- Rules modeled
- Standard Mississippi Stud, single 52-card deck, independent hands. The player antes and receives two hole cards; three community cards complete the final five. Before each community card is revealed (3rd, 4th, and 5th street) the player must either raise 1×–3× the ante or fold, forfeiting everything already wagered. Every wager, the ante and all street bets, is paid by the final 5-card hand: jacks-or-better 1:1, two pair 2:1, trips 3:1, straight 4:1, flush 6:1, full house 10:1, quads 40:1, straight flush 100:1, royal 500:1; a pair of 6s–10s pushes; anything less loses all bets. Stakes are fun credits in integer cents.
- Assumptions
- Hands are independent (a freshly shuffled deck each round). Optimal play: the 3rd-street decision comes from the frozen exact table (169 canonical two-card classes, derived, not transcribed); the 4th- and 5th-street decisions are computed exactly at runtime from the state's expected values. Fun credits only, no real money.
- Mathematical basis
- Every figure is EXACT; no dealer means the whole game is enumerable. The house edge (4.9149% per ante), element of risk (1.3691%), average total wager (3.5898 antes), fold rate (43.6%), and the final-hand distribution are derived by a 3-street backward induction over all 1,326 starting hands × 50 × 49 × 48 ordered reveals (~156M states), tracking value and expected wager through every optimal decision. The derived 3rd-street strategy independently reproduces the published expert rules, including the 6-5-suited exception. The Lab's Monte-Carlo (one continuous seeded RNG stream) only validates the derivation.
- Engine version
- mississippi-stud engine 1.0
- Validation
- 18 unit tests + an opt-in slow test, the 5-card payer (all tiers incl. the jacks-pay / 6s–10s-push / 5s-lose splits, wheel + royal), the frozen exact figures vs published (4.91% / 1.37% / 3.59), the full 169-class 3rd-street table (3× any pair; 1× jack-plus, two mids, and 6-5 suited; fold 6-5 offsuit), exact 4th/5th-street decisions on canonical states, payout mechanics (all wagers pay; pushes return; folds forfeit exactly the wagered amount), determinism, and a 100,000-hand continuous-stream convergence. The slow test re-runs the full ~156M-state derivation and must reproduce the frozen figures AND the strategy table bit-for-bit.
- Last reviewed
- Verified by exact enumeration end-to-end. The strongest cross-check of the trio: the derivation independently reproduced the published optimal strategy, including its least-obvious rule, before matching all three published financial figures to 4 decimal places. Last reviewed 2026-07-13.
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