The Right Price

Room settings

Guests play unrated games against the bot. A guest-created room contains only the guest and the bot, and Add bot is fixed to yes; every other setting remains configurable. Guest rooms are public to view but cannot be joined remotely.

Viewing and joining

Every room is public to view. Registered waiting rooms accept any number of human players until the host starts. For a registered room, the host chooses Joining: Open joins eligible players immediately, Host approval lets the host Accept or Decline each request, and 4-digit passcode requires the exact code chosen at creation. A player may cancel a pending request, and stays in any existing waiting room unless the request is accepted. Only the host can see the passcode. Guest-bot rooms use Open.

Item types

Choose one scoring goal for every round in the room.

Range-max

Goal: get the maximum value.

Each item's minimum and maximum are integers from 1 through the room's configured Max range: 10, 25, 50, or 100.

Value-sum

Goal: get the maximum sum.

Each item's value is an integer from 1 through the configured Max item value. A recorded combination may total at most the configured Sum limit.

Square-grid

Goal: cover as many panel tiles as possible.

Loading the configured panel ...

Loading the configured panel and all 21 possible pieces ...

Triangular-grid

Goal: cover as many panel tiles as possible.

Loading the configured panel ...

Loading the configured panel and all 22 possible pieces ...

Point-Voronoi

Goal: own the highest total area in the square.

Bid for fixed random points. Each location in the square belongs to its nearest purchased point. Your total area is the sum of the cells around all your points. A gold ring marks the current ordinary auction point. During bidding, the diagram includes this point with a neutral-gray region to preview how it divides the square. This preview does not change scores. After bidding, the region takes the buyer's color or disappears if nobody purchases the point. Mystery points have no preview region, and past unpurchased points do not divide the square.

50.0% 50.0%
Two symmetric points share the square equally.

The highest combined area after the final auction wins. Tied players share the prize. Points are fixed, so there is no selection or placement phase.

Round funding

The bank first raises enough money to create the base prize pool. It charges every active player the smallest equal integer amount that can cover the shortfall. Any extra caused by integer rounding stays in the bank.

A player who cannot pay that equal charge is eliminated: their remaining capital moves to the bank and their capital becomes 0. The charge is then recalculated for the players who remain. If funding leaves only one active participant, whether human or bot, or eliminates everyone, the game ends immediately.

Auctions

  1. When an item opens, the server first applies Random item chance. A normal Range-max item immediately displays two sorted integers from 1 through the configured Max range. A normal Value-sum item displays one integer from 1 through the configured Max item value. A normal Square-grid or Triangular-grid item displays one piece from that grid’s Playground catalog. A mystery Range-max or Value-sum item stores neither its range nor its value while bidding and displays ?. A mystery grid item likewise stores no piece identity and displays Piece ?. After the auction’s bids resolve, the server generates and reveals the data required by the selected item type. A normal Point-Voronoi item shows a fixed random position in a square before bidding; a mystery point stores no coordinates until the auction resolves.
  2. Every active player may submit a non-negative integer bet no larger than their current capital. While the bet input has focus, digit-only intermediate text—including an empty value or an amount outside the current valid range—remains editable through room refreshes, and an invalid draft disables submission. When the input loses focus, or immediately before submission, an empty or below-minimum value resets to the current minimum bid and an over-capital value resets to your current capital, using the latest room state. The slider runs from 0 to the current prize pool in increments of 1 and updates the bet input as you drag it; slider movement commits immediately. Its value labels align with the visible track endpoints at 0 and the current prize pool, as does its thumb while the bet is within the slider’s range. For a normal item, two markers show its lower and upper endpoints as a percentage of the room's configured Max range. Mystery items show no range markers. Editing the bet input also moves the slider; if an affordable bet exceeds the prize pool, the track remains filled to its right endpoint, the thumb is hidden, and the numeric bet remains unchanged. The −10, −5, −1, +1, +5, and +10 buttons commit their adjustments immediately and move the bet toward its minimum or your current capital. For either direction, when the distance to that limit is 1, only the corresponding 1 button is enabled; at 2–5, the 1 and 5 buttons are enabled; and at 6 or more, all three buttons are enabled. No button in that direction is enabled at the limit.
  3. In Blind betting, every active player submits one private bet or Skip. Taking no action before time expires also means Skip. If everyone acts early, the auction resolves immediately; if everyone skips, the item is not awarded. The highest bet wins. On an equal human and bot bid, the human wins. Remaining ties go to the earlier submission, then to the lower-ELO player, then to stable room order. The bid history table is informational and does not replace these tie-break rules.
  4. In Open betting, the current high bidder and amount are always visible. The first bid may be any affordable non-negative integer. Every later bid must come from a player other than the current high bidder and be at least the current high plus the configured minimum increase. Every accepted high bid restarts the full betting clock.
  5. Open Skip offers Skip current bid, which accepts only the displayed leader and amount, and Skip rest of auction, which permanently prevents that player from bidding or winning the item. Before the first bid, the conditional choice is named Skip opening bid. An accepted Open bid clears only current-bid skips and preserves rest-of-auction skips. A stale current-bid choice is rejected if the leader or amount changes before the server accepts it. Any resigned player or player whose current capital is below the new minimum bid is skipped for the rest of the auction automatically. The current high bidder cannot raise or Skip. If every other active player skips, the current bidder wins immediately. If everyone skips before any bid, the item is not awarded. A timeout awards the item to the current bidder, or leaves it unawarded if nobody bid.
  6. Only the winner pays. The payment goes to the prize pool or bank according to the room setting, and the winner owns the item.

