The 7 Pillars of Poker Strategy
and what our solver says about each

Bet sizing is where theory meets money. Get it wrong and you either leave value on the table or torch fold equity you needed. Get it right and your ranges print across all three streets.

Six theories govern how solvers choose sizing. Our model confirmed four of them cleanly, refined one (stack depth turns out to be more interesting than "shallow = small"), and partially confirmed a sixth where the mechanism is real but under-isolated. What follows is what we found — board by board, combo by combo, stack depth by stack depth.

The wetness parabola: why sizing is not monotonic in board texture

You would expect bet sizing to grow as boards get wetter. More draws, more equity to deny, bigger bets. That is half right and half dangerously wrong.

Look at how the solver actually sizes across textures. We tested CO versus BB in a single-raised 100bb pot, holding everything else constant. Sizing behavior tracks a curve — small on dry, larger on semi-wet, then back to checking on the wettest boards:

CO flop sizing behavior across six board textures. Same position (CO vs BB), same stack depth (100bb), same preflop action — only the board changes.

Source: cash-baselines.md Table 3 (CO c-bet by board) + Table 7 (per-class check % by board) + D2 verdict worksheet.

On dry K72r, the solver bets most of its range at a small sizing. On semi-wet T98, it steps up to 50% pot more often — there is equity to deny and the range supports it. But on 543, where BB has the nut advantage (more straights, more two-pair), the solver's premium hands — AA, KK, AK — check 85.3% of the time. Protection bets collapse when the opponent's range is too strong to fold and too connected to be behind.

The two-tone data confirms this shape from the other direction. Introducing a second suit (adding flush-draw potential) pushes c-bet frequency down, not up:

Rainbow vs two-tone CO c-bet frequency on matched boards.

Source: cash-baselines.md Table 8.

Adding a flush draw to K72 costs you 13.8 percentage points of c-bet frequency. Adding it to T98 costs 8.0. The wetter the board already is, the less incremental damage the second suit does — because you were already sizing down or checking.

You cannot bet big unless two things are true

Large sizing requires two conditions simultaneously:

1. Nut advantage — you hold more of the strongest hands.
2. Fold equity — your opponent holds hands that will actually fold.

Miss either one and the big bet stops working. The solver shows this clearly in how it distributes sizes across streets.

The size axis tells the story directly. Flop c-bets land at around 3bb (33% of a roughly 9bb pot). Turn bets jump to 7bb. River top sizes reach bet19.1, bet25.5, and on connected runouts bet63.8 — a roughly 250% pot overbet. The progression is geometric: each street roughly doubles or triples the previous bet. This only works when the bettor's range supports both conditions at each street.

Here is how the river sizes distribute on three runouts where CO maintained aggression flop-through-river:

River bet behavior on three runouts. CO opens, BB defends, CO barrels all three streets.

Source: cash-baselines.md Table 15.

On K72r → 2d → 5h — a dry runout where CO's range dominates throughout — the solver concentrates at bet19.1 (53%). One sizing, high confidence, both conditions fully met.

On T98 → 2s → 5h — a connected runout where CO has nut straights plus bluff candidates — the solver spreads across four sizes, reaching all the way to bet63.8 at 23%. That overbet is only possible because CO's range on this runout has genuine nut hands (straights, sets) and BB's range has hands that fold (missed draws, weak pairs). Both conditions met, extreme sizing unlocked.

On A94r → 4c → 8d, the solver hedges. The 8d turn completes some draws for BB and weakens CO's nut advantage slightly. Bet frequency drops to 66.7% and sizing spreads more evenly — the solver is less certain both conditions hold across its full betting range.

Why flop overbets are vanishingly rare

The solver almost never overbets the flop. Across eight boards at 100bb, the overbet action (bet8.2, approximately 150% pot) appeared on exactly one board — and that board is instructive.

Flop overbet frequency (bet8.2) by hand class on AK6r, CO vs BB 100bb.

Source: cash-baselines.md D1 verdict worksheet + B4 verdict worksheet (sizing_per_combo overbet distribution).

AK6r is the one board where CO's range has extreme nut advantage — AA, KK, AK, every AQ — and BB's range is capped from just defending preflop. On every other board, the nut advantage is either absent (543, 654) or shared (T98). No overbet.

The offsuit broadway class actually overbets at a slightly higher rate (21.76%) than the premium class (18.75%) on AK6r. That is not a mistake. Offsuit broadway hands are the balanced bluff slot — they lack the showdown equity of premium hands but carry enough potential to balance the overbet range. Without enough bluff candidates, the overbet cannot be profitably constructed. This is the range-composition constraint in action: you cannot bet bigger than your bluff availability supports.

