Squid Classic
the first strategy manual

Squid Classic is 6-max No-Limit Hold'em at 100bb deep with standard blinds, plus one rule change. The main pot winner of each hand receives a "squid" — a game-end win token. A player holds at most one squid (binary: you have it or you don't). The game continues until five of the six players each hold a squid. At that point, the sixth player — the one still at zero — is locked in as the loser, and the game terminates.

At game end, the loser pays (N − 1) × val big blinds, split evenly among the squid holders. In 6-max, that's 5 × val. The val parameter is trained at five discrete values: {1, 2, 3, 5, 10} BB. At val=3 the loser pays 15 BB total; at val=10, 50 BB.

That's the entire rule change.

Why this rule reshapes everything

In Cash NLHE, every hand is independent. Each decision is a chip-EV calculation: what's the expected value of calling, raising, or folding given opponent ranges? Nothing about past or future hands enters the math.

In Squid Classic, each hand carries a second dimension of EV — the change in your "squid equity," the probability-weighted reduction in your risk of being the game-end loser. Winning a pot gains squid equity (you're now safe, permanently). Not winning leaves you exposed — someone has to be the one player without a squid at game end, and any hand you don't win is a hand where that outcome gets slightly more likely. This forward-looking term layers on top of the standard chip EV.

The consequences propagate through every decision in the game:

• Every preflop range widens. Hands that are chip-negative to enter can still be overall +EV once the squid-equity term is added. The amount of widening 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 not too weak to play, limping dominates folding.
• Position gradient amplifies. Late positions gain more from the Squid overlay because they already had the highest chip-EV baselines in Cash. BTN and SB widen much more aggressively than UTG.
• Strategy becomes state-dependent. A safe player's squid-equity term drops to zero — they no longer need to win pots. A desperate player's term is large. Hero's optimal range depends on hero's own state AND on each opponent's state.
• Some Cash poker theories reverse. BB overdefends MDF rather than overfolding. AA becomes a protection-bet on 8h6d4h (a pure check in Cash). Pocket-pair blocker logic flattens on A-high boards.
• Late streets revert toward Cash. The squid-equity term is settled at pot completion, not per-street. Turn and river decisions return to near-Cash play because the range filter on the flop has already done its work.

What "compounds" and what doesn't

One clarification that matters, because it's easy to get wrong: the penalty does not compound per hand. At val=3, folding does not cost you 3 BB every time you fold. It costs you nothing directly. What changes is the probability that you end up as the last zero-squid player at game end — and if that happens, you pay 15 BB once, at game end, not 15 BB per fold.

The "squid equity" term is a forward-looking expectation based on that probability. It grows when opponents win pots (fewer safe seats remain); it shrinks to zero the moment you win a pot yourself. It's smooth over the course of the game, not stepwise per hand. If you've read anything elsewhere that describes Squid Classic as having a per-fold penalty or a compounding cost, that description is wrong — it's mixing up Classic mode with Blood Battle mode (a different Squid variant this manual does not cover).

A word on the label "desperate"

In this manual, "desperate" means no squid — the player still at risk of being the loser. "Safe" means has squid — the player who cannot be the loser. Some of our internal research notes used the opposite convention for a while (calling squid-holders "desperate") because they inherited a framing that described the game as a per-fold penalty; under that framing, squid-holders would be the ones carrying the most accumulated cost. That framing was wrong. Squid is a win token, not an accumulated loss, so squid-holders are the safe ones. The data in every chart and table in this manual is interpreted under the corrected labels.

Squid Classic changes the preflop math in a specific way. Every hand is still a chip-EV decision, but it now carries a second term: the change in your chance of ending the game as the one player without a squid. Win pots and that chance goes to zero. Don't win pots and the chance stays non-zero — and someone has to be the loser. That forward-looking "squid equity" term is what moves ranges.

The size of the move depends on three things: the val parameter (how big the game-end payout is), your own squid state, and the squid state of every opponent at the table. This part catalogues what the solver does across all three dimensions, plus how the BB reads the opener's state when deciding how to defend.

2.1 — Every position widens. The gradient amplifies.

Here's the first thing the solver does differently in Squid Classic. Same positions, same stack depth, same rake — the only thing added is the chance to win a squid at the end of each hand.

Preflop VPIP by position at every trained val. "Cash" is standard NLHE (no squids). The val parameter is the game-end payout per squid, trained at {1, 2, 3, 5, 10} BB.

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

Four things jump out:

The button plays two out of every three hands at val=3. BTN VPIP is 67.1% — up from 43.3% in Cash. At val=10 it's 89.3%. You're not deviating from standard ranges; the ranges themselves have moved.

The small blind stops folding. SB goes from 57.9% (Cash) to 99.6% at val=3 and saturates at 100% by val=10. Whatever SB has been dealt, it's entering the pot.

The widening is biggest in late position. UTG adds 8.4pp at val=3. BTN adds 23.8pp. SB adds 41.7pp. Late positions already had the highest chip-EV baselines in Cash — when the squid-equity term layers on top, it compounds most with positions that already had the best starting point.

The position gradient is preserved in direction. Cash runs UTG 17% → BTN 43% → SB 58%. Squid v3 runs UTG 26% → BTN 67% → SB 99.6%. Same monotonic shape, amplified magnitudes.

