Poker 51 tables.

POKER 51 TABLES / LIVE RULE CARD · v2

One deck, one declared card, up to five players.

Poker 51 tables are five-card draw on the 51-card Area 51 deck. The marker Ⅰ = 2♣ is outside the deal, and every player knows it. The same rules file, poker51-multi-v1.js, runs on the table service and in this page.

A table

1. Anyone can open a table. It gets its own link; anyone with the link can watch or take an open seat. There are five seats.
2. To sit, choose a buy-in of 2, 4, 8 or 16 jbits (no more than your bank holds). The buy-in leaves your shared Area 51 bank with its own receipt. When you leave, your stack comes back to your bank with a cash-out receipt.
3. A hand starts when at least two seated players have 1 jbit or more. The button moves one seat clockwise each hand.

A hand

1. Each player dealt in antes 1 jbit. Five cards each, one at a time, starting at the seat after the button.
2. First betting round, starting at the seat after the button. With no bet yet you may check, or open 1, 2, 4 or 8 jbits; if you hold less than 8 and it is not one of those sizes, you may open all in. After an opening bet: call, fold, or raise by the opening amount. There are at most two raises in a round.
3. A player who cannot cover a call goes all in for less. An all-in raise smaller than the opening amount lets the others call or fold but not raise again.
4. The draw, in the same order: keep any cards and replace the rest (0 to 5). Everyone sees how many each player draws. Five seats is the maximum because five hands and five full draws use 50 cards, so the 51-card deck never runs out.
5. Second betting round, with the same rules.
6. Showdown. Pots are split into side pots so no one wins more from a player than they themselves put in. Each pot goes to the best hand eligible for it; equal hands share it. Odd cents go one at a time to the winners in turn from the seat after the button. After every hand, all hands are shown.

Time

Each decision has 45 seconds. If time runs out you check when you can and fold otherwise; at the draw you stand pat. After three timeouts in a row you are marked away and sit out until you press “I’m back”. Leaving during a hand folds your hand at once; your stack is paid out when that hand ends.

Riemann, Steve and abits

Any seated player can add either of two published players to an open seat: Riemann, careful and rule-based, and Steve, loose and aggressive. Both can sit at the same table. They play with abits, not jbits, and everything below that is said of Riemann’s abits holds for Steve’s in the same way. Jbits are held by whichever of them won them, so one can leave while the other stays. They never play a hand without a person in it.

1. Riemann receives abits equal to the stack of the player who added it: if you hold 10 jbits at the table, Riemann gets 10 abits.
2. Pots are paid contributor by contributor. Jbits won from another person are yours. Jbits Riemann wins from you are held for you, and Riemann’s abits grow by the same amount. When you win from Riemann, it first pays back jbits it holds for you; anything more is shown as your abit score, which cannot be bet.
3. When Riemann leaves — someone removes it, the player who added it leaves, it runs out of abits, or the table closes — every held jbit returns to its owner and every abit vanishes.

So each player leaves with their buy-in plus their net result against the other people at the table. Against Riemann or Steve you can neither win nor lose jbits, and neither of them can create or destroy them. Proof: every movement of chips between two people changes both their totals by opposite amounts; every movement between a person and Riemann changes that person’s stack and held jbits by opposite amounts. PP290 §3 gives the argument in full. This is a conservation statement. It does not say Riemann is neutral to the game between people: while Riemann holds jbits of yours, your playable stack is smaller than your total, so you are short-stacked against the other players at the table.

How Riemann plays at a table

Riemann sees only its own cards, the public bets and pot, and the public draw counts. It draws by the House rule. This is the read-and-threshold policy from before the solo table’s solved strategy, extended to several players, with two leaks closed. The complete rule is published here; the earlier v1 is kept.

