PLO4 — Strategy Divergence
from Cash NLHE

Version: 2.0.0
Model: universal-dense-v4-player_20260402_150328.onnx

The headline finding: PLO4 amplifies Cash Hold'em theory in 52% of cases (27 theories), transfers it cleanly in 25% (13 theories), has one clean reversal (paired boards), and six areas that need entirely new mechanics.

Every claim here carries at least moderate evidence — model-tested plus supporting literature. No PLO4 claim reaches the highest confidence tier yet because external PLO solver coverage is limited (GTO Wizard has no PLO; MonkerSolver is paywalled). Claims upgrade as external coverage expands.

Pillar A — Equity & Ranges

All seven Cash equity theories transfer or amplify in PLO4. None reverse. Equity compression (the phenomenon where four hole cards narrow the equity gap between strong and weak starting hands) is the root mechanic — it sharpens every existing effect.

BTN board-coverage advantage widens

In Cash, the button's tight polarized range gives it a coverage edge on high-card boards. In PLO4, that edge extends further. BTN's rundown-heavy opening range covers connected boards too. BTN opens +9pp wider than Cash (52.4% vs 43.3%), which means more interaction points per texture. On Q-high and above connected boards, c-bet elevation runs +4–19pp.

What this means: On both dry high-card AND Q-high+ connected boards, assume BTN has coverage advantage. Only low-connected boards (below Q-high) flip to BB-favored.

The BRAIN framework replaces "nuts advantage"

In Cash, nut advantage is straightforward: who holds the strongest hands on this board? In PLO4, the must-use-2 rule (you must play exactly two of your four hole cards) creates non-intuitive nut boundaries. An Ace in your hand does NOT guarantee a nut flush draw unless that Ace's suit pairs with another hole card that completes the draw combination.

BRAIN — Board coverage, Range/equity advantage, Assets & gaps, Incentives, Nevermind — is the PLO4-native replacement for the simpler Cash nut-advantage check.

What this means: Before assigning nut advantage, verify the actual two-card subset that forms the draw. Don't shortcut from "I have an Ace" to "I have the nut flush draw."

Equity compression sharpens medium-hand under-realization

Medium hands (one pair, weak two pair) already struggle out of position in Cash. PLO4 makes it worse. Equity compression pushes typical matchups into the 55/45–65/35 range, versus Cash's 80/20 peaks. Even "strong" hands land in the medium-equity zone more often. The solver compensates by probing the turn aggressively from out of position — elevated +46–51pp above Cash frequencies. That's a direct response to compression making passive play leak value faster.

What this means: Treat "strong made hand" thresholds as higher in PLO4 than Cash. Two pair and sets are often bluff-catchers, not value hands. Probe to realize equity; don't rely on passive showdown.

Condensing, OOP disadvantage, protection, and IP equity realization

Four more Cash theories carry over cleanly or get stronger:

• Condensing after a check transfers identically — the range-narrowing logic is format-neutral.
• OOP disadvantage amplifies — four-card hand complexity raises the cost of acting first.
• Protection betting becomes even more narrowly correct — PLO4 draws frequently reach 40–55% equity, making protection bets without fold equity even more commonly negative-EV.
• IP equity realization advantage amplifies — acting last with four-card complexity produces wider equity-realization gaps.

What this means: Check strong hands to protect your checking range. Probe aggressively from out of position to compensate for the position disadvantage. Never bet solely for protection unless draw equity is demonstrably below 30%.

Pillar B — Frequencies & Balance

The minimum defense frequency (MDF — the fold rate that makes bluffs break even) formula transfers to PLO4. But PLO4 BB defense is wider than Cash, and the 3-bet rate is narrower. The paradox — defend more, 3-bet less — is the defining PLO4 frequency pattern.

BB defends 59–69% — wider than Cash at every position

In Cash, BB defends at roughly MDF-consistent rates across opener positions (36–60%). In PLO4, BB defends 59–69% — wider everywhere. The extra defense is absorbed almost entirely by calling, not 3-betting.

(PLO4 vs Cash BB defense by opener position. 6-max · 100bb effective · SRP · 2.5bb open · 3% rake capped at 3bb.)

What this means: Fit-or-fold from Cash is a structural leak in PLO4. With four hole cards, BB has enough equity to defend wide. Call far more; 3-bet selectively.

BB 3-bet versus late position DECREASES with depth — reverses Cash

This is one of the sharpest reversals from Cash intuition. Cash BB 3-bet rate versus BTN increases with depth: 17.0% → 18.1% → 22.3% across 50bb, 100bb, and 200bb. PLO4 reverses: 17.8% → 10.1% → 2.8%.

(PLO4 BB 3-bet rate by opener × depth. 6-max · 3% rake capped at 3bb · SRP · 2.5bb open.)

Based on general poker theory: pot-limit SPR arithmetic. In pot-limit structures, the maximum bet each street equals the current pot, which caps how fast SPR collapses — so at shallow stacks, 3-betting commits a dangerous fraction of your stack OOP, and at deep stacks, calling preserves implied odds for connected hands. Falsifier: if this were a rake artifact rather than pot-limit SPR, Cash at the same rake would show the same inversion — it doesn't.

What this means: At 50bb, 3-bet late-position openers aggressively from BB (~18%). At 200bb, almost never 3-bet BTN or CO from BB — call instead and realize implied odds with connected hands.

MDF formula, indifference, bluff ratios, and balancing

Four more Cash frequency theories carry over with modifications:

• MDF formula transfers, but pot-limit compresses Alpha to 0–0.5 (no overbets above pot). PLO4 defenders never face Alpha above 0.5.
• Indifference at equilibrium transfers identically — it's a game-theoretic property, format-neutral.
• Bluff-to-value ratio transfers. Pot-limit adds a ceiling on achievable Alpha.
• Balanced ranges amplify — PLO4's richer draw universe means more hands qualify as semi-bluffs, making accidental over-bluffing more common.

What this means: Apply standard bluff-ratio math but cap Alpha at 0.5 (max bet = pot). Expect to need tighter balance discipline in PLO4 — there are more natural semi-bluff candidates than in Cash.

Pillar C — Position & Information

All five Cash position theories transfer or amplify. PLO4 position advantage is stronger because four-card hand complexity makes acting last more valuable on later streets. The positional gradient is confirmed at +9–19pp over Cash at all positions.

Positional VPIP gradient amplified

PLO4 opens substantially wider than Cash at every position. The effect is largest at UTG and narrows toward BTN.

(PLO4 vs Cash VPIP gradient by position. 6-max · 100bb effective · SRP · 3% rake capped at 3bb.)

Based on general poker theory: equity compression. With four hole cards the gap between strong and weak starting hands narrows, so more hands at every position clear the threshold for profitable entry — widening ranges uniformly, with the largest jump where Cash was tightest. Falsifier: if the widening were driven by rake reduction rather than equity compression, we'd see position-flat widening; instead it compresses from +19pp at UTG to +9pp at BTN, consistent with equity compression's interaction with positional tightness.

What this means: Do not apply Cash opening hand selection. PLO4 opens substantially more from all positions — the cutoff for "worth playing" is lower because four cards hit more board types.

Range-shaping logic transfers cleanly

The logic "early position tight, late position wide" transfers identically. The number of opponents remaining and their positional advantage is format-neutral. PLO4 just applies the same logic to wider absolute ranges.

Connected boards bifurcate at Q-high

Cash says connected boards favor the BB caller. PLO4 splits that rule at a Q-high threshold. Q-high and above connected boards amplify the raiser's advantage (+4–19pp c-bet elevation). Below Q-high, the Cash BB-favored pattern holds. Full board data appears in Pillar E.

OOP disadvantage and SB versus BB structure

• OOP disadvantage amplifies. The solver shows PLO4 out-of-position play compensates via +46–51pp turn probing.
• SB versus BB structure transfers identically — it's seating-defined and format-neutral.

Pillar D — Sizing

Pot-limit caps overbets — pot-sized bets play the overbet role. Shallow-stack limp dynamics are dramatically more extreme. Blocker effects amplify with four cards.

Pot-limit changes the overbet ceiling

Polar ranges should use the maximum available size. In Cash that means overbets. In PLO4, pot-limit sets the ceiling at 100% pot, so pot-sized bets serve the structural overbet role. The direction holds; the achievable maximum differs.

Shallow-stack limp dynamics invert versus Cash

This is one of the most distinctive PLO4 patterns. Cash BTN limp rate is near-zero at all depths. PLO4 flips completely across the stack-depth range.

(PLO4 BTN raise vs limp rate by stack depth. 6-max · 3% rake capped at 3bb.)

Based on general poker theory: pot-limit SPR arithmetic. At 50bb, a pot-raise preflop commits a large fraction of the stack with little implied odds for rundown hands — so the solver limps cheaply instead of building pots it can't navigate. Falsifier: if limping were driven by rake rather than pot-limit commitment, Cash at equivalent rake would also show elevated limping at shallow depths — it doesn't.

What this means: At 50bb, limping BTN ~37% is solver-consistent — not weakness. At 200bb, almost always raise to build pots where PLO4 nut potential extracts full value.

Four cards mean more blockers and wider sizing divergence

PLO4 gives you C(4,2) = 6 two-card subsets per hand versus one in Cash. That means six potential blocking pairs per hand. Blocker-based sizing decisions are more frequent and more decisive. The divergence between "has blocker → bet larger" and "no blocker → bet smaller" is wider than in Cash.

Double-suited hands carry two flush-suit pairs, creating double-blocker scenarios unavailable in Cash. River bluff frequency with double-flush-blocker hands should show a wider spread between blocker categories than Cash equivalents.

What this means: Weight blocker-motivated sizing decisions more heavily in PLO4. Holding two cards that block your opponent's nut combos is more common — exploit it.

Thin value, turn polarization, and size tells

Three more sizing theories carry over:

• Thin-value sizing amplifies — PLO4's richer draw universe means more semi-bluff raises against thin-value bets. The small-size preference for non-nut hands strengthens.
• Turn polarization toward larger sizes transfers — Bayesian range-updating is format-neutral.
• No size tells transfers — it's a game-theoretic principle, format-neutral.

Pillar E — Board Texture

This pillar contains the single clean reversal in the entire PLO4 framework. Paired boards flip from raiser-favorable to raiser-unfavorable. Dry high-card boards amplify raiser advantage. Connected boards split at Q-high.

Paired boards — the one clean reversal

In Cash, the in-position player c-bets 70–83% on paired boards because a tight opening range holds most pairs. PLO4 flips this completely. BB's wide calling range (+23pp versus UTG) contains more of the paired card than BTN's tighter raising range.

(PLO4 vs Cash flop c-bet on paired boards. 6-max · 100bb effective · SRP · BTN vs BB · 2.5bb open · 3% rake capped at 3bb.)

AAx is the partial exception — BTN's tight opening range retains more Aces, so the suppression is milder.

Based on general poker theory: equity compression. With four hole cards, BB's wider defending range holds more of the paired card than BTN's tighter raising range, so the nut-advantage assumption from Cash inverts — BB is favored on paired textures. Falsifier: if this were a rake effect rather than range-width interaction, we'd see uniform suppression across all paired ranks; instead AAx suppresses only −19pp while QQ5 suppresses −64pp, matching the rank-dependent range-width prediction.

What this means: Check back paired boards at dramatically higher frequency than in Cash. On KK9, QQx, JJx — almost always check (BTN c-bet below 27%). On AAx — still c-bet less than Cash (63% versus 82%), but not as dramatically.

