# Short Deck starting-hand equity study

This bundle supports the GTO Gecko article **“Short Deck Starting-Hand Equity: 12 Exact Hold’em Matchups.”** It publishes the fixed cards, rules, complete board counts, generator, independent verifier, and machine-readable results behind every reported percentage.

## Question

How much does a familiar heads-up all-in matchup change when we move from standard 52-card Hold’em to one named 6+ Hold’em rules profile? How much comes from removing ranks 2–5, adding A-6-7-8-9 as the low straight, and ranking a flush above a full house?

## Rules profiles

The article follows the current PokerStars 6+ Hold’em rules page, accessed 2026-09-04:

- **Standard Hold’em:** 52 cards from 2 through ace; A-2-3-4-5 is the lowest straight; a full house beats a flush; a straight beats trips.
- **Short Deck official profile:** 36 cards from 6 through ace; A-6-7-8-9 is the lowest straight; a flush beats a full house; a straight beats trips.
- **36-card deck-only counterfactual:** ranks 6 through ace, only ordinary consecutive straights from 6-7-8-9-10 through 10-J-Q-K-A, and the standard category order. Against standard Hold’em, this isolates rank removal for the fixed cards.
- **Low-straight counterfactual:** the same 36-card deck plus A-6-7-8-9, but the standard full-house-over-flush category order. Against the deck-only profile, this isolates the low-straight convention. Against the official profile, it isolates the category-order swap.

Other Short Deck rooms can use different hand-ranking conventions. Results here do not silently transfer to a trips-over-straight game.

Primary rules source: <https://www.pokerstars.com/poker/games/six-plus/>

## What is enumerated

Each row fixes four collision-free hole cards, including suits. The programs enumerate every legal five-card board:

- standard: `C(48,5) = 1,712,304` boards per matchup;
- Short Deck: `C(32,5) = 201,376` boards per matchup.

Win, tie, and loss counts partition the entire board space. Equity is `(wins + ties / 2) / boards`. No random number generator, sampling error, solver range, betting tree, rake model, or population data enters these calculations.

The twelve rows are deliberately **fixed-suit examples**, not suit-averaged hand classes. Suit alignment affects blockers and flushes. Reverse the two named hands to obtain the complementary equity, but do not relabel a row as every possible `AKo`, `JTs`, or pair-versus-overcards configuration.

## Decomposition

For each fixed matchup:

1. `deckRemovalEffectPp = shortDeckConventionalStraightStandardCategoryOrder.equityPct - standardHoldem.equityPct`
2. `lowStraightEffectPp = shortDeckLowStraightStandardCategoryOrder.equityPct - shortDeckConventionalStraightStandardCategoryOrder.equityPct`
3. `rankingSwapEffectPp = shortDeckOfficial.equityPct - shortDeckLowStraightStandardCategoryOrder.equityPct`
4. `totalEffectPp = shortDeckOfficial.equityPct - standardHoldem.equityPct`

All three transitions use the same fixed hole cards. The two Short Deck transitions also use exactly the same 201,376 boards, so they change one rule at a time. This is an arithmetic decomposition of equity under four declared models, not a claim that players historically adopted the rules in that order.

## Reproduce

From the repository root:

```bash
node public/data/short-deck-equity/short-deck-equity-generator.mjs
node scripts/generate-short-deck-equity-chart.mjs
python public/data/short-deck-equity/short-deck-equity-verifier.py --workers 4 --report public/data/short-deck-equity/verification-report.json
```

The JavaScript program is the primary generator. The Python standard-library verifier does not import it; it separately parses cards, ranks seven-card hands, enumerates boards, and compares every integer win/tie/loss partition. Use `--quick` to check the frozen schema, formulas, and evaluator edge cases without repeating the full enumeration.

The separate chart generator reads only the frozen JSON and deterministically writes `public/images/blog_images/short-deck-equity-recalibration.svg`. The data test rebuilds the SVG in memory and requires a byte-for-byte match, so a stale chart fails CI.

The frozen production run used Node.js 24.11.1 and Python 3.11.9 on Windows. The recorded full verifier used eight workers and finished in 831.329 seconds; runtime depends on hardware and worker count.

## Files

- `short-deck-equity-matchups.json` — complete structured results and rules.
- `short-deck-equity-matchups.csv` — the same twelve result rows in audit-friendly form.
- `short-deck-equity-generator.mjs` — primary exhaustive enumerator.
- `short-deck-equity-verifier.py` — independent exhaustive verifier and quick integrity checks.
- `verification-report.json` — result of the frozen full independent verification.
- `MANIFEST.sha256` — checksums for the frozen evidence files.
- `scripts/generate-short-deck-equity-chart.mjs` — repository-local deterministic SVG generator.

## Interpretation boundary

These are fixed-card, heads-up, all-in showdown equities. They are not preflop ranges, opening frequencies, pot-odds decisions, tournament recommendations, or solver outputs. Real decisions also depend on position, antes, blind structure, stack depth, action history, ranges, bet sizes, fold equity, and any rake or fees.

The current Short Deck Poker Trainer store listing, accessed 2026-09-04, describes preflop range study and an equity lab. That first-party product context is separate from this article's open enumeration; no app binary was installed or tested for this study: <https://play.google.com/store/apps/details?id=com.shortdeck.shortdeck_app&hl=en&gl=US>