JEFFERY LYN HUCKSTEAD · CEREBRAL GRAPHIX
Project 51.
One identity can have a card face, an exact paper symbol, and several mathematical readings. Prospect 51 turns that distinction into a five-reel poker game.
Latest record: 10.5281/zenodo.23048482, which carries the Area 51 games and exhibit research (51 SEDAPS, 51 Twins, Formula 51, and the PP292 wild-card note). Previous deposit, 27 September 2026: 10.5281/zenodo.22985771 (all versions: concept 10.5281/zenodo.22862811). It carries Project 51 v0.4 (8 pp), Telescope 51 v0.7 (4 pp) and the Formula 51 concise method (3 pp).
Original source, demo & verification package
Poker 51 · unpublished working draft
Play Poker 51 beta v0.3 · Poker 51: One Card Declared, Five Probabilities Preserved · PDF. The heads-up draw game has one declared card, exact draw-category odds and betting before and after the draw against Riemann, a dealer with a published policy. The working paper is prepared for this Project 51 collection but has not been deposited; the existing collection DOI is not a DOI for the draft.
Riemann v0.6 · a solved dealer · v4.1
Since Poker 51 v0.6 Riemann bets from a solved strategy in all three games. The whole hand, your draw included, was written as one game on an abstraction and solved by CFR+; each published table is a restricted Nash response tuned against player types modelled by a language model. In the abstraction a perfect player gains about 0.1 jbits per hand from a v0.6 table, against about 3 from the v0.5 policy (computed). Results against the modelled players are evidence, not a measurement of real players, and nothing is claimed for the real card game. Solving Riemann: the study · working note (unpublished; no DOI yet).
The declared card as a wild card · v3.5
Poker 51 v0.4 can put Ⅰ = 2♣ back in the deck. In Wild Ⅰ it stands for any card; in the bug it stands for an ace or completes a straight or flush. Counting every hand shows that no ranking of the ten categories is consistent under Wild Ⅰ, that the bug keeps the standard ranking as its only consistent one, and that a suit-wild Ⅰ keeps the five repeated-rank categories at their exact 52-card counts, the companion of the removal theorem. Riemann plays the same published policy with a belief table rebuilt for each game. Working note: PP292 · The declared card as a wild card (PDF), deposited in Project 51, 10.5281/zenodo.23048482.
Poker 51 tables and two-spot Blackjack · v3.3
Poker 51 tables seat 2 to 5 people by invite link on a separate table service that deals, so no browser sees another player’s cards; each deck is committed before the deal and revealed after. Riemann can join with abits matched to the stack of the player who adds it: jbits it wins are held for their owner and returned when it leaves, so everyone cashes out buy-in plus net against the other people. Since v4.2 a second published player, Steve, can join the same way: loose and aggressive where Riemann is careful, and built from the answers a language model gave in the Riemann v0.6 study. Blackjack 51 · two spots deals two hands face up by casino rules; with one spot it reproduces the classic engine card for card. Working note: PP290 · Tables, abits and jbit flows (unpublished; no DOI yet).
The paper and the live game
The supplied 13-page paper is retained exactly. It uses the game’s first name, “Rotor 51”, for the original isolated-point prototype. The game is now Prospect 51 everywhere on the site and uses the shared jbit bank. Saved-hand keys keep their original id, so no unfinished hand is lost to the rename. The identity dictionary, rotor sampling, poker awards, draw rules, and initial-order jackpot condition are unchanged.
| Action | Current website rule |
|---|---|
| Opening deal | 1 jbit from the shared bank |
| Hold and redraw | Keep any subset; replace the rest once, free |
| Bank a hand | Gross poker award returns to the shared bank |
| Archive jackpot | Exact initial order only; starts at 51 jbits and adds 0.01 per entry |
| Paper-symbol view | Display only; same card, hold, and score |
The shared bank and archive meter belong to this browser. jbits have no cash value. The jackpot is not a global pool across visitors. The prior demo points are not converted into jbits.
What the mathematics establishes
The five opening rotors select without replacement, with moduli 51, 50, 49, 48, and 47. Coprime affine gearing permutes the eligible positions. Under independent uniform input digits, every ordered hand has probability 1 / 281,887,200.
After the opening deal, all five initial identities stay out of the replacement pool, including discarded cards. Replacing r cards has C(46, r) possible unordered completions. The opening census contains 2,349,060 hands; its counts are not an optimal-play return calculation.
Poker forgets order; the archive lock retains it. Swapping two cards can preserve the poker award and destroy the jackpot match. The archive match is fixed by the opening deal and survives a later redraw.
Why 51, by deduction
Formula 51 builds the 51 identities from the Hangul syllable block with radix N = 1438, and any radix from 1177 to 1764 also gives 51 symbols. A sharper statement holds. Call a radix self-describing when its number of symbols equals its number of complete syllable contexts. Then 51 is the only possible count, reached exactly for N = 1428–1455. Among those, 1437–1440 score best on Project 51’s decoders, and only 1438 has two nine-member partial classes. So the data-given radix is picked out exactly. Proved, with an exhaustive check over all 11,172 radices. One step of the first proof was repaired on 27 September; an independent recomputation reproduces all 588 band tables.
A more legible table does exist: at N = 1353–1356, class, polar address and color identify every card. It gives up self-description, so it is a design choice, not a correction. Read the deduction (in Project 51: Reading the Record Across Rules, 10.5281/zenodo.23048482) · script · all 11,172 radices · independent replay
Order twins
Poker forgets order; the archive lock keeps it. Swap the two red jacks of the archive key and the hand is still two pair, but the lock stays shut. See it on the 51 Twins plate.