Dry high-card boards amplify raiser advantage

On boards like A72r and K84r, BTN's coverage advantage widens in PLO4. BTN opens wider AND with Broadway combinations that maintain high-card board coverage. C-bet frequency is comparable to or higher than Cash on dry boards.

Connected boards bifurcate at Q-high

Cash says connected boards favor the BB caller. PLO4 splits the rule sharply.

(PLO4 flop c-bet on connected boards, Q-high bifurcation. 6-max · 100bb effective · SRP · BTN vs BB · 2.5bb open · 3% rake capped at 3bb.)

The BTN's rundown composition (K-Q-J-T, Q-J-T-9, J-T-9-8) structurally explains the threshold. These hands connect to Q-high+ boards and miss low boards.

What this means: The Cash rule "wet = less c-bet" only holds for monotone and low-connected (below Q-high) in PLO4. On Q-high+ connected boards, c-bet at above-Cash frequency (70–90%). On low connected (8-high or below), c-bet less.

Suit isomorphism, flush draws, and dynamic boards

Five more texture theories carry over:

• Suit isomorphism transfers — it's a mathematical property and must-use-2 doesn't break it.
• Flush draw equity premium amplifies — double-suited hands carry two flush paths, making the premium available more frequently.
• Turn-card variance amplifies — more draws in play means higher turn-card variance in strategy terms.
• BB probes on low boards amplifies — PLO4 OOP turn probe runs +46–51pp above Cash on most textures.
• Draw-completing versus blank turn transfers — direction holds across board classes.

Pillar F — C-Betting

The c-bet pillar is where PLO4's texture sensitivity shows most clearly. Connected boards split at Q-high (wider c-bet above, narrower below). Monotone boards amplify suppression with a critical A-high exception. And out-of-position turn probing is a completely different animal.

C-bet frequency splits at Q-high

In Cash, the rule is simple: dry boards get more c-bets, connected boards get fewer. PLO4 breaks that into three subclasses:

• Q-high+ connected: IP c-bet elevates +4–19pp. BTN's rundown opening range hits these boards hard.
• Low-connected (below Q-high): BB probe and donk amplify; IP suppresses.
• Monotone exception: A-high monotone suppresses IP less than mid-rank monotone.

Full board data appears in the E3 table above.

What this means: The single Cash rule "connected boards = c-bet less" is wrong in PLO4 for the majority of connected boards you'll face. Separate Q-high+ from low-connected in your decision tree.

Monotone boards — double-suited amplifies suppression with an A-high exception

In Cash, monotone boards suppress IP c-bets because both ranges hold flush draws. PLO4 amplifies the suppression — double-suited hands increase flush draw frequency in both players' ranges, intensifying equalization. But A-high monotone is milder.

(PLO4 vs Cash turn probe on monotone boards. 6-max · 100bb effective · SRP · BTN vs BB · 2.5bb open · 3% rake capped at 3bb.)

Mid monotone suppresses PLO4 OOP probe by −26pp. A-high monotone elevates it by +12pp. The same rank-threshold split seen in the connected-board data.

What this means: On monotone flops, check more than Cash — unless A-high. On mid monotone turns after checks through, BB probes less than Cash (−26pp). The monotone exception overrides the usual OOP probe amplification.

Value-bluff tradeoff, river probing, multi-street planning, and semi-bluffs

Four more c-betting theories amplify:

• C-bet value versus bluff tradeoff: c-bet range across 26 boards spans 14–91% in PLO4, wider than Cash. Equity compression makes "mixed" boards harder to categorize.
• River value-bet threshold: compression means thin value is more viable. More hands clear the 55%+ threshold in PLO4 than Cash's 60%+ threshold.
• Multi-street planning: amplified constraint. Two pot-sized bets commit stacks at 100bb; the geometric commitment path is more rigid.
• Semi-bluff frequency: amplified. Nearly every PLO4 flop has multiple semi-bluffable draws for both players.

What this means: Plan stack commitment at the start of each hand — pot-limit makes the path more deterministic. On draw-heavy boards, expect both players to have more semi-bluffs simultaneously. Your hand classification changes faster.

Post-check condensing and turn polarization transfer cleanly

• Check-through condensing transfers identically — Bayesian inference is format-neutral. The solver confirms PLO4 OOP exploits via elevated probing.
• Turn polarization toward larger sizes transfers — range-narrowing from flop action produces more polarized turn ranges in any format.

Pillar G — Advanced

Depth effects partially reverse Cash SPR intuition. Mixed-strategy equilibria multiply. Blocker effects strengthen across the board.

Depth effects partially reverse Cash

Cash intuition says deeper stacks mean more aggressive preflop raises. PLO4 partially reverses this. Limping dominates at 50bb, raising dominates at 200bb (the limp-depth inversion from Pillar D). BB 3-bet versus late position decreases with depth (the 3-bet depth reversal from Pillar B). PLO4 depth effects run opposite to Cash in both these dimensions, while deepening postflop complexity in the same direction as Cash.

The root mechanic is pot-limit commitment risk. BB avoids deep 3-bet pots out of position and prefers calling to realize implied odds.

What this means: Do not assume "deeper = more aggressive preflop" from Cash intuition. In PLO4, deepening stacks suppress BB 3-bets dramatically and shift BTN from limp to raise — but for different structural reasons than Cash.

More mixed-strategy equilibria make heuristics fail more

C(4,2) = 6 two-card subsets per hand versus one in Cash. More hands fall near equilibrium indifference thresholds. More decision points require mixing. Solver-derived frequencies are harder to approximate in PLO4 with heuristics.

What this means: PLO4 is more resistant to heuristic shortcuts than Cash. Pure-strategy rules ("always c-bet dry boards," "never c-bet paired boards") are directionally useful but wrong at higher frequencies. Use model data for specific textures rather than rules.

Multiway, blocker effects, crystallization, slowplaying, and protection

Five more advanced theories carry over:

• Multiway aggression amplifies — nutness requirement scales with player count, and equity compression removes the safety margin.
• Blocker river bluffing amplifies — 6× the potential blocking pairs per hand makes blocker decisions more decisive.
• Range crystallization transfers — Bayesian range-narrowing is format-neutral.
• Slowplaying transfers — the game-theoretic reason for checking strong hands is format-neutral.
• Protection betting amplifies narrowing — PLO4 draws reach 35–55% equity, making protection-only bets even more rarely correct.

ICM is not applicable — it's tournament-only and irrelevant to PLO4 cash games.

Pillar H — 3-Bet Pots

The defining PLO4 3-bet pot result: c-bet collapses to 100% on all textures. The Cash bimodal pattern disappears entirely.

PLO4 3-bet pot c-bet = 100% on all textures

In Cash, IP c-bets at bimodal frequencies in 3-bet pots — very high on favorable textures, very low on unfavorable. PLO4 wipes out the bimodal pattern. IP c-bets 100% on all textures, including paired boards and low-connected boards where single-raised pots show suppression.

Based on general poker theory: equity compression. At 3-bet pot SPR (~2–3 at 100bb), PLO4's equity compression makes almost no hand a clear check — every hand has meaningful equity to protect or semi-bluff with. Falsifier: if the 100% c-bet were driven by range polarization rather than equity compression, we'd see the same bimodal Cash pattern at higher frequencies; instead we see a flat 100% across all textures, consistent with compression erasing texture-sensitivity.

What this means: In 3-bet pots, forget board-texture-based c-bet decisions from Cash. C-bet 100% as IP. The texture-sensitive framework from single-raised pots (Pillars E and F) does not apply at 3-bet pot SPR.

BB 3-bet versus LP decreases with depth — direction reverses Cash

Same data as the Pillar B section. Cash BB 3-bet versus BTN: 17.0% → 22.3% (increases with depth). PLO4: 17.8% → 2.8% (decreases with depth).

At 200bb PLO4, BB almost never 3-bets BTN. Pot-limit commitment risk at deep OOP stacks is the root mechanic.

Must-use-2 tightens multiway overcall hand requirements

In Cash, overcalling 3-bets requires strong connected hands. PLO4 amplifies this and adds a hard constraint: must-use-2 creates non-intuitive hand strength boundaries. A hand like AhKhJdTc on a heart-heavy board provides no nut flush draw if you use Ah with Kh for a pair-of-Kings type holding. Double-suited rundowns with interacting suits are materially stronger than "good-looking" hands with non-interacting suit combinations.

What this means: In multiway 3-bet pots, explicitly verify each two-card subset's draw strength. Don't rely on visual suit patterns.

Pillar P — PLO4-Specific

These ten theories describe mechanics that are structurally unique to PLO4 — there is no Cash equivalent. If you retain one section from this manual, retain this one.

P1: BRAIN nut-advantage framework

Must-use-exactly-2 fundamentally changes nut-presence computation. An Ace in your hand does not guarantee a nut flush draw unless that Ace's suit pairs with a hole card that forms the draw against the board.

Build the habit of iterating through C(4,2) = 6 two-card pairs before assigning hand class. Tools exist for this; don't eyeball from Cash intuition.

P2: Paired board raiser-weakness

The single most counterintuitive PLO4 fact for Cash players: BTN is weak on paired boards, not strong. BB's wider four-card calling range contains more of the paired card than BTN's tighter raising range. BTN c-bet collapses to 14–27% on J–K-high paired boards (versus Cash 70–83%). AAx is the partial exception: 62.6% PLO4 versus 82.0% Cash.

Full board data appears in the Pillar E paired-board section.

P3: Limp-depth inversion

BTN limp and raise frequencies completely invert across stack depths. Cash BTN limp is near-zero at all depths. PLO4: 50bb = 36.9% limp / 12.8% raise; 200bb = 4.4% limp / 49.7% raise. Pot-limit bounding plus rundown implied-odds structure is the root mechanic.

Full depth table appears in Pillar D.

P4: 3-bet depth reversal

BB 3-bet rate versus late position decreases with depth in PLO4; it increases in Cash. Deep OOP 3-bet pots in PLO4 are dangerous — pot-limit commits stacks quickly and equity compression provides little protection against runout variance. BB prefers calling to realize implied odds.

Full depth table appears in Pillar B.

P5: Connected board Q-high+ bifurcation

PLO4 connected boards bifurcate at Q-high. Q-high+ elevates IP c-bet +4–19pp. Below Q-high retains Cash IP-suppression. BTN's rundown composition (K-Q-J-T, Q-J-T-9, J-T-9-8) structurally explains the threshold — these hands connect to Q-high+ boards and miss low boards.

Full board data appears in Pillar E.

P6: BB defense paradox — wider defense AND narrower 3-bet simultaneously

PLO4 BB simultaneously defends wider (59–69% versus Cash 36–60%) AND 3-bets less (4–10% versus Cash 7–18%). The excess defense is absorbed almost entirely by calling. PLO4 hands gain implied-odds value from calling OOP; 3-betting creates deep OOP commitment risk.

What this means: This is a single coherent strategy, not a contradiction. Defend wide by calling, 3-bet only with the strongest hands (typically only at shallow stacks versus late position). At 200bb versus BTN, fold or call — almost never 3-bet.

P7: OOP turn probe amplification

After a flop check-through, PLO4 BB probes the turn +46–51pp above Cash on most textures. The amplification is stack-depth-independent (confirmed at 50, 100, 150, and 200bb on A72r).