In a Square-grid or Triangular-grid room, the Current auction box labels the item Piece and shows its shape. Items this round is a grid of piece cards rather than a table; each card shows the auction index, owner, and paid amount. A completed card with at least one available bid has a separate bottom-right history icon that opens the bid modal without picking up or placing the piece. During an auction, every player and viewer may select a revealed owner’s card to pick that piece up directly from the Pieces box for a local test arrangement in the inline grid panel. There is no separate piece tray in the panel. That owner’s other revealed pieces and the currently auctioning piece, when known, are also available from their cards. Selecting the current card makes that piece available alone. An unrevealed mystery piece and an older unawarded piece cannot be picked up. If the current piece is already on the panel, selecting an owner’s card keeps the current piece in its exact orientation and panel position. Switching owners removes the previous owner’s pieces from the panel but keeps every piece’s latest local rotation or flip. The browser retains those orientations through refreshes, the final arrangement, and later rounds of the same game. At a round boundary, the lowest auction-index occurrence of each catalog piece sets its carried orientation; a piece absent from that round keeps its previous orientation. Reset panel returns every placed piece to the Pieces box without changing its latest rotation or flip. In both testing and final arrangement, Reset panel is disabled whenever no piece is placed on the panel. Before a piece is selected, the inline panel shows an empty board. Test arrangements never change the auction or record a server-side Best.

Value-sum selection

After the last Value-sum auction, its item and revealed bets remain visible for the same four-second settlement window used between items. The server then starts the full configured Selection time, so the reveal window does not reduce the combination-building deadline. Choose any subset of your own item indexes whose values total at most the configured Sum limit. Equal-valued items remain separate choices. The items table plots every revealed value on a scale from 1 through the configured Max item value; an unrevealed mystery value has no marker. The selector disables any unselected value that would push the current total over the Sum limit and restores an unfinished draft after a refresh on the same browser. Separately, every player and viewer may click revealed numbers in the Value column to preview a local sum. A preview may contain owned items from one player plus the item currently being auctioned. After an owned value is selected, values owned by other players are disabled until the last selected value from that owner is deselected; the value being auctioned remains available throughout. Unrevealed mystery items and previously unawarded items are unavailable. The Selected sum box beside the table stays green through the configured Sum limit, turns red above it, and returns to a green zero after a click outside the table. This preview does not change a combination draft or recorded Best submission.

The game automatically records a combination whenever its sum is strictly higher than your current Best submission. You may keep editing until time expires; later lower choices do not replace the recorded Best. Rapid edits retain the highest combination reached, and an unfinished browser draft restored after refresh is recorded if it improves the authoritative Best. The server validates ownership, unique indexes, and the maximum, and stores both the best sum and its components. Other players see only how many participants have a best submission during selection.

