# Missed flush draws: selected river study data

Study and retrieval date: September 15,2026. Article: https://gtogecko.com/blog/missed-flush-river-study

## What was tested

Eight selected 100bb BTN/BB six-handed cash histories. BTN opens 2.5bb; BB calls. BB checks flop; BTN bets 1.8 into 5.5bb; BB calls. Turn 2d: BB checks; BTN bets 6.8 into 9.1bb; BB calls. River:22.7bb pot,88.9bb behind, BB checks; BTN can check or bet 9.1/15.2/28.4/88.9bb. BB's river leads and raises remain in the full conditional tree. Flop check was imposed upstream.

Original cash catalogue:5% rake,4bb cap, no ante. Original solver/version/achieved convergence/settings unavailable. New river jobs use neutral action incentives and no additional river rake, with the existing engine's SPR size preset. Requested accuracy setting 0.05 has unreturned units; iteration ceiling 500; achieved accuracy and stopping reason not returned. No whole-tree cash re-solve, ICM, empirical population, causal mechanism or human outcome is claimed.

The candidate heuristic is an existing give-up idea, not a newly invented rule. Discovery:Qs 9s 4h 2d 3c andAs 7s 4h 2d 8c. Six other flop rank families were held out. Eligible exact hands:two spades, seven distinct ranks and no straight/flush, positive serialized BTN weight, complete finite actions/EVs. Ace-high is included.169 original hand/scenario rows,127 held out. Reruns contain 182 eligible rows.

Screen declared before validation: checking within 0.1bb of best available action for 95% or more of eligible BTN marginal range mass in each scenario. Sensitivity thresholds 0.05/0.2bb are in summaries. Local loss=max available action EV minus check EV, against fixed returned continuations. Within-scenario own marginal weights; equal-scenario means; not occurrence-weighted results. Original screen fails 6/8,5/6held out. Rescaled screen fails 7/8;Ks 8s 3h 2d 5c flips around 0.1bb.

## Input and output handling

Fresh turn-export seed ranges are authoritative. They differ slightly from multiplying rounded flop exports. Apply each turn actor's stored action probability once, normalize only within the rounding allowance, remove river cards, retain positive inputs. No pinned/injected hands or minimum-weight floor.

Original inputs serialize weights to two decimals; all supplied primary weights match the app's toFixed(2) output. After discovery revealed sparse BTN weights, all 8 scenarios were rerun after dividing each whole range by its maximum before serializing. Common positive scaling leaves relative probabilities unchanged before rounding. These reruns are a specified alternative approximation, not additional independent scenarios.

The sensitivity uses Python's two-decimal float formatting. In scaledTs 7s 3h 2d 4c, three exact 0.125 entries QhTc,QhTd,Ks 2s become 0.12, where JavaScript would produce 0.13. Preserve that actual solved input convention. No headline 9s 8s or eligible missed-draw row is among these three. Serialized inputs are retained privately.

The original and rescaled omitted masses and total absolute changes are in the scenario summaries. Scaled omission is quoted on the original weight scale. Directly comparing unnormalized mass totals between differently scaled models is meaningless.

Output probabilities have two decimals and can sum to 0.98/0.99/1.01/1.02. Validate each element, permit at most 0.005 per action of total rounding deviation, then normalize. Retain original output privately. EVs have 0.001bb display granularity after unit conversion, not established 0.001bb accuracy. At BTN after BB check, add half the initial pot to raw EV before dividing by 10; same-node action losses need no offset.

Independent checks verified all 16 summaries,338 public range cells, both ranges' category composition, all response exclusions, and 6 selected hands across both variants.199,746 raw fold EVs at 576 nodes match contribution origin exactly. Zero-added-rake check-through reconstruction across 6,452 positive-input BTN hands differs by at most 0.009409bb. Full fixed-policy recomputation using exported frequencies preserves the main three 9s 8s choices. Residuals are not all proven to arise solely from rounding.

Some supported actions elsewhere are more than 0.1bb below their best listed EV (up to 0.369bb in primary BTN data). Those inconsistencies and unknown convergence prevent an exact-equilibrium interpretation. Original selected 9s 8s preferred actions are pure in the rounded output and survive the independent calculation and input sensitivity.

## Data index

- board-summary.json:8 original-input aggregates, thresholds, input-rounding diagnostics and consistency-flag counts.
- board-summary-scaled.json:same 8 scenario aggregates under proportional scaling before rounding.
- selected-hands.json:6 featured exact hands, all 5 available actions, frequencies, local EVs and corresponding sensitivity results.
- range-views.json:2 illustrative 169-class grids, per-available-combo entry weights, weighted masses and action mixtures. These selected public illustrations are not full proprietary tree exports.
- range-composition.json:current marginal BTN and checked BB ranges on the primary ace-high and ten-high comparison boards. High-card and pair categories are made-hand rankings, not equity.
- response-composition.json:BB fixed response at the named bet, before/after excluding the named hero cards, with weighted category mass. Counts and percentages have explicitly different denominators.
- check-cost.svg:aggregate original/rescaled chart. Its exact plotted values are in the two board summaries.

Header: original Gemini editorial artwork. Tables/grids/SVG: owned deterministic evidence visuals. Full input ranges, private endpoint details, entire solver exports and private research ledgers remain private.