(PLO4 vs Cash BB turn probe after flop check-through. 6-max · 100bb effective · SRP · BTN vs BB · 2.5bb open · 3% rake capped at 3bb.)

The exception: mid-rank monotone (987s) suppresses PLO4 BB probe by −26pp. A-high monotone does not follow this exception.

What this means: On dry or coordinated turns after checks through, probe aggressively — especially A-high textures (+51pp). On mid monotone turns, check more than Cash (not less). Rivers extend the same pattern (+5–28pp on JT9r, A72r).

P8: 3-bet pot texture-independence

In 3-bet pots, PLO4 IP c-bets 100% on all board textures. The single-raised-pot texture-bimodal pattern (Pillars E, F) does not apply. At 3-bet pot SPR (~2–3 at 100bb), equity compression makes every hand worth protecting or semi-bluffing.

Full explanation appears in Pillar H.

P9: Must-use-2 blind spots

Must-use-exactly-2 creates non-intuitive hand-class boundaries that require explicit verification. Common Cash shortcuts that fail in PLO4:

• "I have an Ace in the suit → nut flush draw" — only if that Ace pairs with another hole card of the same suit.
• "Top pair top kicker → strong made hand" — in PLO4, usually a bluff-catcher.
• "Two pair → value bet" — in PLO4, usually a bluff-catcher on draw-heavy boards.

What this means: Verify each two-card subset explicitly before assigning hand class. The six possible pairs from a four-card hand include some that produce strong draws and some that don't — they cannot be assumed equivalent.

P10: Equity compression shifts all value and bluff thresholds

PLO4 matchup equity clusters 55/45–65/35 versus Cash reaching 80/20. All decision thresholds shift simultaneously:

• River value-bet threshold: lower (more hands qualify)
• Bluff-catch threshold: lower (opponent holds more equity on average)
• Semi-bluff qualification: lower (more draws meet the equity threshold)
• Protection-only bet threshold: rarely met (draws are near coin-flips)

Every frequency number from Cash theory requires recalibration in PLO4. BB calls more, probes more, and 3-bets less — those are the downstream effects.

Board Data Reference — 26 Boards

All data from universal-dense-v4-player_20260402_150328.onnx, 100bb unless noted.

(PLO4 flop c-bet reference — 26 boards. 6-max · 100bb effective · SRP · BTN vs BB · 2.5bb open · 3% rake capped at 3bb.)

3-bet pots: 100% c-bet all textures (no PLO4 versus Cash delta — both converge at 100%).

River bet direction after BB turn probe

After BB probes the turn and BTN calls, PLO4 completely inverts Cash's river betting frequency ordering by texture. (BTN was the caller on the turn, so BTN's river bet is not a barrel.)

(PLO4 vs Cash river bet frequency after BB turn probe. 6-max · 100bb effective · SRP · BTN vs BB · 2.5bb open · 3% rake capped at 3bb.)

Cash bets this river more on A72r than on JT9r. PLO4 inverts the order: JT9r > A72r. On dry boards, BB's probe range is strong on A-high and K-high turns — BTN has little to bet for value. On connected boards, BB's draw-heavy probe frequently misses blank rivers — BTN bets for value.

What this means in practice: After BB probes, check rivers on A72r and K84r (~18% bet). Bet rivers on JT9r (64%). Near-neutral on mid-coordinated and monotone (0–4pp delta).

What this manual does not cover

These are scope gaps, not pending items — new queries are required before testing.

Every Hold'em principle you know gets stress-tested when you move to four cards. Some survive. Some amplify. Some reverse entirely. This chapter walks through nine mechanisms the solver surfaced — each one a specific, measurable way PLO4 strategy diverges from Cash NLHE.

All data comes from a single model checkpoint (plo4_3T.pt), confirmed 55/55 on B1 property tests. Every mechanism carries a single-checkpoint flag — the patterns are real within this model, but cross-checkpoint stability hasn't been tested yet.

How Cash theory transfers to PLO4

Not every Hold'em principle survives the move to four cards. Some reverse entirely.

M1 — Paired-board cbet suppression

The paired-board suppression effect

If you carry your Hold'em c-bet habits onto paired boards in PLO, you are lighting money on fire. The solver checks back paired flops at a rate that would shock any NLHE player.

PLO4 BTN c-bets (continuation bets — betting the flop after raising preflop) dramatically less than Cash on paired boards:

• KK9: PLO4 22.2% vs Cash 70.3% → −48pp
• AAx: PLO4 62.6% vs Cash 82.0% → −19pp
• QQ5: PLO4 14.1% vs Cash 77.9% → −63.8pp
• JJ7r: PLO4 26.7% vs Cash 82.6% → −55.9pp

The depth test on KK9 shows this isn't a stack-depth effect. C-bet rates at 50bb, 100bb, 150bb, and 200bb come in at 25.4%, 22.2%, 24.7%, and 26.2% — flat within noise. The suppression is depth-independent.

Why this happens

BB's PLO4 calling range is much wider than in Cash (see the wider BB defense effect below). That wider range contains far more hands holding the paired card. On KK9, BB has more Kxxx combos than BTN does in their respective ranges. BTN loses the range advantage that makes c-betting profitable in NLHE — so checking back is the better play.

This isn't about BTN having fewer strong hands overall. BTN c-bets 80.7% on K84r (another K-high board, unpaired) and 80.8% on JT9r. The suppression is specific to the PAIRED texture, not to K-high boards generally.

Based on general poker theory: range advantage. BB's wider 4-card range holds more paired-card combos, flipping range advantage on paired boards from IP to OOP — which is why the solver checks back at 14–27% instead of Cash's 70–83%. Falsifier: if this were a pure hand-strength effect rather than a pairing-specific range-coverage effect, we'd see similar suppression on all boards where BTN's range is weaker — but K84r (unpaired K-high) c-bets at 80.7%.

What this means: Don't apply your NLHE c-bet frequency on paired boards. The solver's wider BB range holds more of the paired card, so your range advantage flips. Check back far more often.

M2 — Limp-depth inversion

In PLO4, shallow stacks make you a limper

In Cash, solvers never limp — it's strictly dominated by raising or folding at every stack depth. In PLO4, limping isn't just viable. At 50bb it's the dominant BTN action.

Total VPIP (voluntarily put money in pot — the combined raise + limp rate) stays stable across depths at 49.7–54.1%. The composition completely inverts; the total frequency barely moves.

CO shows the same pattern at smaller magnitude. CO limp rate at 50bb is 7.6%, falling monotonically to 0.7% at 200bb. UTG and MP are depth-flat (34–36% VPIP constant across 50–200bb, under 0.5% limp at all depths) — the inversion doesn't apply to early positions.

Why this happens

Based on general poker theory: pot-limit SPR arithmetic. In pot-limit structures, the maximum bet each street equals the current pot, which caps how fast SPR (stack-to-pot ratio) collapses — so at shallow stacks, limping to see cheap flops dominates, and at deep stacks raising is required to build pots that rundowns can extract from. Falsifier: if this were a rake artifact rather than pot-limit SPR, Cash at the same rake would show the same inversion — it doesn't; Cash BTN at 50bb shows ~43% VPIP with negligible limp rate.

The strictly monotonic pattern across all four tested depths (36.9% → 13.8% → 6.9% → 4.4%) rules out a training artifact. A spurious model quirk at four evenly-spaced depths producing perfect monotonicity is implausible.

What this means: At shallow PLO4 stacks, limping the button isn't a leak — it's the equilibrium play. The pot-limit structure makes raising at 50bb inefficient for the rundowns and suited connectors that form the core of your range.

M3 — Connected-board cbet elevation

On connected boards, PLO4 c-bets MORE — but only above J-high

This one surprised us. In NLHE, connected boards generally suppress c-bets because the defender's range connects with them. In PLO4, the direction flips — but only when the top card is high enough.

PLO4 c-bets more than Cash on connected boards:

• T98tt (two-tone): PLO4 71.9% vs Cash 53.4% → +18.5pp
• JT9r (rainbow): PLO4 80.8% vs Cash 68.7% → +12.1pp
• A76tt: PLO4 70.4% vs Cash 64.6% → +5.8pp

But low connected boards go the other direction:

• 876r: PLO4 54.3% vs Cash 81.4% → −27.1pp

Monotone connected boards also suppress: 987s shows −10.1pp.

The depth test on JT9r confirms this is depth-independent: 85.4%, 80.8%, 80.8%, 80.1% across 50bb through 200bb — flat.

The card-rank threshold

The scope of this mechanism narrowed during testing. Originally the claim was "connected boards" broadly. The 876r falsifier forced a revision. The threshold is more precisely: top card ≥ Q, OR a board with ≥3 consecutive ranks and top card ≥ J.

Evidence supporting the threshold:

• K76tt: +10pp (top card ≥ Q — elevates)
• Q97r: +13pp (top card ≥ Q — elevates)
• A98tt: +19pp (top card ≥ Q — elevates)
• J98r: +4.1pp (J-high sequential — elevates, barely)
• T76r (T-high with gap): −8pp (suppresses)
• 876r (low connected): −27.1pp (suppresses)

Why this happens

BTN's PLO4 opening range is loaded with rundowns — J-T-9-8, Q-J-T-9, K-Q-J-T. These hit connected boards hard. On T98tt and JT9r, BTN's rundowns produce wraps, two-pairs, and straights at high frequency. BB's wider calling range includes more non-rundown hands that miss these boards. BTN has range advantage and c-bets to protect equity.

The suitedness of the board doesn't drive it. JT9r (rainbow) still elevates by +12.1pp. Connectivity is the primary driver, not whether the board is two-tone.

Based on general poker theory: nut advantage. BTN's rundown-heavy PLO4 range gives BTN more wraps, straights, and two-pairs on high-connected boards, creating the range advantage that justifies a higher c-bet frequency than Cash. Falsifier: if the wider PLO4 range universally elevated c-bets on all textures, we'd see elevation everywhere — but KK9 shows −48pp and 987s shows −10pp, confirming the elevation is texture-selective.

What this means: On J-high or higher connected boards, you should c-bet more aggressively in PLO4 than you would in NLHE. Your rundown-heavy range connects with these boards better than BB's wider but less coordinated range. Below J-high, the advantage flips — check back more.

M4 — PLO4 opens much wider than Cash

Four cards means wider opens everywhere

Equity compression (the phenomenon where four hole cards narrow the gap between strong and weak starting hands) rewrites preflop ranges from the ground up. PLO4 VPIP exceeds Cash by +9–19pp at every position.

(6-max · 100bb effective · SRP · 3%/3bb rake both formats)

The delta is largest at UTG and compresses toward BTN. This makes sense: UTG was the tightest position in Cash, so equity compression has the most room to widen it. BTN was already loose, so the additional widening is smaller.

SB exception: PLO4 SB VPIP is 52.5%, which is actually lower than Cash SB at 57.9%. This mechanism does not hold for SB.

Why this happens

With four hole cards, more starting hands exceed the equity threshold for profitably entering the pot. The gap between the strongest and weakest starting hands shrinks. Premium hands stay premium — they're just less dominant.

Based on general poker theory: equity compression. With four cards instead of two, more hands clear the profitability threshold for open-raising, so VPIP rises at every position — with the largest widening where Cash was tightest (UTG +19.3pp). Falsifier: if the wider opening were a model overtraining artifact rather than equity compression, B1 A1 (position → range width monotonicity) would fail — but it passes; BTN remains wider than CO wider than MP wider than UTG.

