# Odd-chip settlement: reproducible teaching example

Created and primary sources accessed September 7, 2026. Original GTO Gecko
editorial example; no customer data, app telemetry or third-party hand history.

## Question and scope

Can two players with the same tied winning hand receive different gross awards
from two separate pots? This fixed, single-board, high-only Hold'em tournament
example answers yes at a 100-chip minimum denomination. It uses exactly two
established tied winners per pot, the button-based priority in TDA 2024 v1.0
Rules 20–21 and corroborating 2026 WSOP Rules 73–74 (page 18).

- https://www.pokertda.com/view-poker-tda-rules/
- https://assets.wsopcdn.com/wsop/1a72ba28-781c-409d-a9c3-5ca13c4c5718.pdf
- https://www.pokertda.com/ (2026 revision expected mid-September when checked)

Use the event's adopted version for actual play. This is arithmetic for known
pots and winners, not a venue ruling or an automated action/hand evaluator.

## Fixture and pot provenance

Seats clockwise A,B,C,D,E; button E; blinds 100/200; no ante, rake or uncalled
excess. A/B start with 500 each; C/D with 100 each; E at least 500. A posts100,
B posts200, C and D call100 all-in, E calls200, A raises all-in to500, B calls
to500, E folds. All values are tournament chip values, not physical chip counts.
A and B are declared tied best live hands; C and D lose. All hands and pot
eligibility are resolved before this calculation.

Contributions: A500+B500+C100+D100+E200=1,400. First100 from each contributor
makes main500, eligible A/B/C/D. Remaining A400+B400+E100 makes side900,
eligible A/B only. E's contribution layers above100 have the same eligibility
and form one side pot. Main and side remain distinct because their eligibility
sets differ, even when their final winning hands coincide.

At unit100, main pays A300/B200 and side A500/B400, for A800/B600. Merging1400
first or alternating remainder recipients would incorrectly give700each.
At unit50 or25, both actual pots divide evenly and totals correctly become
700each. Those are separate denomination regimes, not post-showdown changes.

## Method

For each pot P, minimum denomination u and two winners, P/u must be an integer.
Let q and r be the quotient and remainder of (P/u) divided by2. Each winner
receives q*u; if r=1, give one more unit u to the first winner clockwise after
the button. Apply independently per actual pot, then add player receipts.

The study enumerates five declared button inputs and three denomination inputs:
15 configurations, two pots each, 30 CSV rows and15 hand totals. Button rotations
are isolated settlement-order checks with fixed pots/winners, not replays of
the original preflop action. No random sampling, iterations or seed applies.

The generator uses quotient/remainder and circular seat distances. The independent
verifier reconstructs contribution layers with live eligibility and distributes
individual minimum-denomination units in winner order. Neither evaluates cards.
Checks establish arithmetic/data agreement; interpretation of rules was reviewed
separately against the named primary sources.

## Reproduce (Python 3.10 or later; standard library only)

Keep inputs.json, generate.py and verify.py in the same folder. To compare newly
generated output without overwriting the published files:

```text
python generate.py --output reproduced
python verify.py --directory reproduced
```

To check the published JSON/CSV beside the scripts:

```text
python verify.py
python -O verify.py
```

The generator copies inputs.json into a separate output directory; the verifier
reads inputs and outputs from the directory being checked. The generator refuses contribution/pot/eligibility
changes: it is a reproducible article fixture, not a general pot calculator.
The independent verifier's literal oracles bind it to the published five-button,
three-denomination study; changing the fixture requires a separate study/review.

## Files and limitations

inputs.json defines the fixture; results.json and settlements.csv contain all
awards. settlement.svg is the inline diagram; hero.svg supplies the article
hero source. settlement-sheet.html is a manual, printable review sheet with
an answer key. SHA256SUMS records the public bundle file hashes, excluding itself.
SVGs and worksheet are original editorial assets, not copied source diagrams.

Excluded: more than two tied winners per pot; high-low, stud, multiple boards;
disputed hands, refunds, unknown contributions, house exceptions, rake, ante,
ICM, bounty awards, strategy and learning-effect claims. Gross receipts include
previous contributions and are neither profit nor expected equity. Smaller
denominations and different rules must be confirmed, never inferred from a
preferred award. Official rules/store descriptions require later revalidation.