2.2 — Limping comes back. SB limps almost everything.

In modern Cash NLHE, open-limping is dominated. The solver raises or folds; limping gives up initiative without buying anything back. Squid changes that — because the squid-equity term doesn't require you to win the pot with a raise, just to win the pot.

Preflop limp % by position. SB limp % is "complete + check" since SB has already posted 0.5bb.

Source: squid-deltas.md lines 315–319, 787

Two numbers are the headline. SB limps 98.3% of hands at val=3. SB barely ever raises in Squid — the limp (plus hoping to win the pot cheaply) dominates every other action for essentially the entire range. And at val=10, 99% of CO's entered hands are limps (75.5% limp out of 76.4% VPIP). As the game-end stakes grow, CO pivots from "widen by raising more" to "widen by limping more."

2.3 — When hero is safe, ranges tighten toward Cash (suggestive, not a clean control)

M1 ("every hand is a chance to win a squid, so ranges widen in pursuit of squid-equity") is supported by two robust pieces of measured evidence in the sections above: the val-scaling on CO (Cash 28.1% → v3 42.9% → v10 76.4%, measured at legal game states) and the position-gradient amplification (UTG narrows, BTN and SB widen more aggressively). Those are what make the mechanism testable.

There's a third piece of evidence that's often cited as the "critical control" for M1 but deserves a methodology asterisk when you look at what's actually being measured. The research queried hero's VPIP at a specific per-seat squid configuration where hero holds a squid and every one of hero's five opponents also holds a squid. At that configuration, the solver responds:

Hero-has CO at val=3, 0 "desperate" opponents: VPIP = 26.7% (Cash baseline 28.1%; delta 1.4pp).

Source: squid-deltas.md line 163

Taken at face value, this number looks like a clean confirmation: hero plays near-Cash when surrounded by safe opponents, which would directly confirm that the widening in §2.1 is driven by hero's own squid-equity incentive rather than a general "Squid mode" effect.

The asterisk: this configuration is not a legal in-game state. Classic mode allows at most N − 1 = 5 squids in play at any moment (once the fifth is distributed, the game ends and the zero-squid player is the loser). "Hero has 1 squid + all 5 opponents each hold 1 squid" sums to 6 squids, which violates the rule. The source acknowledges this at squid-deltas.md:169:

a state the training pipeline fed to the model as an input feature even though it may not correspond to a legal in-game state under the strict N−1 total squids rule

The individual per-seat squid_count feature values (0 or 1) are each in the training distribution — the model has seen seats at both values thousands of times. What may not have been in training is the combination of six seats simultaneously at squid_count = 1 during a live hand. Depending on how the training pipeline was structured — which R21 audit open-question 5 flags as unresolved — the model's response at this configuration is either a learned policy for synthetic per-seat configurations that the pipeline injected as input features, or an extrapolation into a game state it never actually played through.

2.4 — State dynamics: who's safe, who's desperate, and how hero reacts

This is the biggest departure from Cash theory. In Squid, hero's optimal range is not just a function of cards + position — it's a function of cards + position + hero's own squid state + each opponent's squid state.

A quick terminology note before the tables. "Safe" means a player who already has a squid — they cannot be the game-end loser. "Desperate" means a player without a squid — they're still at risk. The tables below use these labels throughout.

Table A — Hero desperate (no squid), CO position at val=3.

Source: squid-deltas.md lines 150–160

Table B — Hero safe (has squid), CO position at val=3.

Source: squid-deltas.md lines 163, 379–384

State legality note: Classic mode has at most N−1 = 5 squids in play at any moment. "Hero has squid + N desperate opponents" implies total squids = 1 (hero) + (5−N) safe opponents = 6−N. The 0-desperate row requires 6 squids (impossible); the 1-desperate row is exactly 5 squids (the terminal game-end state); the 2- and 3-desperate rows are 4 and 3 squids respectively, which are legal mid-game states. The 2- and 3-desperate rows are the cleanest measurements in this table; the 0- and 1-desperate rows are either non-physical or at the game-boundary and should be read with the §2.3 caveat in mind. The data pattern "hero tightens as desperate-opponent count grows" is still directionally supported by the legal rows alone.

The pattern in each table is different but internally consistent:

When hero is desperate, more safe opponents means hero plays wider. Why: safe opponents can afford to fold, so hero has fold equity against them. Hero uses that fold equity to take down pots and grab a squid. At hero-last (3 safe opponents), hero enters 88.8% of hands — hero has to win this pot soon or become the loser, and the safe opponents will actually fold to aggression.

When hero is safe, more desperate opponents means hero plays tighter. Why: desperate opponents won't fold to aggression (they need the pot), so hero has no fold equity. At the same time, hero doesn't need to win this pot — hero is already safe. The rational move is to play only strong hands and realize chip EV, not burn chips on marginal spots against opponents who will call anything.

When hero is safe and nobody is desperate, the game is Cash. Hero-safe with 0 desperate opps plays 26.7% VPIP, within 1.4pp of Cash 28.1%. The squid-equity term contributes nothing on either side of the table.

2.5 — BB reads the opener's state too

The per-seat squid awareness runs in both directions. BB adjusts its defense based on whether the CO opening has a squid or not.