What this means: Open significantly wider in PLO4 than you would in NLHE. The effect is strongest from early position — UTG in PLO4 plays more hands than Cash CO does.

M5 — BB defends much wider than Cash

BB calls almost everything

PLO4 BB defends +9–23pp wider than Cash across all tested spots. The 3-bet rate is actually lower — BB calls more, 3-bets less.

All 8 cells of the position × raise-size grid show PLO4 BB defending wider, with deltas ranging from +8.8pp to +23.5pp.

Why this happens

The same equity compression that drives wider opens (M4) also drives wider defense. More PLO4 hands meet BB's equity threshold for calling. Additionally, with four hole cards BB always has some board connectivity — pure folding is suboptimal more often than in NLHE.

The defense isn't indiscriminate. PLO4 BB defense scales correctly with opener position: BTN (69.2%) > CO (64.9%) > MP (61.5%) > UTG (59.4%). BB defends widest against the weakest opener, just like in Cash — but at a uniformly higher level.

Based on general poker theory: equity compression. With four hole cards, the gap between strong and weak starting hands narrows, so more of BB's defending combos clear the pot-odds threshold — widening defense uniformly against every opener position. Falsifier: if rake drove the widening, we'd expect position-flat widening; instead widening compresses from +23pp vs UTG to +9pp vs BTN, consistent with equity compression's position-gradient prediction.

What this means: Expect BB to call far more often in PLO4. Your c-bets face wider ranges, your isolation raises work less often, and your postflop range advantage on many textures flips. Adjust sizing and frequency accordingly.

M6 — Turn probe elevation (BB out of position)

After BTN checks back the flop, BB fires the turn

In NLHE, when both players check the flop, the turn often checks through again. In PLO4, BB fires a probe bet (a bet on the turn by the out-of-position player after the flop checks through) at dramatically higher rates.

• A72r + blank turn: PLO4 68.1% vs Cash 17.4% → +50.8pp
• JT9r + blank turn: PLO4 62.8% vs Cash 54.3% → +8.5pp
• K84r + blank turn: PLO4 55.2% vs Cash 46.6% → +8.6pp
• 987r + blank turn: PLO4 76.5% vs Cash 65.4% → +11.1pp
• KK9 + blank turn: PLO4 53.4% vs Cash 43.8% → +9.6pp

The exception is monotone boards: 987s shows PLO4 42.0% vs Cash 67.8% → −25.8pp.

Probing increases with stack depth

The depth test on A72r shows BB probes more often as stacks get deeper:

From 50bb to 200bb, PLO4 probe rate rises from 61% to 69%. Deeper stacks give draws better implied odds, and that's what the solver is reacting to. The delta versus Cash stays massive at every depth — between +46pp and +52pp.

Scope is narrower than it first appears

The full texture × depth sweep revealed important exceptions. The mechanism holds on dry boards and paired boards but breaks on connected-mid boards and at short stacks on some dry-K-high boards:

• 987r breaks at 50bb (−12.3pp), 150bb (−8.1pp), and 200bb (−8.2pp) — even though 987r at 100bb holds (+11.1pp)
• K84r breaks at 50bb (−6.2pp), though it holds at 100bb (+8.6pp), 150bb (+3.4pp), and 200bb (+4.7pp)
• 987s (monotone) suppresses at every depth, from −25.8pp to −36.4pp

Scope qualifier for monotone turns: A-high monotone turns elevate (+12pp on A87s). Q-high and below monotone turns suppress (Q65s −11pp, 987s −26pp). The threshold differs between flop and turn.

Why this happens

BB's wider calling range creates more hands with partial equity — draws, backdoor draws, pairs — that want to bet the turn for fold equity. After BTN checks back the flop, BTN's range is capped (they missed the c-bet opportunity). BB uses this information to probe with a wide range.

Monotone boards suppress probing because BB's one-card flush draws are weaker. Probing risks running into BTN's nut-flush continuation.

Based on general poker theory: fold equity realization. BB's wider PLO4 range (from equity compression) holds more partial-equity hands OOP, and after BTN's capped flop check-back, BB realizes equity by probing the turn — which is why A72r elevates by +51pp while monotone 987s suppresses by −26pp. Falsifier: if BB were indiscriminately over-probing rather than strategically exploiting fold equity, probe rate wouldn't vary by board texture — but 987s shows −25.8pp while A72r shows +50.7pp.

What this means: When you check back the flop in PLO4, expect to face a turn probe far more often than in NLHE — especially on dry boards. BB is not bluffing randomly; the wider range creates legitimate semi-bluff equity. Prepare for the turn bet before you check back.

M7 — BB defense narrows with depth versus early-position openers

Deeper stacks make BB fold more against tight openers

This narrowing is a PLO thing. In Cash, BB defends UTG at roughly the same rate whether stacks are 50bb or 200bb.

BB defense vs UTG decreases monotonically with depth in PLO4:

• 50bb: 61.2%
• 100bb: 59.4%
• 150bb: 57.8%
• 200bb: 56.5%

The pattern holds at MP (62.5% → 59.2%) and CO (64.5% → 62.8%), though CO's magnitude is smaller at −1.7pp. BTN is the exception — defense versus BTN is flat across depths (67.2% / 69.2% / 68.3% / 67.1%).

Cash BB vs UTG tells the opposite story: 36.3%, 36.5%, 36.1%, 36.0% — essentially flat with a total range of 0.5pp.

Why this happens

At deeper stacks facing UTG's tight range, BB faces more SPR risk out of position. If BB calls and the flop is bad, a deep-stack pot has higher absolute EV stakes for folding to pressure. BTN's wide range doesn't pose the same risk because BTN has more speculative hands that check back or bet small.

The narrowing isn't driven by 3-bet rate changes. PLO4 BB 3-bet vs UTG is approximately 4.4% at all tested depths — flat. It's the calling rate that compresses with depth.

Based on general poker theory: pot-limit SPR arithmetic. In pot-limit structures, deeper stacks push the BB-vs-EP SPR into territory where commitment risk exceeds the equity benefit of defending — so BB's calling rate compresses with depth even though 3-bet rate stays flat. Falsifier: if this were a general SPR effect (not PLO-specific), Cash BB defense vs UTG would also narrow with depth — but Cash shows a total range of just 0.5pp across 50–200bb.

What this means: Tighten your BB defense in PLO4 as stacks get deeper, especially against UTG and MP opens. The commitment risk of calling out of position into a tight range outweighs the equity you gain from seeing a flop. Against BTN opens, defend at your normal rate regardless of stack depth.

M8 — River bet direction reversal after BB turn probe

The river ranking completely inverts

This is the most unintuitive finding. After BB probes the turn and BTN calls, BTN's river bet frequency versus Cash flips entirely depending on texture. The board that BTN bets most often in Cash becomes the board BTN bets least in PLO4.

A72r drops from Cash rank #1 to PLO4 rank #5. JT9r rises from Cash rank #4 to PLO4 rank #1. A complete inversion.

Why the texture matters

The direction depends on what BB's turn probe represented:

Pre-condition: On dry boards (A72r, K84r), BB's probe represents made hands and top pair. BTN called with a capped range. On the river, BTN cannot credibly represent strength against BB's strong probe — so BTN checks back far more.

Post-condition: On connected J-high boards (JT9r), BB's probe is draw-heavy — wraps, flush draws hitting connected boards. When a blank river misses BB's draws, BTN can bluff-bet into the missed range — so BTN bets far more.

Why it splits: The composition of BB's turn-probe range flips from value-heavy on dry boards to draw-heavy on connected boards, and BTN's river response adjusts accordingly.

Based on general poker theory: range composition. BB's turn-probe range is value-heavy on dry boards and draw-heavy on connected boards — so BTN's river bet inverts: checking back when BB probed with strength (A72r −27pp), betting when BB probed with draws that bricked (JT9r +27pp). Falsifier: if BTN were blindly exploiting BB's over-probing, river bet rate would be uniformly elevated — but BTN bets LESS on dry boards and MORE on connected, a texture-selective bidirectional response.

What this means: After you call BB's turn probe in PLO4, your river strategy depends on the board texture. On dry boards, check back more often — BB's probe was real. On connected boards above J-high, bet the river more aggressively — many of BB's probing hands were draws that just missed.

M9 — BB 3-bet rate versus late-position openers decreases with depth

In PLO4, deep stacks kill the 3-bet

This is the cleanest reversal of Cash logic in the entire study. In Cash, BB 3-bets BTN MORE at deep stacks. In PLO4, the opposite: BB 3-bets BTN dramatically LESS at deep stacks.

Cash BB 3-bet vs BTN moves the other way: 17.0% at 50bb, 18.1% at 100bb, 22.3% at 200bb — increasing.

Total defense vs BTN stays flat in PLO4 (67.2% / 69.2% / 67.1%). The 3-bet decline is offset by a call increase: 49.4% → 59.1% → 64.3%.

The reversal is cleanest at BTN

The reversal is confirmed at different raise sizes too. PLO4 BB vs BTN at 3.0bb: 18.0% at 50bb → 4.4% at 200bb (decreasing). Cash BB vs BTN at 3.0bb: 14.6% at 50bb → 17.8% at 200bb (increasing). The directional pattern holds at both 2.5bb and 3.0bb opens.

SB defense pattern

SB defense is extremely high in PLO4 — 80–83% VPIP across depths. SB 3-bet rate gently decreases with depth (14.0% → 12.4% → 11.4%), consistent with the same mechanism but at much smaller magnitude than BTN's −15pp swing.

Why this happens

At deep stacks in PLO4 versus a wide BTN opener, 3-betting OOP creates a very large pot. The pot-limit structure means the pot grows fast postflop. PLO4's four-card hands — rundowns and double-suited combos — have enormous implied odds at deep stacks. Calling preserves those implied odds. 3-betting destroys them by bloating the pot preflop.

At shallow stacks, the equation flips. A 3-bet at 50bb creates a manageable pot with an SPR around 3–4. Small pots limit the implied-odds advantage of calling. Might as well build equity preflop via the 3-bet.

In Cash (no-limit), deep-stack 3-betting gives you more control of the pot size because you can bet any amount each street. That no-limit dynamic reverses the tradeoff.

Based on general poker theory: pot-limit SPR arithmetic. In pot-limit, the maximum bet each street equals the current pot — so at deep stacks, 3-betting creates an uncontrollably large pot that destroys the implied odds PLO4 hands need, making calling dominant over 3-betting. Falsifier: if this were a rake effect rather than pot-limit geometry, Cash BB 3-bet vs BTN would also decrease with depth — but Cash shows the opposite direction, increasing from 17.0% to 22.3%.

What this means: At deep PLO4 stacks, stop 3-betting wide versus BTN opens. Call instead. Your rundowns and double-suited hands make far more money seeing flops cheaply at deep stacks than they do in bloated 3-bet pots. At 50bb, 3-betting is fine — the commitment math works out at shallow depths.

Cross-mechanism patterns

These mechanisms don't operate in isolation. Several share causal chains.

Wider opens drive wider defense drive suppression

The wider-opens effect is upstream of both the wider BB defense and the paired-board suppression effect. Because BTN/CO/UTG enter with wider ranges, BB's defense threshold rises — producing the wider defense. BB's wider calling range then creates the paired-card coverage that suppresses BTN's c-bet incentive on boards like KK9. If PLO4 had Cash-equivalent BB defense, paired-board suppression would be smaller.