Finalize, beside the Best submission display, irreversibly marks you done and locks your recorded Best submission, if one exists. It becomes available after any outstanding automatic update finishes. While it is available, five seconds without a combination-selection click makes it glow; another selection click removes the glow and restarts that delay. You may finalize without any combination when you no longer want to compete for the round; you then receive no round score and cannot record one later in that phase. A recorded total equal to the Sum limit is unbeatable and finalizes automatically. A valid recorded combination that contains every item you own also finalizes automatically, provided their combined total is within the configured Sum limit.

During the following round intermission, Value-sum replaces the last-auction display with a standings table. Recorded totals use competition ranking, so tied totals share a rank and skip the corresponding following ranks. Players with items but no recorded combination appear next, followed by players with no items; both groups show - for Ranking and Total. Each player's items are ordered by value from largest to smallest, then by item index when values tie, and recorded items contributing to the total are highlighted.

A player who owns no items, or who never records a combination, has no round score. Resigning prevents further improvements but preserves a best submission already recorded. The phase normally lasts for its full timer; it ends early only when every eligible player owns no selectable items, has resigned, has finalized, or has recorded the configured Sum limit. Highest recorded sum wins, with equal highest sums sharing the prize equally.

The bot uses the same exact Knapsack dynamic program as the Playground tab to record and finalize its maximum legal subset once. For auction pricing it uses 1,000 coupled future worlds from seed 42. Every future item receives one uniform integer from 1 through the configured Max item value and one uniform eligible owner. Possible owners of the current item share those same future values and owners; a mystery current value is sampled once per world. Every simulated score is the exact maximum subset sum no greater than the configured Sum limit.

Square-grid and Triangular-grid arrangement

Both grid types reuse the pieces, panel, and manual controls from their Admin Playground tabs. Square-grid draws without replacement from the 21-piece polyomino catalog, while Triangular-grid draws without replacement from the 22-piece polyiamond catalog. These catalogs are fixed and are not changed by Grid panel customization. The database-backed Admin panel is the suggested room shape; the creator may toggle its tiles before creating the room. The lobby room card and Room info preview the resulting room-specific snapshot; later Admin edits do not change it, and the room customization is never written back to the database. The catalog resets for each new round, so a piece identity cannot repeat within one round.

Before gameplay, every participant and spectator can try the room’s captured panel with all 21 Square-grid pieces or all 22 Triangular-grid pieces. This waiting-room practice is independent for each browser and offers only the manual place, rotate, flip, return, and reset controls—there is no Select or Solve. Practice survives room updates while everyone is waiting, does not affect the game or send an arrangement to the server, and is cleared when gameplay starts or you leave the room.

After the last grid auction, its revealed piece and bets stay visible for the normal four-second settlement window. The server then starts the full configured Selection time and automatically replaces the test area with the player’s arrangement in the inline grid panel. Polling preserves the live controller, and a refresh restores the unfinished browser draft from session storage. Pick up owned pieces directly from their cards in the Pieces box, then drag, rotate, flip, return, and reset them manually. The panel has no separate piece tray, so its board uses the full available width in both grid types. The live panel has no Select or Solve action.

The game automatically records an arrangement whenever its covered unit-tile count is strictly higher than your current Best arrangement. Later equal or lower edits do not replace that recorded Best. Rapid edits retain the highest arrangement reached, and an unfinished browser draft restored after refresh is recorded if it improves the authoritative Best. The server validates ownership, unique auction indexes, each piece’s exact rotation or reflection, panel bounds, and non-overlap. Other players see only how many participants have a Best arrangement until settlement.

Finalize irreversibly marks you done and locks the recorded Best arrangement, if one exists; it becomes available after any outstanding automatic update finishes. Five seconds without a piece or panel click or an active drag makes it glow; another such interaction removes the glow and restarts that delay. You may finalize without any arrangement when you no longer want to compete for the round; you then receive no round score and cannot record one later in that phase. An arrangement that uses every piece you own, fills all configured Square-grid tiles, or fills all configured Triangular-grid tiles finalizes automatically. The timer remains the fallback unless every eligible player owns no pieces, has resigned, or has finalized. A resigned player cannot improve again, but a previously recorded Best remains valid. A player with no pieces or no recorded arrangement has no round score.