BB defense vs CO 2.5bb open, val=3.

Source: squid-deltas.md lines 328–331

A squid-holding CO has no squid-equity pressure to open marginal hands — the widening effect from M1 is off for that seat. So a safe CO's opening range is effectively Cash-shaped (tighter and stronger than a desperate CO's Squid range). BB reads this correctly and defends less wide against it.

The 3-bet drop (−23.9pp) is larger than the raw defense drop (−14.7pp). Against a wider opener, 3-betting picks up fold equity from the marginal hands in the opener's range; against a tighter one, there are fewer marginal hands to fold out and more value hands that will 4-bet back. BB correctly shifts from "3-bet to punish width" to "call or fold, don't reraise light."

The mechanism registry for preflop

Three mechanisms drive the preflop patterns in this part. All three cleared the multi-checkpoint stability check in Round 17. Naming reflects the R21 rebuild, which re-derived each mechanism from the literal Classic mode rules rather than an earlier inverted framing.

Source: hypotheses-and-mechanisms.md §§M1, M2, M6 · causal-explanations.md §§M1, M2, M6

M8 (Desperation Polarization) — the mechanism behind the hero-last row's raise-everything behavior — is covered in depth in Part 6 because it's specifically about pocket-pair thresholds and hand-level raising structure, not about whether to enter.

The val parameter is a dial, not a switch

One more view of the same data. The val parameter controls the game-end payout, and CO's VPIP scales smoothly and concavely with it across all five trained values.

Val sensitivity on CO preflop opening. Cash is the no-squid baseline; val=0 is unsupported.

Source: squid-deltas.md Table 1 line 68

VPIP grows concavely with val. Big jumps at low vals (Cash → val=3 adds 14.8pp); smaller jumps at high vals (val=5 → val=10 adds only 20.3pp despite the val doubling). The squid-equity term matters most at low val where it's pushing marginal hands from fold to play; at high val, most hands are already in the play region and the extra effect pushes them from raise to limp (which is covered in §2.2).

The five practical preflop takeaways

1. Every position plays wider. At val=3, expect roughly +8pp for UTG/MP, +15pp for CO, +24pp for BTN, and SB near 100% entry. At higher val, every position moves further wide.
2. Limping is equilibrium, not a leak. BTN limps 30%, CO limps 15%, SB limps 98%. When you see it, it's the solver, not a weak player. Counter by 3-betting from BB with a wider range to punish limped ranges.
3. Safe hero plays Cash ranges. If you already have a squid, don't reflexively widen. The widening effect is specifically about getting a squid — once you have one, the reason to widen is gone.
4. Count the squids before every decision. Hero safe + 3 desperate opponents → tighten to 12.9%. Hero desperate + 3 safe opponents → widen to 88.8%. Same cards, completely different strategy.
5. Watch the opener's state from the BB. A squid-holding opener has a Cash-shaped (tighter) range; defend at Cash frequencies, tighten your 3-bets. A fresh opener has a widened Squid range; defend everything and 3-bet wide.

The wider preflop opens from Part 2 cascade into BB's defense math. When the button plays 67% of hands in Squid (up from 43% in Cash), BB is facing a wider, weaker range — and BB's own cost of folding now carries a forward-looking squid-equity term on top of chip EV. Both effects push in the same direction: BB defends much, much wider.

The consequences are large enough to break one of the cleanest findings in Cash poker: the "BB overfolds MDF" result that's been standard theory for years. In Squid, that direction flips.

3.1 — BB defends almost every hand

The second-largest delta in the entire preflop-to-flop tree — bigger than every individual preflop position shift and second only to M5's monotone-board c-bet effect — is BB's defense expansion.

BB defense vs 2.5bb opens, by opener position × val. "Defense" here means call-or-raise (any non-fold action).

Source: squid-deltas.md Table 2 lines 77–89

The Cash → val=1 step alone is +24 to +30pp across every opener — that's the single largest "switch to Squid at minimum penalty" effect in the research. By val=3, BB is defending 85%+ against every position. By val=5, defense saturates near 100% and stays there through val=10.

The headline: BB vs CO at val=3 is 95.8% defense — up from 51.8% in Cash. That's a +44 percentage point delta at the standard test configuration. BB is defending nearly every hand it's dealt.

This is M1 applied on the other side of the preflop raise. BB faces the same squid-equity math as the opener — folding forgoes the chance to win this pot and gain a squid. BB also has the structural advantage of already having 1 BB invested in the pot and closing the action heads-up, which makes its chip cost to defend small. Both factors combine to push the defense threshold well below what Cash theory says it should be.

3.2 — What BB adds is offsuit junk

Here's the finding that's easy to miss but that matters for everything that happens on the flop. When BB widens its defense range in Squid, the hands it adds are overwhelmingly offsuit junk, not marginal playable hands.

BB defense composition by hand category, vs CO 2.5bb open. Reach is measured in combos (total preflop range = 1326 combos).

Source: squid-deltas.md Table 9 lines 423–437

The pattern is almost entirely one-dimensional. Every "quality" bucket — premium, strong, medium pair, suited Ax, suited broadway, offsuit broadway — already defends 100% in Cash. They can't grow. The suited connector and suited junk buckets move a small amount (suited connector +6 combos Cash → v1; suited junk +74 combos). Offsuit junk does essentially all of the widening. From 102 combos in Cash to 463 at val=1 to 730 at val=3 to 815 at val=10 — almost the entire 816-combo offsuit junk pool is eventually defending.