The magnitude of paired-board suppression (48pp on KK9) is proportional to the magnitude of wider BB defense (+23pp). This co-variation is predicted by the upstream-downstream relationship.

Turn probe is downstream of wider defense

The turn probe elevation is a downstream consequence of wider BB defense. BB's wider calling range creates more hands with partial equity OOP at the turn. If BB defended at Cash frequencies, the turn probe frequency would be lower — fewer hands worth semi-bluffing with.

River reversal follows from turn probe

The river bet direction reversal is only observable because turn probe elevation first generated the probe → call → river sequence at high frequency. Without the elevated turn probe, the conditioning event would be too rare to produce a stable signal.

Limp-depth and connected-board elevation are independent

The limp-depth inversion operates via pot-limit SPR mechanics at preflop. Connected-board elevation operates via range-board interaction at the flop. They share no causal chain steps. At the hand-composition level they interact (the hands that limp at 50bb affect the flop range), but their causal explanations are independent.

Turn probe and defense narrowing are both OOP depth patterns — but not contradictory

Turn probe elevation goes up with depth (61% → 69% from 50bb to 200bb). BB defense narrows with depth versus EP openers. These seem contradictory but aren't. Defense narrowing applies to initial pot entry risk — BB committing OOP into UTG's tight range before seeing a flop. Turn probe applies after position mismatch is resolved — BTN already checked back, capping their range. Deeper stacks make the initial entry riskier (defend less) but also make the fold-equity value of subsequent probes larger (probe more once you're in).

What we didn't test

• Position × depth cross-product: each axis was tested independently (4 positions at 100bb; 4 depths at BTN). The full position × depth matrix is untested except for specific mechanism sweeps.
• SB open range: SB raise-range composition in PLO4 is undocumented. The SB VPIP and SB defense numbers exist, but the open-raise construction is absent.
• 3-way+ pots: All postflop data is heads-up. A coach applying these c-bet or probe numbers to multiway PLO4 pots has no solver backing.
• PLO5/PLO6: All data is PLO4 (four hole cards). Five-card and six-card variants are entirely out of scope.
• Turn and river board matrix: Turn probe data covers 6 flop textures; river data covers 5. The full texture matrix is far from complete.

9 practical takeaways for PLO4

1. Check back paired boards. The solver c-bets KK9 at 22% in PLO4 vs 70% in Cash. BB's wider range holds too many trips.
2. C-bet connected boards aggressively — if the top card is J or higher. JT9r and T98tt both elevate. 876r and T76r suppress. The card-rank threshold matters.
3. Open much wider from every position. UTG in PLO4 plays 36.5% of hands — wider than Cash CO.
4. Expect BB to call almost everything. BB defends 59–69% depending on opener. Your isolation raises and c-bets face wider ranges.
5. Limp the button at shallow stacks. At 50bb, BTN limps 37% and raises only 13%. At 200bb, the ratio inverts.
6. Probe the turn aggressively when BTN checks back. BB probes at 55–68% on non-monotone boards — double or triple Cash rates.
7. After calling BB's turn probe, adjust river strategy by texture. Check back dry boards; bet connected J-high+ boards.
8. Tighten BB defense as stacks get deeper versus EP openers. Defense vs UTG drops from 61% at 50bb to 57% at 200bb.
9. Stop 3-betting wide versus BTN at deep stacks. BB 3-bet vs BTN drops from 18% at 50bb to 3% at 200bb. Call and use implied odds instead.

Research notes

Details for readers interested in the methodology behind the findings above. Skip this section if you just want the practical takeaways.

• All mechanisms are single-checkpoint. Every pattern described above comes from one model checkpoint (plo4_3T.pt). B1 passes 55/55, confirming valid policy outputs, but no cross-checkpoint stability test has been run. Directional claims and structural patterns are high-confidence; specific per-cell magnitudes should be treated as illustrative until a second checkpoint confirms them.

• Rake parity across formats. Both PLO4 and Cash queries ran at 3%/3bb rake. Earlier documentation versions referenced an asymmetric rake configuration (5%/1bb vs 3%), but this was documentation drift citing training config rather than query config. The parity-contract audit confirms matched rake at query time.

• M3 scope revision (connected-board elevation). M3 originally claimed "connected boards" broadly. The 876r falsifier (−27.1pp) forced a revision to J-high or above. Further testing narrowed the threshold to top card ≥ Q or (≥3 consecutive ranks with top card ≥ J). The T76r (T-high with gap) result (−8pp) supports the gap exclusion. PL4 in the B1 property list should be updated in methodology notes to reflect this scope.

• M6 scope revision (turn probe elevation). The full texture × depth sweep revealed that the "turn probe universally elevates on non-monotone boards" claim is falsified. The mechanism holds on dry boards (A72r) and paired boards (KK9) at all tested depths, and on K84r at 100bb+. It breaks on connected-mid boards (987r at 50/150/200bb) and at short stacks on K84r (50bb). The likely mechanism for the connected-mid break: on mid-connected boards, PLO4 BB holds more made-straight and combo-draw equity than Cash BB, so BB's optimal response shifts from probe-and-realize to check-wait-for-value. Filed as KI-8 for methodology-notes update.

• M7 axis disambiguation from M5. Both M5 and M7 predict higher BB fold rates, but on orthogonal axes. M5 is cross-format at fixed depth (PLO4 BB folds less than Cash BB at 100bb — wider defense). M7 is within-PLO along the depth axis (BB folds more as stacks grow from 50bb to 200bb). They don't compete — they operate simultaneously on different measurement axes.

• M9 BTN-specific reversal. The "reversal vs Cash" claim is cleanest at BTN (Cash 3-bet increases with depth; PLO4 decreases). MP and UTG both decrease in Cash too — same direction as PLO4, just smaller magnitude. CO is intermediate (Cash flat; PLO4 strongly decreasing). The pot-limit calling-preference mechanism applies across all LP positions; the Cash comparison is strongest for BTN. Internal classification for BTN is reverse; for MP/CO it's amplify on magnitude rather than direction.

• Discovery rate and stopping criterion. v1.5 expanded M9 scope. v1.6 ran 14 adversarial queries and found 0 new mechanisms. Two consecutive batches with zero new mechanisms. Remaining open items (SB open range, full raise-size matrix, position × depth cross-product) are expected to confirm or bound existing mechanisms, not generate new ones. Recommendation is to stop unless a specific anomaly is identified.

Everything in this chapter happens before the flop is dealt. That matters because preflop is where PLO4 departs most visibly from Hold'em — wider ranges, more calling, more limping, and several depth-dependent patterns that reverse what you know from no-limit.

The five findings below are the structural foundation. Every postflop mechanism we cover in later chapters traces back to at least one of these preflop shifts.

Measurement conditions: PLO4 6-max, 3% rake / 3bb cap (matched to Cash baseline). Stack depths noted per table.

2.1 Every position opens wider — except SB

PLO4 opens substantially wider than Cash at every position. The effect is largest at UTG and narrows toward BTN.

PLO4 vs Cash VPIP by position. 6-max · 100bb effective · 3% rake / 3bb cap

Source: plo-canonical-tables.md Table 1; plo-deltas.md §1

UTG doubles its participation rate — from 17.2% in Cash to 36.5% in PLO4. That is a +19.3pp jump at the tightest seat in the game. BTN widens by the smallest absolute amount (+9.1pp) but lands above 50% for the first time.

SB is the single exception. PLO4 SB VPIP (52.5%) is actually lower than Cash SB (57.9%), a −5.4pp difference. The reason is structural: PLO4 SB limps heavily (45.1% at 100bb), and that massive limp frequency belongs in a separate category from voluntary open-raising. When SB does raise, the range is narrow. The net result is fewer total chips voluntarily committed than in Cash, even though SB enters many pots cheaply.

The widening pattern is driven by equity compression — the phenomenon where four hole cards narrow the gap between strong and weak starting hands. In Cash, the worst hand (72o) has roughly 32% equity against a random hand. In PLO4, even the weakest four-card combinations sit around 35–40% equity because four cards nearly always connect to some board. More hands clear the profitability threshold. More hands play.

The gradient — largest delta at UTG, smallest at BTN — follows from Cash ranges already being wider in later positions. UTG had the most room to widen; BTN was already open enough that equity compression adds less marginal volume.

What this means in practice: Your preflop ranges in PLO4 are wider than you think they should be if you are calibrating against Hold'em. UTG in PLO4 plays more hands than Cash CO. Adjust your mental model of "tight" and "loose" accordingly — a 36% VPIP at UTG is equilibrium, not a leak.

2.2 BB defends wider against every opener

The widening does not stop with opening ranges. BB's defense frequency jumps too — by +9 to +23pp depending on who opened.

PLO4 vs Cash BB defense by opener position. 6-max · 100bb effective · 2.5bb open · 3% rake / 3bb cap

Source: plo-canonical-tables.md Table 4; plo-deltas.md §3

The delta is largest against early position. Against UTG, PLO4 BB defends 59.4% — more than 22 percentage points wider than Cash. Against BTN, the gap shrinks to +8.8pp because Cash BB was already defending broadly.

The pattern holds at a larger open size too. At 3.0bb, the deltas shift slightly but the shape stays:

BB defense at 3.0bb open. 6-max · 100bb effective · 3% rake / 3bb cap

Source: plo-deltas.md §3 (3.0bb table)

Look at the 3-bet column in the first table. PLO4 BB 3-bets less than Cash at every position — 4.4% vs UTG versus Cash's 6.8%, and 10.1% vs BTN versus Cash's 18.1%. This is not a typo. PLO4 BB calls more and 3-bets less, simultaneously.

The reasoning has the same root as §2.1: equity compression. More four-card holdings clear the pot-odds threshold for calling. Meanwhile, 3-betting in a pot-limit game creates a bloated pot that BB must play out of position — the pot-limit structure caps the maximum raise, which means a 3-bet is always a large fraction of the effective stack. BB resolves this by calling with a wider range and reserving 3-bets for the strongest hands.

What this means in practice: If you are folding BB in PLO4 at anything close to your Cash fold frequency, you are overfold­ing. The solver defends nearly 60% even against UTG. And the way it defends is by calling, not by 3-betting — so if you are 3-betting BB at Cash rates, you are building pots out of position that the pot-limit structure makes hard to control.

2.3 The limp-depth inversion — BTN preflop composition flips with stack depth

This is probably the single most counterintuitive preflop finding in PLO4. At 50bb, BTN mostly limps. At 200bb, BTN mostly raises. The total VPIP — the fraction of hands played — barely changes.

BTN preflop composition by stack depth. PLO4 · 6-max · 3% rake / 3bb cap

Source: plo-canonical-tables.md Tables 2–3; plo-deltas.md §2

At 50bb, BTN raises only 12.8% of hands — and limps 36.9%. That is a three-to-one preference for limping over raising. By 200bb, the numbers have completely flipped: 49.7% raising, 4.4% limping.

Total VPIP is stable across the entire depth range (49.7% to 54.1%). The composition inverts; the frequency does not.

CO shows the same pattern at a smaller scale. At 50bb, CO limps 7.6%; at 200bb, just 0.7%. UTG and MP are entirely flat — near-zero limp rate at every depth, VPIP between 34% and 36% regardless of stack size. The inversion is position-dependent: it is strongest at BTN and fades as you move toward earlier positions.

