# Top set vs bottom set: study data

Research date: September 14, 2026. Published by the GTO Gecko team.

## Model and sample

NLHE six-max cash, 100bb starting stacks. BTN opens to 2.5bb; BB calls. The flop pot is 5.5bb. The library imposes BB's initial check. BTN can check or bet 1.8bb/4.1bb. The catalogue labels rake as 5% with a 4bb cap; the original legacy solve settings, solver/version, abstraction and achieved convergence are unavailable.

Twelve unpaired rank patterns were declared before EV retrieval, each with rainbow and two-tone suits. Discovery: K95, Q82, J74, A96 (eight classes). Held out: K72, Q95, J86, T74, 984, 876, 754, 654 (sixteen classes). Suit counterparts share a rank family and are not independent validation samples. All 24 requested trees were available. All 216 exact set rows had positive reach: three legal combinations each of top, middle and bottom set on every board. No eligible row was excluded.

## What the files mean

- `board-summary.json`: all 24 board summaries, including all three set ranks' checking frequency, mean local losses, median, 95th percentile, maximum and shares below 0.05/0.10/0.20bb thresholds.
- `selected-hands.json`: eight illustrative exact hands with ordered actions, conditional frequencies and EVs. These are selected examples, not the complete private database.
- `range-views.json`: the two displayed 169-cell ranges on K♠ 9♥ 5♦. BTN chooses a c-bet/check; BB responds to 1.8bb. `mass` is summed exact-combo reach; `legalCombos` counts unblocked physical combinations; `weight = mass / legalCombos`; frequencies are the reach-weighted action mix among present combinations. Absent cells have no mix. A class average can hide suit differences.
- `range-composition.json`: current five-card made categories for both players on K♠ 9♥ 5♦ and 8♠ 7♥ 6♦. Categories partition each marginal range. Top pair excludes two pair/sets; a straight outranks a set. These counts are not showdown equity or a range-advantage measure.
- `response-composition.json`: BB responses to each allowed bet, both before and after removing exact hero cards. Response masses multiply each hand's reach by its normalized action probability. Category counts partition each response. Holding the stored strategy fixed while removing cards is not a re-solve or a causal decomposition of EV.
- `check-regret.svg`: mean checking-loss chart. Its numbers are derived from `board-summary.json`; the article supplies the same values in a mobile HTML chart.

The article also uses owned poker styling and AI-generated header artwork. Neither is numerical evidence.

## Calculations and weighting

For exact hand h, local checking loss is `max(EV(h,bet4.1), EV(h,bet1.8), EV(h,check)) - EV(h,check)`.

Example: K♦ K♣ on K♠ 9♥ 5♦ has best stored action EV 13.782bb and check EV 13.658bb, a 0.124bb difference. 5♠ 5♣ has best EV 12.295bb and check EV 11.803bb, a 0.492bb difference. Compare alternatives within one row; absolute EVs across different boards are not a controlled comparison.

Within a set class, means use positive exported marginal combo reach. Across boards the article gives each class equal weight. These are descriptive selected-class means, not real-game occurrence probabilities. We do not reconstruct folded-player card bunching or a complete joint distribution.

Positive-reach strategy vectors in inspected nodes sum to 0.99, 1.00 or 1.01. Frequencies are divided by their vector sum. EV fields are converted to bb with the current application's divisor of ten. Three-decimal EV displays describe file resolution, not numerical accuracy. Percentages round independently and need not add to exactly 100 in display.

## Hypotheses and outcomes

1. Top set checks at least as often as bottom set on at least 75% of selected classes. Discovery: 8/8. Held out: 10/16, below 75%. Overall: 18/24. The held-out result prevents treating the full-sample percentage as successful general validation.
2. Top set has lower/equal mean local check loss than bottom set. Observed on 22/24 classes, 15/16 held out. Equal-board mean losses are 0.033569bb top, 0.134292bb middle, 0.221375bb bottom. The two reversals (A96 rainbow and 876 two-tone) are small and are not established as precise optimal rankings.
3. Automatic checking with top set stays within 0.10bb of the best action for at least 95% of top-set marginal mass on each board. Passes 21/24; fails K95 rainbow, Q82 rainbow and K72 rainbow. Passes 19/24 at 0.05bb and 23/24 at 0.20bb. These thresholds were study choices, not universal error definitions or numerical error bounds.

## Accuracy and limits

An independent implementation reproduced 216 set rows, 24 summaries, both 169-cell grids, all displayed range/response compositions and the eight selected hands. A numerical consistency screen flags an action when its normalized frequency is at least 10% but its EV trails the best available action by more than 0.10bb. No BTN decision node failed, including all set rows. BB response nodes contained 56 flagged hand/action entries against 1.8bb and 209 against 4.1bb; the largest gap was 0.357bb. The featured K95 rainbow small-bet response has no such flags; its four large-bet flags involve high-card hands, not top pair. A stricter tolerance reveals further discrepancies; passing this chosen screen is not proof of equilibrium or exact indifference.

Results compare local actions against stored continuations. We did not evaluate a changed whole strategy, adapting opponents, human behavior, different stacks, other position pairs, ICM or multiway play. Full raw trees and reproduction scripts remain in the owner's private research bundle. Selected results and illustrative range views are published here; internal endpoints and full library exports are not included.