Cash → val=1 growth decomposition:

• Total defending reach: 524 → 965 combos (+441 combos added)
• Offsuit junk: +361 combos (82% of the added hands)
• Suited junk: +74 combos (17%)
• Suited connector: +6 combos (1%)
• All other categories: 0 combos added (already at max)

Cash → val=3 growth decomposition:

• Total defending reach: 524 → 1240 combos (+716 combos added)
• Offsuit junk: +628 combos (88% of added hands)
• Suited junk: +82 combos (11%)
• Suited connector: +6 combos (1%)

Source: squid-deltas.md lines 439–450

Why this matters for the flop. When CO c-bets on any dry, paired, or A-high board, the new-defending hands (offsuit junk like K4o, J6o, Q8o, low gappers) are exactly the hands that can't make pairs or draws most of the time. They were forced into the defense range by M1's squid-equity term, not by hand strength. On the flop, they fold. This is the compositional signature that drives Mechanism M3 (fold-equity amplification on standard boards) and Mechanism M5 (non-flush fold equity on monotone boards). Parts 4 and 5 cover the flop-side consequences in detail; this section is the reason they happen.

3.3 — BB overdefends MDF. The Cash "BB overfolds" finding reverses.

One of the cleanest and most-cited findings in modern Cash NLHE theory is that the big blind systematically overfolds relative to the MDF (minimum defense frequency) formula. Facing a bet of size R, pure chip-EV math says BB should defend at least 1.5 / (R + 0.5) of its range to prevent the opener from auto-profiting with any two cards. Measured solver data in Cash shows BB underdefending that threshold by 7–13pp across all common raise sizes.

In Squid, the direction flips. BB overdefends MDF by roughly 40 percentage points at val=3.

BB vs CO, MDF deviation table:

Source: squid-deltas.md Table 18 lines 681–695

In Cash, the deviation is consistently negative (underdefense) across all raise sizes from 2.0bb to 5.0bb — that's the "BB overfolds MDF" finding. In Squid v3, the deviation flips to positive (overdefense) and runs from +39.2pp (at 2.0bb) to +43.5pp (at 2.5bb) depending on raise size — all more than 39 percentage points above MDF. The direction has completely reversed.

Why the Cash finding existed in the first place. MDF is a pure chip-EV formula: it assumes the opener's range is random (all-bluff) and asks what defend frequency prevents auto-profit. But opener ranges are not all-bluff — they're value-heavy. Against a value-heavy range, a strictly MDF-based defense calls too many hands as bluff-catchers against too few bluffs. BB's correct defense against a realistic narrow-opener range (UTG/MP/CO) is below MDF, which is exactly what Cash solvers show.

Why Squid flips it. Two independent effects add up to push BB's defense well above MDF:

1. The opener's range is much wider in Squid. M1 widens every preflop range, so the opener has many more bluff-candidate hands in range. Against a wider range, MDF is no longer overfit to value — it's now a lower bound that BB's correct defense exceeds.
2. Folding carries a forward-looking squid-equity cost. BB's fold decision isn't just losing the already-invested 1 BB; it's also forgoing the chance to win this hand's main pot and collect the squid. That cost is large at higher val, and it raises BB's break-even defense threshold above MDF.

Both effects push the same direction. Squid v3+ BB should defend well above MDF vs every opener.

The R17 caveat: Cash "BB overfolds" is position-dependent

Before you go tell your friends that Squid reverses a universal Cash theory, here's the refinement Round 17 added. The Cash "BB overfolds" finding is specific to defending against narrow openers (UTG/MP/CO). Against wide openers, BB already overdefends MDF in Cash, before Squid enters the picture.

BB vs SB, 2.5bb open (SB is the widest opener in Cash at 57.9% VPIP):

Source: squid-deltas.md Table 22 lines 798–805

Against SB in Cash, BB's defense is already +20.9pp above MDF. The crossover between "BB overfolds" (narrow openers) and "BB overdefends" (wide openers) happens somewhere between BTN and SB. Squid just amplifies the overdefense direction across all positions — it doesn't create the overdefense pattern from nothing.

Refined statement: In Cash, BB defense-vs-MDF direction depends on opener width — underdefend against narrow openers, overdefend against wide openers. In Squid v3+, BB overdefends against every opener, because every opener has a wider range and because the squid-equity cost of folding pushes defense higher. The clean reversal is only clean against narrow openers; the rest is amplification.