In Cash no-limit, solvers do not limp. It is strictly dominated by raising or folding. The pot-limit constraint changes this calculus entirely. At 50bb, the maximum postflop bets are small enough that a raise does not build the kind of pot that lets strong PLO4 hands extract full value. Limping is the cheaper way in — and when you miss, you lose half a big blind instead of 2.5.

At 200bb, the math reverses. Rundown hands and double-suited holdings have enormous implied odds at deep stacks. Raising builds the pot geometry they need to realize that equity across multiple streets.

What this means in practice: Limping from the button in PLO4 is not a leak. It is the equilibrium strategy for the middle of BTN's range at short stacks. If you see a BTN limp at 50bb, respect it. And if you are playing 50bb PLO4, you should be limping the majority of your playable hands from the button.

2.4 BB defense narrows with depth against early-position openers

In Cash, BB defends UTG at roughly the same rate regardless of stack depth. In PLO4, BB gets tighter as stacks get deeper — but only against early-position openers.

PLO4 BB defense vs opener by stack depth. 6-max · 2.5bb open · 3% rake / 3bb cap

Source: plo-canonical-tables.md Table 4; plo-deltas.md §4f

Against UTG, BB defense drops from 61.2% at 50bb to 56.5% at 200bb — a monotonic decline of −4.7pp. Against MP, the narrowing is −3.3pp. Against CO, only −1.7pp. Against BTN, the defense is flat across all depths.

This is a PLO4-specific pattern. In Cash, BB defense vs UTG at 50/100/150/200bb is 36.3%/36.5%/36.1%/36.0% — essentially flat (total range 0.5pp, within noise floor).

The deeper the stacks, the more chips BB risks when calling a tight UTG range out of position. In pot-limit, BB cannot control the pot with small bets the way a no-limit player can. A deep-stack call against UTG commits BB to a pot where subsequent streets can escalate sharply if UTG holds a strong range.

Against BTN, no such penalty exists. BTN's wider range bets smaller, checks back more often, and holds more speculative hands — all of which reduce BB's commitment risk.

What this means in practice: At deep stacks against early-position openers, tighten your BB calling range. The 4–5 percentage points you shed between 50bb and 200bb vs UTG are the solver telling you that the marginal calls stop being profitable when the pot can grow fast against a tight range.

2.5 BB 3-bet rate against LP openers collapses with depth — the Cash BTN reversal

This is the sharpest format-level reversal in the preflop data. In Cash, BB 3-bets BTN more at deep stacks. In PLO4, BB 3-bets BTN less — dramatically less.

PLO4 BB 3-bet rate by opener × stack depth. 6-max · 2.5bb open · 3% rake / 3bb cap

Source: plo-canonical-tables.md Table 14; plo-deltas.md §4k

At 50bb, PLO4 BB 3-bets BTN at 17.8% — almost identical to Cash (17.0%). By 200bb, PLO4 BB 3-bets only 2.8%. Cash BB, by contrast, increases to 22.3% at 200bb.

Cash vs PLO4 BB 3-bet rate vs BTN by depth. 6-max · 2.5bb open · 3% rake / 3bb cap

Source: plo-deltas.md §4k

The two formats start at the same point (50bb) and diverge in opposite directions. By 200bb, the gap is over 19 percentage points — Cash BB 3-bets more than seven times as often as PLO4 BB against the same opener.

The reversal is clean at BTN. Against CO, Cash is flat (14.9% at both 50bb and 200bb) while PLO4 drops from 14.7% to 1.5%. Against MP, both formats decrease with depth, but PLO4's decline is roughly four times steeper (−10.4pp vs −2.7pp). Against UTG, PLO4 BB 3-bets at a flat 4.4% at every depth — too low to show any directional effect.

This pattern also holds at a larger open size. At 3.0bb vs BTN, PLO4 BB 3-bets 18.0% at 50bb and 4.4% at 200bb (decreasing), while Cash BB 3-bets 14.6% at 50bb and 17.8% at 200bb (increasing). The directional reversal is raise-size-robust.

The total defense rate against BTN stays flat across depths (67.2%/69.2%/67.1%). The 3-bet collapse is fully absorbed by a call increase — from 49.4% at 50bb to 64.3% at 200bb. BB is not folding more; it is shifting from 3-betting to calling.

In Cash no-limit, deep-stack 3-betting gives BB more control — you can choose your sizing across streets. In pot-limit, that control is capped. BB resolves the tradeoff by calling with hands that would be 3-bets in Cash and letting the implied odds work postflop.

What this means in practice: At 200bb in PLO4, your BB 3-bet range against LP openers should be nearly nonexistent — the solver 3-bets BTN only 2.8%. Call with the hands you would 3-bet in Cash. The pot-limit structure makes deep-stack calling far more profitable than deep-stack 3-betting from out of position.

The Cash mental model — and what it gets wrong

You already know the Cash c-bet heuristic. Dry high-card boards: bet a lot. Wet connected boards: check more. The logic is solid in No-Limit Hold'em. In PLO, the same heuristic gets the direction backwards on two entire board categories.

Paired boards — the most reliable c-bet textures in Cash — become checkback boards in PLO. Connected boards — the ones that scare Cash players into checking — become PLO's highest c-bet textures. The mechanism is the same in both cases: the wider ranges that four hole cards create change who has the board covered. This chapter walks through exactly where and why.

All tables in this chapter measure BTN vs BB in a single-raised pot, 100bb effective, 6-max PLO4 vs Cash NLHE. Baseline comparisons use matched rake (3% / 3bb cap) across both formats.

Paired-board suppression: check back, don't fire

The biggest single c-bet shift between Cash and PLO happens on paired boards. In Cash, paired high-card flops like KK9 are textbook c-bet spots — you have range advantage, your opponent's range is capped, and you fire big. In PLO, that logic inverts.

PLO4 vs Cash flop c-bet frequency on paired boards, BTN vs BB single-raised pot. 100bb effective · 6-max · 3% rake / 3bb cap

Source: plo-canonical-tables.md Table 6 (paired board rows). Sorted by delta magnitude.

Look at QQ5. Cash BTN c-bets 77.9% of the time. PLO BTN c-bets 14.1%. That is a 64 percentage-point swing — the single largest c-bet delta in the entire PLO dataset outside of trips boards. JJ7r is nearly as dramatic at −55.9pp. Even KK9, a board that Cash treats as a slam-dunk range bet, drops to 22.2%.

The one partial exception is AAx: PLO BTN still c-bets 62.6%, down from Cash's 82.0% but far higher than the other paired boards. BTN retains more Aces in a tighter opening range than BB retains in a wider defending range. The mechanism holds, but the magnitude is smaller because the board-coverage imbalance is less severe.

Why paired boards flip in PLO

The mechanism traces directly to how ranges interact with the paired card.

BB's PLO calling range is roughly 59–69% of hands (chapter 2 covered this — BB defends much wider than Cash at every position). That range includes a lot of hands that contain the paired card. On KK9, BB holds Kxxx combinations at a high rate — those hands were too weak to 3-bet but strong enough to call. BTN's opening range is around 52% wide, and it too contains Kings, but proportionally fewer of them end up in a c-betting situation where BTN wants to fire into BB's K-heavy range.

The result: BB has range advantage on paired boards. BTN checking back is correct. The model's 22.2% c-bet on KK9 signals that only BTN's strongest hands — sets, nut straights if the board allows — warrant immediate aggression.

Depth-independent

The suppression holds equally across stack depths. KK9 c-bet at 50bb is 25.4%, at 100bb 22.2%, at 150bb 24.7%, at 200bb 26.2% — flat within noise. This is not a stack-depth artifact. The board-coverage mechanism operates at the range-composition level, independent of SPR.

Source: hypotheses-and-mechanisms.md §M1 stack-depth axis data.

The trips extreme

The dataset's largest single negative delta comes from a trips board: 999. Cash BTN c-bets 98.7%. PLO BTN c-bets 36.8%. That is −61.9pp. BB's 4-card range holds 9xxx at high frequency — the same paired-board coverage mechanism, pushed to its logical extreme.

Source: plo-deltas.md §4, v2.1.0 final batch.

Connected-board elevation: fire at the boards Cash fears

The second major c-bet shift goes in the opposite direction. On connected rainbow and two-tone boards, PLO BTN c-bets significantly more than Cash.

PLO4 vs Cash flop c-bet frequency on connected boards, BTN vs BB single-raised pot. 100bb effective · 6-max · 3% rake / 3bb cap

Source: plo-canonical-tables.md Table 6 (connected board rows with positive delta). Sorted by delta magnitude.

On T98tt, Cash BTN c-bets 53.4%. PLO BTN c-bets 71.9% — almost 19 percentage points higher. Q97r hits 90.2% in PLO, up from 77.7% in Cash. These are the boards that many NLHE players would instinctively check — "too wet, too many draws, opponent connects easily." PLO's solver does the opposite.

Why connected boards elevate in PLO

BTN's PLO opening range is loaded with rundowns — J-T-9-8, Q-J-T-9, K-Q-J-T. These are the workhorse hands of PLO. On T98tt and JT9r, BTN's rundowns produce wraps, two-pair, and flopped straights at high frequency. BB's wider calling range includes more non-rundown hands that miss connected boards entirely.

The scope boundary: not all connected boards

This pattern does not hold on low connected boards. The card-rank threshold matters:

PLO4 vs Cash flop c-bet frequency on low connected boards, BTN vs BB single-raised pot. 100bb effective · 6-max · 3% rake / 3bb cap

Source: plo-canonical-tables.md Table 6 (low-connected rows).

On 876r, Cash BTN c-bets 81.4%. PLO BTN drops to 54.3% — a −27.1pp suppression, not an elevation. 765r is even more dramatic at −30.7pp. These boards are connected, but the card ranks are too low for BTN's rundown range to dominate. BB's wider calling range has better coverage of low cards.

The boundary sits at roughly Q-high or above. Evidence from the full 26-board panel: K76tt (+9.7pp), Q97r (+12.5pp), and A98tt (+18.7pp) all elevate. T76r (T-high with a gap) suppresses at −8.3pp. T98tt elevates (+18.5pp) because BTN's J-T-9-8 rundowns hit it directly. The refined rule: top card ≥ Q, or board is three-or-more consecutive with top card ≥ J.

Monotone exception

Monotone connected boards go the other way. 987s (monotone mid) shows PLO BTN c-betting 41.1%, down from Cash at 51.2% — a −10.1pp suppression. On monotone boards, BB's wider range includes suited hands with one-card flush draws. That equalizes the flush-draw advantage and narrows the range gap that drives elevation on rainbow and two-tone textures.

The monotone pattern has its own card-rank nuance. A-high monotone boards elevate slightly: A87s (+7.2pp), A98s (+4.1pp). Very low A-high monotone elevates dramatically: A43s (+40.1pp), A32s (+26.7pp) — BTN's wheel-draw range advantage on A+low-card textures is a distinct sub-mechanism. K-high and below monotone suppresses: K76s (−9.0pp), 987s (−10.1pp).

Depth-independent

Like paired-board suppression, connected-board elevation does not depend on stack depth. JT9r c-bet at 50bb is 85.4%, at 100bb 80.8%, at 150bb 80.8%, at 200bb 80.1% — flat. The board-coverage mechanism operates at the range-composition level, independent of SPR.

Source: hypotheses-and-mechanisms.md §M3 stack-depth axis data.

