card of the board — king on K72r — CO actually barrels more in Squid (+9.3pp). The "barrel less" direction applies to blank and non-pairing turns.

Provenance

• Behavioral data and deltas: squid-deltas.md (2,549 queries across trained val × position × board × state)
• Mechanism evidence and causal stories: hypotheses-and-mechanisms.md, causal-explanations.md
• Game rules (source of truth): GAME-RULES.md — Classic mode literal rules
• All findings: Classic mode, 6-max, 100bb, fresh state unless noted