The mechanism registry for Part 3

Source: hypotheses-and-mechanisms.md §M1 / B2 transfer table · causal-explanations.md §M1

The four practical BB-defense takeaways

1. Defend almost everything at val=3. At 2.5bb opens, BB's correct defense is 85–95% depending on opener position. At val=5+, defend literally everything. MDF is a Cash theory and does not apply.
2. Your added hands are junk — and that's fine preflop. Offsuit hands you'd instantly fold in Cash (K4o, J6o, Q8o, T7o, low offsuit gappers) become mandatory calls in Squid. Don't second-guess this — the math isn't about the hand, it's about the squid-equity cost of folding.
3. Don't second-guess yourself on the flop, but remember what you defended. The same junk that's a mandatory call preflop folds to flop pressure because the squid-equity term is settled once the pot is won. If CO c-bets and you have K4o on a dry K-high board, the call is correct; if CO c-bets and you have K4o on 765ss, the fold is correct. Parts 4 and 5 cover the board-specific math.
4. The B2 "BB overfolds MDF" Cash rule is gone in Squid. It was also never fully universal even in Cash — it applied to narrow openers only, and wide-opener BB defense in Cash was already above MDF. In Squid, every position is above MDF.

The flop is where the biggest Squid-specific deltas in the research live. The preflop widening (Part 2) and the BB defense expansion (Part 3) both feed into the flop, and what CO does with the c-bet depends heavily on board texture. The patterns split into four texture categories driven by mechanisms M3, M4, M5, and a texture-dependent split in the Cash slow-play theory G7.

On top of those mechanism-driven shifts, three Cash poker theories that hold in standard NLHE behave very differently in Squid: G8 (protection betting AA on dry middle boards) cleanly reverses, G3 (pocket-pair non-monotonicity on A-high) flattens out, and overbet usage on the flop grows from essentially never to ~5% of bets on dry and monotone textures.

This part walks through all of it — seven short sections, seven takeaways.

The 12 canonical test boards at a glance — CO flop c-bet frequency in Cash vs Squid val=3. Subsections 4.1–4.3 cover the mechanism-driven groups (dry/paired/A-high, M4 exceptions, monotone) in detail; the two "other connected" boards (543 and T98) are summarized here for completeness and covered in prose later.

Source: squid-deltas.md Table 3 lines 96–107

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

On standard "easy to c-bet" textures, the Squid c-bet frequency goes from already-high to near-automatic.

Cash vs Squid v3 c-bet frequencies on dry rainbow, A-high, and paired boards. CO vs BB, single-raised pot, 100bb.

Source: squid-deltas.md Table 3 lines 96–107

The pattern is consistent: Cash frequencies in the 65–85% range rise to 91–99% in Squid v3. The largest delta is on A94r: +33.5pp, because Cash c-bets are suppressed by the ace blocker logic (BB has many Ax hands that the c-bet won't fold) and Squid removes that constraint by widening BB's range with non-ace junk that folds.

Mechanism: M3 (Fold Equity Amplification). This is the payoff from the Part 3 compositional finding. BB's defending range in Squid is 82% offsuit junk — hands with no pair, no draw, no equity. On any dry rainbow, paired, or A-high board, that junk doesn't connect. CO's c-bet folds it out. The wider the BB defense range, the more the c-bet frequency grows, and the texture determines how cleanly the new junk folds.

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

Three specific boards break the M3 pattern entirely. On 654, 765, and 876r in single-raised pots, CO c-bets less in Squid than in Cash — including with premium hands.

Cash → val=1 delta on the M4 exception boards. The effect shows at the minimum Squid penalty and persists through higher vals.

Source: squid-deltas.md Table 27 lines 942–951

Even premium hands slow down. On 765 specifically, the slow-play extends all the way up to the top of CO's range: the Premium (AA–JJ) bucket bet frequency drops from 36% (Cash) to 20% (val=1) — a −16pp drop on CO's strongest hands. CO's nuts are checking more in Squid because the board is dangerous for its range, not because the nuts are less valuable.

Source: squid-deltas.md lines 524–528

Mechanism: M4 (Range Advantage Reversal). BB's Cash→v1 additions on 654/765/876r are disproportionately low connectors and small pairs — 54s, 65s, 76s, 87s, 86s, 97s, plus 22–77. These are exactly the hands that flop two pair, straights, or strong draws on mid-connected textures. Meanwhile, CO's opening range leans toward high cards (broadway, Ax, pocket pairs mostly bigger than the board), which don't improve on 654/765/876. BB's range advantage flips from "I have fewer strong hands" in Cash to "I actually have more strong hands than CO" in Squid. CO responds by checking back.

Scope bounds — and these matter, because M4 is the only Squid mechanism with a tight scope qualifier:

• Only 654, 765, 876r. Other mid/low connected boards do NOT show the reversal: 543 is +2.4pp Cash→v1, 432r is +12.6pp, 987r is +3.9pp, T98 is +25.5pp. The effect is specific to the three boards where BB's widened Squid range lines up with straight-or-better potential AND CO's high-card range lacks the equity to contest.
• SRP only. In 3-bet pots, M4 reverses — BB's 3-bet range is narrow and polarized (AA–TT, AK, AQs), and does NOT contain the low connectors that drive the mechanism in SRP. On 765 in a 3BP, the Cash→v3 delta is +17.5pp — the exact opposite direction. Same board, same val, different action history flips the mechanism.

Source: squid-deltas.md 3BP comparison lines 862–889

4.3 — Monotone boards: bet aggressively, despite the intuition

Here's the finding that surprises everyone who looks at it. The most obvious instinct on a monotone board (three cards of one suit) is that BB's defense range now has many flush draws, so CO should c-bet less. The data says the opposite — monotone boards produce the largest positive c-bet deltas in the entire research.

Cash vs Squid c-bet frequencies on monotone boards, CO vs BB SRP.