Three NLHE heuristics that break in PLO

The two mechanisms above combine to break three specific Cash intuitions that most players carry into PLO.

1. "Paired boards favor the raiser." In Cash, they do. In PLO, paired boards favor BB. PLO BTN checks back KK9 at 78% vs Cash at 30%. The wider BB calling range holds more of the paired card, flipping the coverage advantage. Only AAx partially survives because BTN retains more Aces from the tighter opening range.
2. "Wet boards → check back." In Cash, connected wet boards are danger zones for the c-bettor. In PLO, Q-high-or-above connected boards are where BTN c-bets hardest — up to 90.2% on Q97r. BTN's rundown-heavy range gives it range advantage on exactly the textures Cash players fear.
3. "Range advantage follows the preflop aggressor." In Cash, the preflop raiser has range advantage on most board textures. In PLO, the texture decides. BTN has range advantage on connected Q-high-or-above boards. BB has range advantage on paired boards, low connected boards, and mid-monotone boards. The preflop raiser's identity is necessary but not sufficient — the board texture flips the advantage sign.

The multiway reversal: connected-board elevation disappears with two opponents

The connected-board elevation described above applies to heads-up single-raised pots. In 3-way pots — BTN opens, SB and BB both call — the pattern reverses.

PLO4 vs Cash 3-way flop c-bet frequency, BTN vs SB+BB. 100bb effective · 6-max · 3% rake / 3bb cap

Source: plo-canonical-tables.md Table 15.

JT9r goes from +12.1pp in heads-up to −28.5pp in 3-way. T98tt goes from +18.5pp to −38.6pp. The connected-board elevation doesn't just shrink — it completely inverts. With two opponents, BTN's rundown range advantage evaporates. Two wide ranges hold enough connected combos to neutralize BTN's coverage edge.

Paired-board suppression, by contrast, amplifies in 3-way. KK9 drops from HU's −48.1pp to 3-way's −71.3pp. Two opponents hold even more of the paired card.

Dry boards converge: A72r shows a near-zero 3-way delta (+0.7pp), and K84r is only −4.3pp. Neither format has a strong edge on dry boards when facing two opponents.

The narrow scope of what we tested

PLO4 turn and river coverage is deliberately narrow. Eight turn probe spots and five river-bet-after-probe spots were queried at +50.7-level precision across four stack depths. The mechanisms below hold inside those spots. Do not extrapolate outside the tested lines — the board × depth combinations where they break are documented below, and the untested regions are larger than the tested ones.

Turn probe elevation — texture matters more than you think

After both players check the flop, BB probes the turn more often in PLO4 than in Cash. That much is true everywhere we looked except monotone boards. But the size of the effect, and whether it holds at all, depends entirely on the texture family and the stack depth.

Start with the cleanest signal. On A72r with a blank 2s turn, PLO4 BB probes dramatically more than Cash at every depth tested.

PLO4 vs Cash BB turn probe frequency on A72r + blank turn, by stack depth. BTN opens 2.5bb · BB calls · flop checks through · BTN-vs-BB SRP · 6-max

Source: plo-deltas.md §4g (M6 depth test) / plo-canonical-tables.md Table 12

Cash BB barely probes this turn at all — around 15–17% regardless of depth. PLO4 BB probes 61–69% of the time. The delta is nearly constant across the full 50–200bb range, which rules out rake as a driver (different pot sizes would produce different deltas if rake were the cause).

At 100bb, the effect extends across most non-monotone textures too:

PLO4 vs Cash BB turn probe frequency by board texture at 100bb. BTN opens 2.5bb · BB calls · flop checks through · blank 2s turn · BTN-vs-BB SRP · 6-max

Source: plo-canonical-tables.md Table 12

Six of eight textures probe more in PLO4. The two exceptions — Q65s and 987s — are both monotone boards below A-high. Monotone A-high (A87s) still elevates. The threshold sits at A-high: if the monotone board has an Ace, PLO4 BB probes more; if it doesn't, PLO4 BB probes less.

Where it breaks: the cross-texture depth sweep

The 100bb picture is clean. The cross-texture × cross-depth sweep revealed that the pattern breaks on connected-mid boards at non-100bb depths, and on dry K-high at short stacks.

M6 scope: full 24-cell texture × depth matrix. Same spot as above: BTN opens 2.5bb · BB calls · flop checks through · blank 2s turn · BTN-vs-BB SRP · 6-max

Source: hypotheses-and-mechanisms.md §M6 Multi-Dim Scope Worksheet. "—" = not queried. JT9r was absent from the depth-sweep reference batch at 50/150/200bb.

Three patterns emerge:

1. Dry A-high and paired K-high hold everywhere. A72r and KK9 show positive deltas at every tested depth. These are the safest boards to apply the probe-more rule.

2. Connected-mid boards (987r) only hold at 100bb. At 50bb, 150bb, and 200bb the delta flips negative. PLO4 BB already holds direct made-hand equity (straights, combo draws) on connected-mid boards, so the incentive to probe disappears — BB can check and realize equity passively instead.

3. Short stacks can flip the sign on K-high dry boards. K84r at 50bb shows a −6.2pp delta — BB probes less than Cash. At 100bb and above it reverts to the expected direction.

River bet direction reversal — the entire texture ranking flips

The next mechanism describes what happens when BB probes the turn and BTN calls. On the river, BB checks, and BTN decides whether to bet.

In Cash, BTN bets most on dry A-high rivers and least on connected boards. In PLO4, the ranking inverts completely.

BTN river bet frequency after BB turn probe + BTN call, by board texture. BTN opens 2.5bb · BB calls · flop checks through · BB probes turn · BTN calls · BB checks river · BTN to act · blank runout · 100bb · 6-max

Source: plo-canonical-tables.md Table 13

Look at A72r. In Cash it is BTN's best river-bet board — 45.2%, the highest of the five. In PLO4 it drops to 18.3%, dead last. Now look at JT9r. Cash ranks it #4 at 36.9%. PLO4 promotes it to #1 at 64.2%. The entire ordering flips.

The monotone mid board (987s) sits at exact parity — 37.2% in both formats — forming a clean pivot point. Below it (dry boards), PLO4 bets less. Above it (connected boards), PLO4 bets more.

The total directional separation between the extremes is 54pp — A72r at −26.9pp and JT9r at +27.3pp. That is a massive texture-dependent swing within the same action sequence.

What this implies for later-street play against wide PLO4 ranges

Both mechanisms point to the same lesson. PLO4 requires texture-first reasoning on the turn and river, not position-first or aggressor-first. The NLHE shortcut — "the aggressor barrels wide on scary cards" — breaks down specifically in the probe/call sequence, where BTN is no longer the aggressor. BB's wide PLO4 range creates entirely different range compositions after probing on dry versus connected boards, and BTN's river response must reflect that. If you are thinking "I was the initial raiser, I should be aggressive on the river," you are applying Cash logic to a PLO4 action sequence. The board texture is the variable that matters.

You have the data. Chapters 1–4 walked through nine mechanisms, dozens of board textures, and four stack depths. This chapter distills all of it into the adjustments you actually make when you sit down at PLO4.

Three sections. The first gives you a per-street checklist. The second lists ten NLHE heuristics that break — paired with their PLO4 corrections. The third tells you where this book ends so you know exactly when you are operating beyond its tested scope.

5.1 Per-street adjustment summary

Preflop

• Open wider from every position except SB. PLO4 VPIP runs +8.8 to +19pp above Cash across UTG through BTN. The cutoff for "worth playing" is structurally lower because four cards hit more board types.
• Defend the big blind wider — but by calling, not 3-betting. BB defends 59.4% vs UTG and 69.2% vs BTN. Fit-or-fold discipline from NLHE is a structural leak. The extra defense is almost entirely calls.
• At 50bb, limp the button more than you raise. The solver limps BTN -36.4% of the time — wait, let me restate. BTN limps 36.9% and raises only 12.8% at 50bb. At 200bb the composition completely inverts: 4.4% limp, 49.7% raise. This is not a leak — it is the equilibrium response to pot-limit at shallow stacks.
• Tighten BB defense against UTG and MP as stacks deepen. BB vs UTG defense drops from 61.2% at 50bb to 56.5% at 200bb. Cash stays flat across the same range. Deeper stacks mean bigger commitment risk against tight early-position ranges.
• Reduce BB 3-bets against late-position opens as stacks grow. BB 3-bet vs BTN: 17.8% at 50bb, 10.1% at 100bb, 2.8% at 200bb. Cash goes the other direction (17.0% → 22.3%). At deep stacks, call and realize implied odds instead of building a large OOP pot.

Flop

• Check back paired boards far more than you would in NLHE. On KK9, BTN cbets 22.2% in PLO4 vs 70.3% in Cash. On QQ5, 14.1% vs 77.9%. BB's wider four-card calling range holds more of the paired card than BTN's tighter raising range. The coverage advantage flips — checking back is correct on nearly every J–K-high paired board. AAx is the partial exception (62.6% vs 82.0%) because BTN retains more Aces from a tighter opening range.
• C-bet connected boards at or above Cash frequency — if the top card is Queen-high or above. JT9r +12pp, Q97r +13pp, A98tt +19pp, K76tt +10pp. BTN's rundown-heavy opening range connects to these textures hard. The Cash rule "wet boards = less c-betting" only holds for low-connected (876r −27pp, 765r −31pp) and monotone boards.
• Stay texture-dependent. The "I raised preflop so I c-bet" shortcut from NLHE is more wrong in PLO4 than anywhere else. The solver's c-bet frequency across 26 tested boards ranges from 14% to 91%. Board texture drives the decision — not preflop aggression.

Turn

• After a flop goes check-check, probe aggressively as BB. On A72r + blank turn, PLO4 BB probes 68.1% vs Cash 17.4% — a 51 percentage point elevation. The pattern is depth-invariant: 61% at 50bb, 69% at 200bb. BB's wider calling range holds more partial equity (draws, backdoor draws, pairs) that profits from betting the turn for fold equity after BTN reveals a capped range by checking back.
• The exception: mid-rank monotone boards. On 987s + blank turn, PLO4 BB probes less than Cash: 42.0% vs 67.8% (-25.8pp). On monotone boards where both players hold flush draws, BB's probing advantage disappears. A-high monotone is milder — probe normally on A87s-type boards (+12pp vs Cash).

River

• After BB probes the turn and BTN calls, BTN's river bet frequency depends on the board — and the direction reverses from Cash. Cash bets rivers most on A72r-type dry boards. PLO4 inverts this completely.
• On A72r, BTN bets only 18.3% (Cash 45.2%, −27pp). BB's probe range on dry boards represents strong made hands; BTN's capped range has little to bet.
• On JT9r, BTN bets 64.2% (Cash 36.9%, +27pp). BB's probe range is draw-heavy on connected boards. When a blank river misses BB's draws, BTN bets aggressively into the missed range.
• Mid-coordinated and monotone boards are near-neutral (0 to +4pp delta).

What this means in practice: If you are the BTN caller after a BB turn probe, do not apply your Cash river-betting instincts. Check rivers on dry A/K-high boards. Bet rivers on connected J-high+ boards. The texture of BB's turn probe range — not your own hand strength in isolation — determines the profitable action.

5.2 Ten NLHE heuristics that break in PLO4

1. "BB should fold most hands vs UTG."