On 543, the premium class checks 85.3% of the time. No overbet, barely any bet at all. The nut advantage belongs to BB (more straights, more two pair from the blind defense range), so there is nothing to overbet with.

Multi-street sizing grows geometrically

When the solver barrels across all three streets, the sizing progression is not arbitrary. It follows a geometric pattern: each street's bet is roughly 2.3–3× the previous street's bet. The progression builds the pot toward a target final size.

On the K72r → 2d → 5h runout (the cleanest dry line in our test set), the sizes are:

• Flop: 3bb (33% of a ~9bb pot)
• Turn: 7bb (~47% of pot after flop bet + call)
• River: bet19.1 at 53% — the dominant sizing

That is a 3 → 7 → 19bb progression. Each bet roughly 2.3–2.7× the previous one.

On T98 → 2s → 5h (a connected runout), the solver uses the same geometric structure but pushes the river harder: bet63.8 at 23% of frequency, alongside bet25.5 at 21% and bet19.1 at 17%. The solver spreads across sizes because the range supports both a large overbet (with nut straights as value and busted draws as bluffs) and a medium-sized value bet (with strong pairs).

The key observation from the data: strong hands (sets, two pair) almost exclusively continue betting each street. On boards where CO has nut advantage, these hands use larger sizing. On boards where ranges are closer, they use smaller sizing. But the progression structure — geometric growth street to street — is constant across textures.

Stack depth compresses sizing and reshapes frequency

At 20bb, strategy looks nothing like 100bb. The solver compresses bet sizing toward 33% pot plus all-in (the geometric multi-street plan only has room for one or two bets, not three). At deep stacks (150–200bb), the solver goes the other direction — checking more often because there is more room for multi-street maneuvering and pot-control lines gain value.

The c-bet data shows how frequency shifts across the tested depths. We tested CO vs BB on K72r at 20bb, 100bb, 150bb, and 200bb:

CO flop c-bet frequency on K72r across stack depths. Frequency does not decline monotonically — it is nearly flat from 20bb to 100bb and falls at deeper stacks.

Source: cash-baselines.md D5 verdict worksheet (batches_cash_20bb_shortstack + batches_cash_deep_stack).

The frequency story is more interesting than the sizing story. It does not decline monotonically from shallow to deep. It sits at 83.6–84.4% at both 20bb and 100bb, and falls off only at the deep extensions (78.8% at 150bb, 75.6% at 200bb).

The preflop side of the depth story reinforces the picture. VPIP by position across depths:

Preflop VPIP tightens at 20bb and saturates above 100bb.

Source: cash-baselines.md Table 2.

BTN tightens by 12.7 percentage points from 100bb to 20bb (43.3% → 30.6%). But above 100bb, preflop ranges barely change — BTN at 200bb is 46.9%, only 3.6pp wider than at 100bb. Preflop widening saturates. Postflop softening does not: c-bet frequency continues to decrease from 100bb through 200bb as the solver incorporates more check-back and pot-control lines.

At 20bb specifically, SB opens a new action: all-in at 10.6% frequency. The shove menu opens at shallow stacks, consistent with the sizing-compression pattern — when the geometric plan cannot fit three streets of betting, the solver shortcuts directly to shoving.

River sizing splits by blockers

Blocker structure drives per-combo sizing decisions on the river. Two hands with the same raw strength — both top pair, both the same kicker class — can end up using different sizes because one blocks the opponent's calling range and the other does not.

The clearest signal is on the AK6r flop overbet. The premium class (AA/KK/AK) overbets at 18.75% while offsuit broadway hands overbet at 21.76%. This is backward from a naive "strongest hands bet biggest" expectation. Offsuit broadway plays the bluff slot in the overbet range — weaker showdown value, but the blocker structure supports using the largest size as a balanced bluff.

On the K72r → 2d → 5h river, per-hand call/fold data shows that Kx hands (which block CO's Kx value combos) call at higher frequency than Ax hands without that blocker. The blocker makes BB's call cheaper in an information-theoretic sense: holding a K reduces the probability that CO is value-betting Kx, which shifts the calling threshold.

This theory is pending because the EV-magnitude verification cannot run: the per-hand EV field has known reliability issues (KI-4) that prevent isolating the size of the blocker effect in expected value terms. The frequency-layer signal is present — hand classes with different blocker structures do use different sizes and defend at different rates — but frequency patterns are consistent with either blocker-driven sizing or indifference balancing that happens to correlate with blocker structure. Separating those two causal stories requires per-combo EV comparisons across sizing actions, which is blocked by KI-4. (See the Research notes at the end of this pillar for the full discussion.)