When you have a Best arrangement, its N tiles value in the Best submission display is a button. Activate it to open a miniature, read-only view of that exact saved arrangement without changing your editable panel. The preview updates if the game records a higher Best; activate the value again, click elsewhere, or press Escape to close it.

During intermission, arrangement standings show competition ranking, recorded tile totals, and each winner’s prize share. The inline grid panel initially shows the first winner’s recorded arrangement as a read-only preview. If nobody recorded an arrangement, the panel remains empty. Selecting a recorded total in the Tiles column shows that player’s exact recorded arrangement as a read-only preview in the inline grid panel. Only recorded pieces appear. In the Pieces panel, cards owned by other players are dimmed, the selected player’s recorded pieces receive a yellow border, and their unused pieces remain unchanged. Selecting another total replaces the preview and piece highlighting. The highest recorded tile count wins; equal highest counts share the prize through the normal integer-share and bank-remainder rules. The bot uses the shared exact solver to record and finalize its maximum-tile arrangement once.

For a normal Range-max item, the bot uses the same full-precision engine as Projected winning probability. The server generates 1,000 future worlds from random seed 42. Each world contains normally generated ranges and uniformly random eligible owners for every item after the current auction. Resigned and eliminated players are not eligible, and their items are excluded from these projections.

Every possible eligible owner of the current item is evaluated against those same future worlds. If Qr is the bot’s mean winning probability when recipient r receives the current item, then Pbot = Qbot, Pcurrent is the equal-weight mean of every Qr, and Pworst is the lowest Qr among eligible opponents. These counterfactuals use the raw full-precision results before the Capital table’s equivalent-holdings smoothing and one-decimal rounding.

Within any shared future world, giving the bot an additional item cannot lower its winning probability, while giving an opponent that item cannot raise it. Consequently Pbot >= Pcurrent >= Pworst. The offensive value is the direct difference Pbot − Pcurrent, the defensive value is Pcurrent − Pworst, and their sum is Pbot − Pworst; no zero-clamping is needed. Let D = Pbot − Pworst. When auction payments go to the Bank, the bot calculates rawBet = floor(prizePool × D). When auction payments go to the prize pool and D < 1, it accounts for its winning payment increasing that pool and calculates rawBet = floor(prizePool × D / (1 − D)). If payments go to the prize pool and D >= 1, the raw bid is infinity. These formulas use the current prize pool before the auction payment, and the resulting bid is capped by the bot’s available capital. If no opponent can acquire the item, it bids 0. In Blind betting, a human wins when their bid equals the bot’s, regardless of submission order or ELO.

A mystery item still has no real range during bidding. For projection and pricing only, the server uses the named endpoint list [1, 20, 40, 60, 80, 100]. It enumerates all sorted pairs in nested endpoint order: 6 identical-endpoint cases and 15 distinct-endpoint cases, for 21 cases total. From a budget of 1,000 shared seed-42 future worlds, the first 13 cases receive 48 worlds each and the final 8 receive 47 each.

Each mystery case is averaged using its own 47- or 48-world count before aggregation. The 6 cases with identical endpoints have weight 1 and the 15 cases with distinct endpoints have weight 2, for a total endpoint weight of 36. Pcurrent, Pbot, and Pworst are all calculated this way. If meanPbot and meanPworst are the resulting full-precision weighted means, the mystery item uses the same payment-destination formulas above with D = meanPbot − meanPworst. The actionable bid is capped by the bot’s available capital. It bids 0 when no eligible opponent can acquire the item. In Open betting this becomes the bot’s private maximum while it retains the normal open-at-zero and minimum-increase behavior.