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

K94ss: Cash 32.2% → Squid v3 86.9% = +54.7pp. This is the largest positive delta in the entire research corpus — bigger than every preflop VPIP shift, bigger than every BB defense expansion, bigger than every other flop texture.

Why the intuition is wrong: BB's Squid-added defense range on monotone boards is 82–87% offsuit junk with no spade — the hands that would carry flush potential (suited connectors, suited broadways) were already defending 100% in Cash. They don't grow. What grows is the non-flush junk that the monotone texture doesn't help at all. When CO c-bets K94ss in Squid, BB's added-range hands are in the worst possible shape: they have no pair, no draw, no flush blocker, no nothing.

Source: squid-deltas.md lines 469–474 hand-level K94ss composition

Mechanism: M5 (Monotone Non-Flush Fold Equity). The texture that looks protected by draws is actually the texture where CO has the most fold equity, because the hands BB added to its defense range can't use the draws. The flush-carrying hands were already in BB's Cash defense range and are unchanged. The monotone texture is more folding-profitable than the naive intuition says, not less.

This is also the cleanest validation finding for M3's general principle that the shape of what BB added matters more than the shape of the board. On standard boards, offsuit junk doesn't hit. On monotone boards, offsuit junk also doesn't hit, but you'd guess the opposite because you're pattern-matching on "monotone = lots of flushes."

4.4 — Slow-play theory (Cash G7) splits by texture

In Cash, solver theory prescribes slow-playing premium hands on certain wet textures for pot-control reasons — the idea is that when the board is dangerous, betting invites raises and isolates against better hands, so checking is higher EV. In Squid, this Cash rule splits into two cases depending on why the slow-play existed.

Structural slow-plays survive. A slow-play motivated by structural range danger (the board is bad for your range as a whole, not just your specific hand) still makes sense in Squid:

• KK on K94ss (monotone, KK doesn't have a spade blocker): Cash 0% bet → Squid v3 5.5% bet. Still slow-plays almost entirely. KK is strong but can't block the nut flush draw, and the wet monotone texture doesn't help.
• AA on 765/876r (the M4 exception boards): Cash 0.2% bet → Squid v3 1.5% bet. Still slow-plays. This is the same M4 mechanism from 4.2 — AA can't get value from a BB range that's strong on the board.

Pot-control slow-plays collapse. A slow-play motivated by generic "I'm ahead, protect stack EV" pot control disappears in Squid because the squid-equity calculation now rewards getting chips in the pot while you have the lead:

• AA on T98 (wet but no structural problem — T98 is not in the M4 scope and AA has no blocker issue): Cash 62% bet → Squid v3 89% bet. Slow-play disappears.
• AA on K94ss with the Ace of spades (AA now blocks the nut flush and has both structural and value reasons to bet): Cash 67% bet → Squid v3 97% bet. Slow-play disappears.

Source: squid-deltas.md lines 615–623 G7 slow-play splits

4.5 — Protection betting AA on 8h6d4h (Cash G8 reverses)

In Cash, solver theory says betting AA on 8h6d4h is overvalued. The expected loss of betting vs checking is roughly 7% of pot — small, but consistent. The Cash rationale: BB's calling range on 864 is draw-heavy, betting isolates against a range that has lots of equity, and the strong value hands you'd normally want to fold won't fold to a small c-bet anyway. So check, realize equity, and let BB bluff the turn.

In Squid, this theory cleanly reverses.

AA on 8h6d4h, CO vs BB SRP, bet frequency across val:

Source: squid-deltas.md lines 589–596

From essentially-always-check (0.3%) in Cash to essentially-always-bet (98.9%) at val=10. The reversal is clean across the val grid — every step up in val, the bet frequency rises.

Why the reversal happens. Three things change from Cash to Squid on this specific board:

1. BB's defense range is wider and junkier. Per Part 3, BB adds 82% offsuit junk to its range. On 864, those hands are mostly non-draws (overcards like Q7o, J5o, K3o). When CO bets, they fold.
2. BB's drawing hands still get free cards on check. Checking AA lets BB's straight-draws (57s, 79s, 7x, 5x) realize their equity. In Squid, the cost of those free cards is larger because BB's postflop range is also wider on subsequent streets — equity decays faster through a widened range.
3. Forgoing equity carries a squid-equity cost. Not winning this pot leaves AA's squid-equity term non-zero. Checking is no longer free — it's a non-zero-EV action under the forward-looking term.

All three effects push in the same direction. By val=10, the old Cash intuition is wrong by 98.6 percentage points.

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

In Cash, pocket pair bet frequencies on A-high boards show a classic non-monotonic pattern driven by blocker logic. KK checks almost always because it's a vulnerable overpair and KK-blockers are already ahead. 99 hits its set and bets almost always. The pairs in between (JJ, TT, 88, 77) show an irregular, non-monotonic pattern because blocker logic fights with raw strength.

In Squid v3, this pattern flattens. All pocket pairs bet 70–100%.

Pocket pair bet frequency on A-high board, Cash vs Squid v3.

