# Overpair bet-size study

Study date: September 11, 2026. Article: https://gtogecko.com/blog/overpair-bet-size-study

## Model and coverage

NLHE cash, six-max preflop configuration, 100 bb before posting, no ante, 5% rake capped at 4 bb. One 2.5 bb opener (BTN in the main study, CO in a separate comparison) and a BB call, with the folded 0.5 bb SB giving a 5.5 bb flop pot. BB has only check at the exported root. IP actions are check, bet 1.8 bb and bet 4.1 bb. These are stored library outputs, not new solves.

Twenty BTN flop classes contain 564 positive-weight exact overpairs; four separate CO trees contain 126. Overpair means a pocket pair strictly above the highest flop rank. All eligible combo weights happen to equal 1 in these exports. Eight BTN discovery boards preceded protocol freezing; 12 validation boards from six new rank patterns followed it. Six validation rank patterns each have rainbow and two-tone versions; these versions are comparisons, not 12 independent rank families. Ten main boards are two-tone and ten rainbow. This is a chosen sample, not a chance-weighted population estimate. A separate ace-high feasibility fetch contained no eligible overpairs and is outside the 24-tree study.

Discovery: T85r, 974r, J96r, 863r, 987tt, T98tt, 876tt, 753tt. Validation: K83, Q94, J72, T62, 654, 543, each rainbow and two-tone. Exact suits are in the data files. CO comparison: T85r, 974r, 987tt, 753tt. No study trees were missing or excluded.

## Definitions

For each exact combo, local action loss = maximum available action EV minus the EV of the tested action. This measures one decision against stored continuations. It does not evaluate a whole changed policy or an opponent adaptation. Values were converted to bb using the current app's divide-by 10 convention. The exported EV resolution is 0.001 bb after conversion; that resolution is not an accuracy guarantee.

The predeclared shortcut bets 4.1 bb with every overpair. It passes a board only when at least 95% of that board's overpair marginal reach has loss at most 0.10 bb. Sensitivity thresholds: 0.02, 0.05, 0.10, 0.20, 0.50 bb. The near-gap description uses 0.02 bb. These are editorial screens, not universal poker error definitions or solver error bounds.

Within a board, use exported exact-combo marginal reach with no extra hand multiplicity. Across board classes, each board has equal weight within its named group. Quantiles are computed from the equal-board mixture, not by averaging board quantiles. Do not convert these figures to dealt-hand frequencies or bb/100.

Raw probabilities and reach are rounded to two decimals. Positive action rows with totals 0.99 or 1.01 are normalized by their own total. Original EVs are preserved. In range grids, hand-class conditional mixes average exact combos by reach; entry weight is weighted combo mass divided by the number of legal class combos after board blockers. Missing preflop hands have zero entry weight, not a fold strategy.

Both displayed range grids exclude flop cards but are not conditioned on a single opposing hole-card combo. For the response table only, remove all BB combos overlapping AsAh, then weight each BB action by remaining reach times normalized response probability. Its denominator is 322.75 compatible weighted combos. BB retains the stored response strategy to BTN’s betting range, without knowledge of the exact aces; this is card-removal reweighting, not a re-solve against AA. There is no earlier discretionary BB flop action to filter, since checking is imposed.

Made-hand groups compare exact five-card ranks on the flop. Direct draw means four cards to at least one five-rank straight (including the wheel), provided a straight is not already made, or four cards of one suit. It is an additional, nonexclusive flag; some pairs can have a draw and an already-made straight can still have a flush draw. No showdown equity is computed and no claim of a causal range/blocker advantage follows from these summaries.

## Check the main arithmetic

BTN AsAh on `7s5s3h`: large EV 5.805 bb, small EV 6.084 bb, check EV 6.087 bb. Large loss=6.087-5.805=0.282 bb; small loss=0.003 bb. Frequencies normalize the raw [0.01,0.08,0.90] row to about [1.0%,8.1%,90.9%].

Four of ten BTN two-tone boards fail the 95%-cheap screen: 753tt, 876tt, 654tt, 543tt. Two of six held-out two-tone boards fail. Across those ten boards, the equal-board mean large-bet loss is about 0.0223 bb and the fraction exceeding 0.10 bb is about 7.17%. Held-out two-tone pooled cheap share is 95.95%, which does not override the individual 654/543 failures.

As a secondary exploratory finding, every tested BTN overpair's small-bet loss is at most 0.061 bb. Checking can be costly: QsQh on `Js7s2h` has large EV 6.907 bb, small 6.904 bb and check 6.715 bb (check loss 0.192 bb). On `Js7h2d`, those values are 7.766, 7.765 and 7.462 bb (check loss 0.304 bb).

## Files

- board-summary.csv: all 24 scenario summaries, frequencies as fractions and EV/loss in bb.
- aggregates.json: equal-board summaries and threshold sensitivities; CO kept separate.
- chart-data.json: 10 individual BTN two-tone bars, showing share above 0.10 bb large-bet loss.
- selected-hands.json: eight exact rows used in the main comparison tables.
- range-views.json: two selected 169-class range figures, including legal combo counts and mass.
- range-composition.json: both current ranges by made-hand category.
- response-composition.json: both BB response menus conditioned on AsAh.
- large-bet-loss.svg: deterministic plot from chart-data.json.

Solver/version, achieved convergence, requested accuracy and future-street abstraction details are unavailable. There are no statistical confidence intervals and no verified equilibrium error bound. Full proprietary trees and private access information are not distributed. Primary calculations were independently recomputed from retained raw exports before publication.