For example, suppose three eligible players auction three items from a $1,000 prize pool and payments go to the Bank. For a first item with range [10, 20], the shared-world calculation gives Pcurrent = 0.325659, Pbot = 0.329729, and Pworst = 0.323624, producing floor(1000 × (0.329729 − 0.323624)) = $6. If the bot wins, the Bank setting leaves the prize pool at $1,000. For a second item with range [30, 40], the bot has Pcurrent = 0.327451, Pbot = 0.524397, and Pworst = 0.228978, producing floor(1000 × (0.524397 − 0.228978)) = $295.

A naive calculation that ignores the remaining future item would instead give Pcurrent = 1, Pbot = 1, and Pworst = 0 for that second auction, producing a $1,000 valuation. Without the representative item, that second calculation would incorrectly treat the current allocation as a certain win or loss and value the item at $1,000, even though the later item can reverse the outcome.

The server records the elapsed betting time of every accepted human Bet from every human player. In Blind betting, timing starts when the item opens. In Open betting, it starts when the item opens or when the previous accepted bid restarts the betting clock. Invalid bets, Skips, timeouts, resignations, automatic actions, and the bot’s own actions are not samples. The bot’s next newly scheduled betting response waits for the rounded arithmetic mean of all samples recorded during the current game. With no samples, it acts immediately. The delay is capped to retain a 250 ms reserve before the authoritative deadline, and an action scheduled at or after that deadline does not run. Samples, the mean, and pending actions remain private server state.

In Open betting, the amount calculated at the beginning of the item is the bot’s private maximum for that auction. When it is first to act, the bot opens at 0 after its scheduled delay. If a human bid arrives before a pending opening or response, the stale action is replaced using the new betting window and updated mean. After each accepted human bid, it raises by exactly the configured minimum increase if that next bid is no greater than its maximum; otherwise it skips the rest of the auction at the scheduled time. The bot never reveals or exceeds its planned maximum. Each bot raise restarts the full betting clock, clears current-bid skips, and preserves rest-of-auction skips like any other accepted Open bid.

The current-capital table shows every participant’s Capital, Winning probability, and round movement. When Show players’ ELO is enabled, a registered human’s rounded ELO appears after their name in lobby cards, waiting-room cards, and this table. Bots, guests, and unrated players remain name-only. For Range-max, Winning probability is calculated from the inclusive ranges of items already held: every possible combination of randomized values is equally likely, and tied winners divide that case equally. A player without an item has 0.0% once at least one scoring player exists. Before anybody holds an item, or if every item is unawarded, every row shows — because there is no eligible winner. The full-precision probabilities are normalized to total 100% internally. Each value is independently rounded to one decimal for display, so the displayed values need not total exactly 100.0%; for example, three equivalent players each display 33.3%.

For Value-sum, the column instead compares each player's exact maximum legal subset from the fixed values currently held. During the Selection phase it therefore describes each player's mathematical potential, without revealing another player's submitted components. After settlement it shows the shares produced by the actual best submissions.

For Point-Voronoi, Winning probability compares the total territory of purchased points. Current leaders share 100%, and the column shows a dash before any purchase. Projected probability uses 1,000 seeded future point-and-owner simulations, sharing each diagram between possible auction winners. The bot uses those same results with the ordinary capital-limited bid formulas.

For Square-grid and Triangular-grid, Winning probability compares the exact maximum tile count each player can arrange from the pieces already held. Current leaders split 100% equally and players behind them receive 0.0%; every row shows — before any awarded piece exists. During arrangement this remains the exact potential of each holding without revealing another player’s submitted placements. After settlement it shows the shares produced by the actual best arrangements.

Grid Projected winning probability uses 1,000 deterministic seed-42 coupled future worlds. Each world draws the current mystery piece when needed and all later pieces uniformly without replacement from the selected grid’s remaining catalog, assigns each projected item uniformly to an eligible owner, and solves every resulting holding exactly. Every possible owner of the current item shares the same future piece draw and owner assignments. Players who started with the same multiset of pieces receive their group’s average result. The grid bot derives Pcurrent, Pbot, and Pworst from the same counterfactuals and applies the payment-destination bid formulas below.