Source: squid-deltas.md lines 705–716

The Cash non-monotonicity (99 high, KK and 88 low, with TT/JJ somewhere in between) collapses into "bet everything 70–100%" in Squid v3. The spread of Cash bet frequencies (2.1% to 98.1% = 96pp range) compresses into a Squid spread of (70.4% to 100.0% = 29.6pp range), and the ordering is no longer the weird blocker-driven Cash ordering — it's now mostly monotone in raw pair strength.

Mechanism: Squid simplifies the bet-check decision on A-high boards. Penalty pressure (the squid-equity cost of not winning) overrides the Cash blocker logic. The Cash rule "apply blocker math to decide whether checking overpairs protects against Ax" gets replaced by "if you have any pocket pair on A-high in Squid, it has enough equity against BB's widened calling range to bet."

4.7 — Overbet usage grows

In Cash, the solver essentially never overbets the flop. The measured frequency is 0.09% of all bets — once every ~1100 bets. In Squid, overbet usage rises to about 5% of bets on dry rainbow and monotone boards. That's roughly 50–60× more frequent than Cash.

Source: squid-deltas.md lines 752–758

Mechanism: Overbets require extreme nut advantage to be profitable — the bettor needs a range that's much stronger than the opponent's. In Cash, this condition is rarely met on the flop because both ranges contain reasonable equity distributions. In Squid, the widened BB junk range creates exactly the "extreme nut advantage" structure that overbets need. On a dry rainbow board like K72r, CO's high-card and pocket pair range is much stronger than BB's 82%-junk defense range. Overbet sizing (150%+ of pot) maximizes fold equity against the junk while charging draws correctly — and it only works because the junk is truly weak.

Overbets are still rare overall — 5% of bets is far from common — but the underlying structure that makes them correct exists in Squid and doesn't in Cash.

The mechanism registry for Part 4

Source: hypotheses-and-mechanisms.md §§M3, M4, M5

Cash poker theories that change on the flop

The seven practical flop takeaways

1. C-bet almost everything on dry rainbow, A-high, paired boards. K72r, J72r, Q83r, A94r, KK5, 772 all hit 91–99% at val=3. Use sizes in the 2.5–3.5 BB range.
2. On 654, 765, 876r in single-raised pots, check back more — including your premiums. BB's range on these textures is actually stronger than CO's. AA on 765 checks 98% of the time. But in 3-bet pots, the reversal reverses: bet 765 aggressively in 3BP.
3. On monotone boards, c-bet aggressively. K94ss, 652ss, Q73ss all hit 87–94% at val=3. The flush-draw-protection intuition is wrong for the range BB is actually defending with — it's offsuit junk without a spade.
4. Slow-play structure, not mood. If the Cash slow-play is "because the board is dangerous for my range" (KK on K94ss), keep it. If it's "because I'm ahead and want pot control" (AA on T98), bet in Squid.
5. Bet AA on 864-type boards. Cash says check for 7% EV loss; Squid says bet 98.9% at val=10. Clean reversal.
6. Bet all pocket pairs 70–100% on A-high boards. Cash blocker logic doesn't apply in Squid. KK, QQ, JJ, TT, 99, 88, 77 all bet 70–100% on A-high — no non-monotonic ordering.
7. Use overbets 5% of the time on dry rainbow and monotone boards. Cash essentially never overbets the flop (0.09%). In Squid, the widened BB junk range creates the nut advantage that overbets need.

Twenty-four practical takeaways from the full strategy manual, compressed into a single reference sheet. Each is sourced from the body of the research — for the data behind any takeaway, follow the part reference.

Status notes: Parts 1–4 are published in this draft. Takeaways from Parts 5–8 (Later Streets, Hero-Last, 3-Bet Pots, Open Questions) are included here for completeness; the parts themselves will be filled in after the initial review pass.

Preflop (Part 2)

1. Expect wider ranges at every position. At val=3, add roughly +8pp for UTG/MP, +15pp for CO, +24pp for BTN, and SB near 100% entry. At higher val, every position moves further wide. Source: Part 2 §2.1
2. Limping is equilibrium, not a leak. BTN limps 30% at val=3, CO limps 15%, SB limps 98%. When you see it, it's the solver, not a weak player. Source: Part 2 §2.2
3. If you're safe, tighten — but don't assume exactly Cash ranges. Once you have a squid, the reason to widen is gone, and hero-has ranges are consistently tighter than hero-desperate ranges across the tested configurations. The specific "safe hero at 0 desperate opps plays 26.7% (≈ Cash 28.1%)" measurement is suggestive but depends on a non-physical state configuration (6 squids > 5 max); the direction is solid but the exact "how far back to Cash" magnitude has a methodology asterisk. Source: Part 2 §2.3 — read the full caveat before applying this in a high-stakes spot.
4. Count the squids before every decision. Hero safe + 3 desperate opponents → tighten to 12.9%. Hero desperate + 3 safe opponents → widen to 88.8%. Same cards, completely different strategy. The 75.9-point spread is driven entirely by table state. Source: Part 2 §2.4
5. Watch the opener's state from the BB. A squid-holding opener has a Cash-shaped (tighter) range — defend at Cash frequencies and tighten your 3-bets. A fresh opener has a widened Squid range — defend everything and 3-bet wide. Source: Part 2 §2.5

BB Defense (Part 3)