1. Before the draw it averages v0.3’s 128 projected completions of its own draw against the random-hand row, since no draw counts are announced at a table. [design choice]
2. After the draw it reads its hand against the smallest draw count among players still in. New in v2: it believes a stand-pat with weight 0.25, not 0.60. An honest stand-pat happens on 0.78% of deals, so a few bluffs make most stand-pats bluffs. Every other draw count keeps 0.60.
3. With several opponents, its narrowed score is raised to the number of opponents, as if each had to be beaten separately. [design choice]
4. Facing a bet, it calls when its score is at least toCall / (pot + toCall).
5. It raises once per round at a score of 0.70 or more, only while someone can answer. It also bluff-raises below 0.10 in the published 1-in-8 hash class; new in v2: only against a 1-jbit bet. With no bet yet, it opens 2 jbits on the value rule or the hash-class bluff, and otherwise checks. [design choice]

Both changes were measured heads-up in the Riemann v0.6 study. In seeded table simulations of 20,000 hands each, against a script that stands pat on anything and then bets 8 jbits, v1 made −0.19 jbits per hand and v2 +0.84; against a script that bets 8 only with a strong hand, v1 made +0.09 and v2 +0.39 (receipt, script). Those scripts are testers, not players. Riemann’s table policy is not a solved strategy, and nothing is claimed for it.

How Steve plays

Steve is a name. Steve is a fixed table, steve-jev-v1-data.js, read by a published rule. The table holds the probabilities a language model (TypeSafe System One, jev-1.13.0, asked to play its best) gave for each spot of heads-up Poker 51 in the Riemann v0.6 study: 760 answers before the draw and 7,580 after it. Nothing calls that model when you play; there is no learning and no hidden state.

1. The draw. By the class of his dealt hand he takes the House-rule draw, stands pat (a bluff unless the hand is made), keeps a kicker with a pair or three of a kind, or keeps his two highest cards with no pair. The choice is fixed when the hand is dealt.
2. With no bet yet he checks or opens 1, 2, 4 or 8 jbits, from the table’s opening row.
3. Facing a bet he folds, calls or raises. If he has put nothing in this round he answers as the model answered a 2-jbit bet after checking; if he has, as it answered a raise of its own bet. Among the pots and bet sizes the model was asked about, the one whose price is nearest is used. [design choice]
4. After the draw the row is his own draw count, the strength of his final hand (40 buckets) and the smallest draw count among players still in. [design choice]
5. A public hash decides. Each entry is a probability for every action. A hash (FNV-1a) of Steve’s own cards and the spot picks one, so the same cards in the same spot always give the same action, and the table log shows the probabilities and the hash draw.
6. Several opponents: no adjustment. Every answer in the table was given heads-up, so at a full table Steve plays looser than the model would. [design choice]

The contrast. Heads-up against each other over 20,000 seeded hands, Steve bet 78 times per 100 hands and Riemann 48; Steve stood pat on 6% of his draws and Riemann on 0.7%. Riemann made +0.43 ± 0.03 jbits per hand from him (computed, a simulation between two published players). Steve is a model’s judgments distilled, not a solved strategy; nothing is claimed about how well he plays, and people will play him differently.

A fair deal you can check

Before each hand the table service shuffles with the platform’s secure random source and publishes a SHA-256 commitment to the deck and a random salt. When the hand ends, the log shows the deck and the salt; “Check the deck” recomputes the hash in your browser. A match shows the order was fixed before anyone acted.

Who sees what

The table service holds every hand, because it deals. Each browser receives only its own cards until the hand ends. Seat tokens are stored only as hashes. Jbits have no monetary value and cannot be bought, sold or cashed out; your bank lives in your browser, so this is a research table, not a secure casino. For the same reason the service cannot check that another seat’s buy-in was really paid, and one person can hold more than one seat.

Status

Limits

Tables close after two idle hours and pay out every stack; closed tables keep cash-outs for 30 days, then delete. The Area 51 recovery clock does not count jbits sitting at a table, so while you play it can refill your bank toward 8 as it would if you were idle. This is recorded for the jbit economy notes in PP290. There is no chat and no rebuy; to add jbits, leave and sit again.

These are exact results about a card model. There is no zero data and no inference about the Riemann hypothesis.

Poker 51 against Riemann · Blackjack 51 · two spots · Project 51: Reading the Record Across Rules · 10.5281/zenodo.23048482