While a normal Range-max item is being auctioned, Projected winning probability estimates the end-of-round result with 1,000 deterministic simulations. Each simulation retains the ranges and owners of items already awarded, gives the current item uniformly to one eligible player, generates every later item from two independent endpoints between 1 and the configured Max range, and gives each later item uniformly to one eligible player. It then applies the same full-precision winning-probability calculation to those projected holdings. A player is eligible only when neither eliminated nor resigned as the item opens; every other participant receives 0.0%.

During mystery-item bidding, Projected winning probability displays the weighted estimate from the 21 projection-only endpoint cases. These cases do not generate or retain the real mystery range or any item value. The six projection support points are 1, one-fifth increments of the configured Max range, and the configured maximum. When the auction resolves, the server generates the real endpoints within that range for the first time and fixes the actual owner. It then recalculates the projection from that revealed range and owner with at most 1,000 shared seed-42 future worlds for the remaining items. The column switches to this second result while the revealed endpoints are shown; the recalculation cannot change the completed bid or payment. A newly opened item’s projection replaces it.

A separate pseudorandom sequence starts with seed 42 once per projection and runs through all 1,000 simulations for a normal item, so the projection is reproducible and does not affect any real game randomization. Mystery cases instead split that same total budget 48 or 47 worlds at a time and normalize each case before weighting. After the results are averaged, eligible players who started the auction with the same multiset of held item ranges receive their group’s average result. Item order and auction metadata do not affect the comparison, so all players without items belong to the same group. The smoothed full-precision probabilities are normalized to total 100% internally. Each value is independently rounded to one decimal for display, so the displayed values need not total exactly 100.0%; for example, three equivalent players each display 33.3%. The current projection remains fixed while bidding. A mystery item’s revealed-range projection then remains visible through settlement until the next item opens; otherwise the column shows — when no projection is available.

For each player, the probability calculation keeps one item with the greatest left endpoint Q and removes every other held item whose right endpoint is no greater than Q. Such an item can never increase that player’s maximum value, so removing it does not change any winning probability. The remaining equally likely cases are aggregated through maximum-value distributions. During intermission and after completion, the column uses the completed round’s final item holdings.

Round changes is the sum of To bank, Auction payments, Prize, and From bank. To bank includes round funding and any capital transferred on elimination. Auction payments includes only winning bids that were actually paid. To bank and Auction payments are 0 or negative; Prize and From bank are 0 or positive. The Capital ($) heading identifies the currency; Capital values and the five change columns display plain integers, with no plus sign on positive values.

Resigning

Resigning is irreversible. If you have not acted on the current Blind item or are not the current bidder in an Open item, the server immediately skips the rest of that auction for you; an already-submitted Blind bet or current leading Open bid stays unchanged. A resigned Open bidder is skipped for the rest of the auction automatically if another player later raises. Every later auction is skipped automatically. During Value-sum selection or grid arrangement you cannot improve again, but a best combination or arrangement already recorded remains available. You remain a participant for round funding, capital, final ranking, and ELO in rated games, but skipped auctions cannot award you an item and you receive no later bank distributions. The confirmation offers Resign to keep watching or Resign & Exit to return to the lobby after that same resignation succeeds. When you remain, the same navbar control changes from Resign to Exit without ending the room. A direct active Exit request uses the same resignation transition. Top-left navigation and closing the page only change presence.

Resolving a round

In Range-max, after all item auctions and their bid reveals resolve, each item independently generates an integer inside its displayed inclusive range for the first time. No item value exists in server room state before this settlement. A player’s round score is the highest generated value among their awarded items. A player with no item has no round score and is excluded from scoring. In Value-sum, item values were fixed when their auctions resolved; a player's round score is instead the sum of their recorded Best submission. A player without a recorded combination has no round score. In Square-grid and Triangular-grid, a player’s score is the number of unit tiles covered by their recorded Best arrangement. A player without a recorded arrangement has no round score. In Point-Voronoi, the server adds the Voronoi cell areas of each player's purchased points and awards the round to the largest total. The board resets each round. A player without points has no round score, and purchased points remain on the board after resignation. Display percentages are rounded independently; the server uses unrounded area with only a tiny numerical tolerance for ties.