6. Defend 95%+ at val=3 across the board. At 2.5bb opens, BB's correct defense is 85–95% depending on opener position. At val=5+, defend literally everything. Source: Part 3 §3.1
7. Your added hands are offsuit junk — and that's fine preflop, but remember it on the flop. 82–88% of the hands BB adds to its defense range are offsuit junk (K4o, J6o, Q8o, T7o, low gappers). They're mandatory calls preflop because of the squid-equity cost of folding, but they fold to flop pressure. Source: Part 3 §3.2
8. BB overdefends MDF in Squid — the Cash "BB overfolds" rule is gone. Cash: BB underdefends by 7–13pp across all raise sizes. Squid v3: BB overdefends MDF by +39.2pp (at 2.0bb open), +43.5pp (at 2.5bb), and +41.8pp (at 3.0bb). The Cash MDF formula does not apply. Caveat: the Cash underdefend is specific to narrow openers; vs wide openers (SB), BB already overdefends MDF +20.9pp in Cash. Source: Part 3 §3.3

Flop C-Bet (Part 4)

9. C-bet almost everything on dry rainbow, A-high, and paired boards. K72r, J72r, Q83r, A94r, KK5, 772 all hit 91–99% at val=3. Use sizes in the 2.5–3.5 BB range. Source: Part 4 §4.1
10. Check back more on 654, 765, 876r in single-raised pots — including your premiums. BB's range on these textures is actually stronger than CO's. AA on 765 bets 0.2% in Cash and 1.5% in Squid v3. The premium (AA–JJ) bucket average drops from 36% to 20% Cash→v1 on 765. But in 3-bet pots, the reversal reverses: bet 765 aggressively in 3BP (+17.5pp Cash→v3). Source: Part 4 §4.2
11. On monotone boards, c-bet aggressively despite the flush-draw intuition. K94ss Cash 32.2% → Squid v3 86.9% = +54.7pp (largest positive delta in the research). BB's added defense range is 82–87% offsuit junk with no spade. Same for 652ss and Q73ss. Source: Part 4 §4.3
12. Slow-play structure, not mood. Structural slow-plays survive (KK on K94ss without A♠, AA on 765 for M4). Pot-control slow-plays collapse (AA on T98: Cash 62% → Squid 89%. AA on K94ss-with-A♠: Cash 67% → Squid 97%). Source: Part 4 §4.4
13. Bet AA on 8h6d4h-type boards. The Cash G8 "protection overvalued" theory reverses cleanly. AA on 864: Cash 0.3% → val=1 20.6% → val=3 47.4% → val=5 83.4% → val=10 98.9%. Source: Part 4 §4.5
14. Bet all pocket pairs 70–100% on A-high boards in Squid. The Cash G3 non-monotonic blocker logic (KK 2%, 99 98%, 88 16%) flattens out. In Squid v3, every pocket pair from 77 to KK bets between 70.4% and 100%. Source: Part 4 §4.6
15. Use overbet sizing on dry rainbow and monotone boards. Cash essentially never overbets the flop (0.09% of bets). In Squid, overbets rise to ~5% of bets on K72r-type and K94ss-type textures — roughly 50–60× more frequent than Cash. Source: Part 4 §4.7

Later Streets (Part 5, stub)

16. Barrel less on the turn. Despite wider flop c-bet frequencies, turn barrel frequency drops −9 to −13pp across tested barrel cards. Give up weak bluffs after the flop c-bet got called.
17. Delayed c-bet more after checking the flop. Delayed c-bet is the exception in the later-streets story — it rises +12 to +17pp in Squid because checking the flop doesn't filter BB's range.
18. Probe less after IP check-backs. Turn probe frequency drops −2 to −8pp. IP's check-back range is less cleanly capped in Squid than in Cash, so BB's probe gains less fold equity.
19. Limped pots: play cautiously postflop. Limped-pot flop bets drop −14 to −20pp. Both ranges are wide and weak after a limp-limp.
20. Facing check-raise: fold more, re-raise less. CO folds +19pp more and re-raises −37pp less facing a check-raise on K72r. Once aggression is concrete, chip-EV dominates again — squid equity alone doesn't justify calling or repopping. Only one board tested so far.

Hero-Last & Desperation Polarization (Part 6, stub)

21. When hero is desperate and all opponents are safe, raise TT+ and broadway — fold 99 and below. Hero-last enters 88.8% of hands but limps only 2.4%. The pocket-pair threshold is sharp: AA–QQ raise 100%, JJ 98%, TT 73%, 99 only 5%. Polarized, not just wide. Don't limp.

3-Bet Pots (Part 7, stub)

22. C-bet 765/654/876r aggressively in 3-bet pots. M4 reverses in 3BP because BB's 3-bet range is narrow and polarized (AA–TT, AK, AQs) and doesn't contain the low connectors that drive M4 in SRP. On 765 in 3BP, Cash→v3 is +17.5pp.
23. 3-bet pot c-bets on dry boards are even more automatic than SRP. The K94ss Cash→v3 delta is +48.4pp in 3BP (vs +54.7pp in SRP). Dry rainbow boards essentially always c-bet in Squid 3BPs.
24. Check more on A-high in 3BP. BB's 3-bet range is Ax-heavy, so A-high boards connect with it. CO's c-bet frequency on A-high is LOWER in 3BP than in SRP.