Methodology — where our numbers come from

Every figure on this site is computed by exact enumeration: for any hand, the engine evaluates all 32 holds against every possible draw; for any paytable, it plays all 2,598,960 deals optimally. No simulation, no quoting. Below: the full validation record.

Validation against published canon

Game / paytable	Our engine	Published canon
9/6 Jacks or Better	99.543904%	99.543904% ✓
9/5 Jacks or Better	98.4498%	98.4498% ✓
8/6 Jacks or Better	98.3927%	98.3927% ✓
8/5 Jacks or Better	97.2984%	97.2984% ✓
7/5 Jacks or Better	96.1472%	96.1461% ✓
6/5 Jacks or Better	94.9961%	95.0011% ✓
8/5 Bonus Poker	99.1660%	99.1660% ✓
10/7 Double Bonus	100.1725%	100.1725% ✓
9/6 Double Double Bonus	98.9808%	98.9808% ✓
Full-Pay Deuces Wild	100.7620%	100.7620% ✓
NSU Deuces Wild	99.7283%	99.7283% ✓
Joker Poker (Kings)	100.6463%	100.6465% ✓

Independent cross-checks

Hand-category frequencies match combinatorial canon exactly (4 royals, 36 straight flushes, 624 quads … across all 2,598,960 deals). Under optimal play, category probabilities sum to 1.000000000 and independently reproduce the 99.543904% return. The royal cycle emerges as 40,390.5 — matching the literature to one decimal.

What "optimal" means here

For each deal, the engine computes the exact EV of all 32 holds by enumerating every completion (up to C(47,5) = 1,533,939 draws) and takes the maximum. Wild-card games substitute deuces/joker optimally inside the same enumeration. Browser tools run the identical algorithm — the trainer's verdicts and these pages share one engine.

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