Every scoring player tied for the highest score wins. Winners split the prize pool equally using integer shares, and any remainder moves to the bank. If nobody has a score, the scoring list and winner list are empty, and the entire prize pool returns to the bank. The full bank is then divided equally among active players who have not resigned; any indivisible remainder stays for the next round. The next round uses that remainder and gathers any additional prize-pool funding required from active players. This distribution also runs after the final round.

Capital and round-movement values update with their corresponding settlement transfers: the Auction payments value changes when the payment leaves the buyer, Prize changes when a payout reaches a winner, From bank changes when a bank distribution reaches an eligible player, and Round changes is recalculated at each stage. After each bank-directed winning payment, the displayed bank increases by that payment and holds the full balance for a distinct pause. When the redistribution action begins, it changes to the indivisible remainder before the equal-share transfers move. The next item opens after those transfers. Resigned and eliminated players receive no share. After each item's payment and any immediate bank redistribution finish, players are sorted by decreasing capital and changed positions animate. The table updates again after the end-of-round prize and bank distributions. Players with equal capital preserve their previous relative order. To preserve the configured 5-, 10-, or 30-second Round break time, which is server-timed from the start of settlement, a client proportionally speeds up settlement effects when the remaining break is shorter than their normal duration. A late client skips directly to the authoritative settled state when too little useful animation time remains. If another round remains, the Info box counts down before that round is funded. Active players may select Agree to next round during this break. Bots agree automatically, while resigned and eliminated players do not block agreement. Unanimous agreement funds and opens the next round; otherwise the original countdown remains the fallback. Auto continue appears below Prize pool and Bank and defaults On for each active human participant. On submits that participant's next-round agreement automatically; Off keeps the agreement button manual. Participants see their own On/Off control. Viewers instead see M/N, where M is the number of eligible participants using Auto continue and N is the eligible total. The bot counts as On; resigned and eliminated participants are excluded. The game and ELO calculation complete immediately after the final round. The podium appears immediately and Info counts down three seconds. Selecting the enabled podium during the countdown opens the final-statistics table early and clears Info for that viewer; otherwise it opens at the deadline. Afterward, select the podium icon to reopen the final capital and ELO results.

Capital and ELO

The total money B is constant: starting capital × the number of participants, including the bot when enabled. It includes all participant capital and any money remaining in the prize pool or bank.

For Money share and ELO scoring, any money remaining in the bank at game end is treated as divided equally among participants whose final capital is greater than 0; this does not change their displayed capital. A participant with 0 final capital receives no share of the bank and normally has playerScore = 0. For every positive-capital participant, effectiveCapital = finalCapital + bank / aliveParticipantCount; every other participant has an effective capital of 0. The final ranking table’s Money share is stored as playerScore and calculated as playerScore = effectiveCapital / B. If B = 0 or nobody has positive final capital, every participant instead receives playerScore = 1 / participantCount.

Expected score is calculated across every participant, including the current participant’s own ELO term and the bot:

expectedScore = 1 / Σ 10^((participantELO - playerELO) / 400)

For rated games, the initial ELO update is newELO = playerELO + K × (playerScore − expectedScore), using the shared server ELO constants and global ELO floor. The bot participates at the default ELO of 1500. At game end, the bot’s hypothetical ELO change is divided equally among all human players and added to their changes. The bot itself stays at 1500, while its ELO change and New ELO cells display dashes. Floor-aware reconciliation keeps every human rating at or above 1 without changing the humans’ combined ELO, so the total ELO of all participants also remains unchanged. With exactly one human and one bot, the human’s ELO therefore never changes. Guest games are unrated and do not update ELO. They display dashes in both ELO columns. Rated registered-human ELO changes and new ratings use exactly one decimal place; increases are green, decreases are red, and unchanged changes are white.

During a rated game, ELO changes in the right panel opens a projection table for every participant, including the bot and anyone resigned or eliminated. Each Score slider accepts a whole number from 0 through 1000 as a relative weight, not as dollar capital. Its exact share of all slider values is the projected playerScore; if every slider is 0, all participants receive equal exact shares. Display-only whole percentages are allocated to total exactly 100%, but the ELO calculation uses the unrounded shares. This preview does not change the completed game's Bank-adjusted Money share rules.

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