PLO4 BB defends 59.4% vs a UTG 2.5bb open — nearly 60%. With four hole cards, almost every hand has enough connectivity or suitedness to justify seeing a flop. Fold less; call much more.

2. "Limping is always a leak."

At 50bb, PLO4 BTN limps 36.9% and raises only 12.8%. Pot-limit constrains the preflop raise size at shallow stacks, making limping the cheaper way to enter pots with implied-odds-dependent hands. At 200bb the composition flips — but at short stacks, limping is the equilibrium.

3. "Wet connected boards — check back more."

In Cash, this is broadly correct. In PLO4, connected boards bifurcate at a Q-high threshold. Q97r +13pp, JT9r +12pp, A98tt +19pp — BTN c-bets these boards more than Cash, not less. BTN's rundown opening range connects to Q-high+ connected textures structurally. The Cash heuristic only survives on low connected boards (876r, 765r) and monotone boards.

4. "Paired boards favor the preflop aggressor."

The single cleanest reversal in the dataset. On KK9, BTN c-bets 22.2% in PLO4 vs 70.3% in Cash. On QQ5, 14.1% vs 77.9%. BB's wider four-card calling range holds more of the paired card. The preflop aggressor is weak on paired boards in PLO4, not strong.

5. "Deeper stacks mean BB defends wider."

In Cash, BB defense is flat across stack depths. In PLO4, BB defense vs UTG actually narrows with depth: 61.2% at 50bb → 56.5% at 200bb. Deeper stacks increase commitment risk OOP against tight early-position ranges.

6. "Deeper stacks mean more 3-betting."

Cash BB 3-bet vs BTN increases from 17.0% at 50bb to 22.3% at 200bb. PLO4 reverses: 17.8% → 2.8%. At deep stacks in pot-limit, 3-betting OOP creates pots that commit stacks fast with little protection from equity compression. The solver calls instead and realizes implied odds on favorable runouts.

7. "I can estimate hand strength by looking at my hole cards."

PLO4's must-use-exactly-two rule creates hand-class boundaries that are non-intuitive from Cash experience. An Ace in hand does not guarantee a nut flush draw unless the Ace's suit pairs with another hole card to form the draw. Two pair is often a bluff-catcher, not a value hand. You cannot eyeball PLO4 hand strength from Cash instincts — verify each of the six possible two-card subsets explicitly.

8. "After the flop checks through, the turn is a spot to check-fold OOP."

In PLO4, it is a spot to probe. BB probes the turn +46 to +51pp above Cash on dry boards after a flop check-through. BTN checked back a flop — that means BTN's range is capped. BB's wider PLO4 calling range holds more partial equity that profits from betting for fold equity against a capped opponent.

9. "River bet-after-probe patterns follow Cash."

They invert. Cash ranks A72r as the most profitable river bet spot after a turn probe. PLO4 ranks A72r dead last (18.3% bet) and puts JT9r first (64.2%). BB's dry-board probe represents strength; connected-board probe represents draws. When draws miss the river, BTN bets into the missed range. When made hands hold up on dry boards, BTN has nothing to bet.

10. "The preflop aggressor's advantage carries through all streets."

5.3 Scope bounds and where this book ends

This book tests PLO4 strategy against Cash NLHE theory using a single verified model across 63 theoretical claims. Of those, 38 are confirmed, 7 are partially verified, and 17 remain untested. That is a tight scope by design — every confirmed claim traces to solver queries on a model that passes all 55 behavioral-property checks.

Here is what falls outside that scope:

• PLO5. The same model architecture is trained on PLO5, but v2.1.0 analysis covers PLO4 only. PLO5 data exists; this book does not include it.
• Multiway pots beyond 3-way. Chapter 4 briefly covers 3-way c-bet data (BTN opens, SB + BB call). Four-way and wider pots are untested. Do not apply these findings to multiway pots without additional data.
• Hand-composition bucket analysis. Preflop bucket data (double-suited vs rainbow starting hands) was added in v2.1.0 for the BTN at 100bb. Full positional bucket analysis across all positions and depths is not yet available.
• Straddled and 3-blind structures. All data is 6-max with standard blind structure. No straddle, no ante, no three-blind formats.
• Turn and river spots beyond the tested set. Eight turn probe spots and five river-bet-after-probe spots are confirmed. The full turn/river board matrix is not covered.

This is a feature, not a limitation. Tight scope is what makes the confirmed findings trustworthy. When you are inside the tested scope — heads-up or 3-way, single-raised or 3-bet pots, 50–200bb, the board textures tested — these findings are strong. When you are outside it, you are extrapolating, and this book is honest about where that line falls.

If you study PLO4 theory from canonical books and solver articles, you have a mental map of how the format diverges from Cash NLHE. This chapter tells you which pieces of that map the model confirms, which it gets directionally right but quantitatively wrong, and which it cleanly contradicts. Think of it as a compatibility report between published PLO theory and the model's output.

Measurement conditions: v2.1.0 dispositions across 63 PLO-TH theory entries; 42-query v2.1.0 batch on universal-dense-v4-player_20260402_150328.onnx; B1 trust gate 55/55 PASS (2026-04-17); noise floor 0.1pp.

PLO-TH category-level verdicts

Dispositions by theory category across 63 PLO-TH claims. Categorization: CONFIRMED / PARTIAL / DISCREPANT / NOT TESTED / OUT OF SCOPE. Category label uses the most-conservative member: any DISCREPANT makes the category DISCREPANT; any PARTIAL makes it PARTIAL; CONFIRMED requires every tested member to pass and no untested members to remain.

Source: plo-baselines.md category rollup. No category is DISCREPANT — every disagreement we found is scoped to PARTIAL (direction matches, magnitude or sub-case incomplete). "NOT TESTED" at the category level reflects untested members, not model failure — the tested theories inside those categories all pass.

PLO-LIT cluster-level verdicts

Dispositions by topical cluster across 58 PLO-LIT literature claims (Clusters 1–8). Each cluster maps to 4–12 individual claims; the cluster-level disposition uses the most-conservative tested member.

Source: plo-literature-extracts.md cluster dispositions. 58 claims; Cluster 3 and Cluster 7 carry the two concrete DISCREPANT flags — both on specific published frequency bands (LIT-15 "45–60%" and LIT-49 "moderate frequency") — rather than on direction.

PLO-SOL solver-anchor verdicts

PLO does not maintain a separate solver-anchor index on the scale of MTT-SOL. Published-solver cross-checks are inline to the baselines entries: MonkerSolver preflop ranges (LIT-44), GTO Wizard cbet sizing (LIT-18, LIT-49), and SPR stack-off benchmarks (LIT-48, LIT-54). A dedicated PLO-SOL file is scoped for the v2.2 version bump and will surface PKO-analogue solver disagreements (if any) at that point.

Top tensions — where the model disagrees with published theory

Three narratives on the most strategically important PARTIAL findings. Each names the divergence, what published theory would predict, what the model produces, and the PLO-specific factor that best explains the gap. We are describing divergence, not declaring theory wrong — in each case the published theory was formulated without direct coverage of the PLO-specific factor the model surfaces.

Tension 1 — Overbet direction holds, but PLO4 never overbets

Published theory predicts: Janda's polarized-range theory and the canonical NLHE overbet literature (Chambers Vol 2, Galfond) predict that on nut-advantage textures with strong range concentration, the bettor prefers sizings above pot to polarize value and bluffs and to extract maximum from capped defenders. In NLHE this manifests as 1.2–2x pot overbets on river spots with sharp range-advantage.

The model produces: PLO4 maxes out at pot-size and clusters sizing below pot more often than the polarized model predicts — in the 3BP data the model goes 100% cbet at low SPR but does so at pot-size, not above. We never observe an overbet because the rules prohibit one.

PLO-specific factor: Pot-limit is a structural sizing ceiling, not a strategic choice. The direction of A2b's claim — "on nut-advantage boards, use maximum available size" — holds, because PLO4 uses the pot-size bet on the analogous spots. What changes is that equity compression and the C(4,2)=6 combo density pull optimal sizing toward mixed, smaller bets across more spots than NLHE theory's polarized model predicts. The polarized model assumes a concentrated nut range facing a defender with many bluff-catchers; PLO4's equity compression reduces both sides of that concentration. The verdict is PARTIAL rather than CONFIRMED because we did not query the sub-pot-vs-pot-size distribution directly — the direction holds, the quantitative test is pending.

Tension 2 — MDF direction holds, but PLO4 BB defends far wider than MDF predicts

Published theory predicts: MDF (1 − α, where α = bet / (bet + pot)) is a game-agnostic pot-odds formula. Against a standard 2.5bb open it prescribes roughly 73% defense to prevent the opener from profitably bluffing any two cards, with the real GTO defense tightened below MDF to reflect rake, OOP disadvantage, and equity realization.

The model produces: PLO4 BB defends 59.4% vs UTG 2.5bb and 69.2% vs BTN 2.5bb — monotonically wider vs weaker openers, consistent with MDF's direction. At depth, BB defense vs UTG flat-declines (61.2% → 56.5% from 50bb to 200bb) rather than tracking the formula's depth-independence. The monotonicity matches; the absolute numbers sit between the Cash floor and the MDF ceiling.

PLO-specific factor: MDF's single-parameter formula treats a bet as a one-shot pot-odds question. In PLO4, the pot-limit sizing cap bounds α at 0.5, so the formula's upper range is structurally unreachable — every PLO4 spot starts inside the formula's "under-folded" zone. Combined with equity compression (PLO-LIT-2: best-vs-second hand edge is ~6%) and the 4-card equity-realization penalty, BB's optimal defense frequency lands closer to MDF's ceiling than NLHE's does, because cold-calling hands retain meaningful equity against any continuing range. The theoretical MDF is not wrong — it is working at the edge of the regime it was derived for. The verdict is PARTIAL because the MDF monotonicity CONFIRMS but the pot-limit Alpha-0.5 ceiling and bet-size-clustering sub-claim remains structurally-argued rather than queried against the sizing distribution.

Tension 3 — Polarization direction holds, but draw density keeps ranges mixed

Published theory predicts: Turn polarization is a game-agnostic solver property: as the street progresses, ranges crystallize, polarized ranges grow relative to flop, and preferred bet sizing concentrates at larger fractions of pot. The standard solver signature is flop mixed-size / turn larger-size / river overbet-or-check.

The model produces: On A72r turn, cbet frequency drops from 73.6% (flop) to 59.8% (turn) — a 13.8pp drop consistent with polarization direction. The B1 A5 (Own Bet Sizing Polarization) check PASSES at the model level. But the full turn sizing distribution remains clustered rather than sharply bifurcated into "bet-large or give-up" — the model retains small-size turn bets on wet textures that NLHE theory would expect to collapse into a single polarized size.

PLO-specific factor: Redraw equity on the turn is materially higher in PLO4 than NLHE because a wrap + flush-draw combo retains 40–55% equity against made hands through the turn. The traditional hand-strength gradient that polarized turn theory assumes — "strong made hands bet, weak air checks or bluffs" — is blurred by the middle category of "made-hand-plus-redraw" combos that are both value and semi-bluff simultaneously. Polarization direction still holds (the drop is real, and crystallization is real) but the mixed-sizing survives into the turn because the redraw distribution makes pure polarization dominated. The verdict is PARTIAL because the direction is confirmed by the A72r turn-drop and by B1 A5 PASS, but the full turn bet-size distribution was not queried against a Cash comparator.