rules.md

Goofspiel / Oshi-Zumo rules

One sim, one image, two modes selected by the mode field of game_config.

Goofspiel (mode "goofspiel", 4 seats, 13 rounds)

• Every seat holds an identical hand of the cards 1..13. The prize deck is the cards 1..13, shuffled once from the episode seed and recorded in the replay as config.prizeOrder. The total pool is 91.
• Resolution order for round r (this is the order the sim executes and the order the events appear in the replay):
  1. beginRound: reveal prize = prizeOrder[r]; emit the prize event.
  2. Build every seat's observation. Scripted seats decide inline; every LLM seat's request goes out in ONE parallel batch.
  3. Each seat returns one integer bid, legal iff the card is still in that seat's hand. Illegal, unparseable or timed out -> one retry in a second batch carrying the legal set -> the match baseline, and the seat's fallbacks counter increments.
  4. All bids are locked server-side, then revealed simultaneously. No seat, spectator socket or player socket sees any bid of round r before every bid of round r is in.
  5. top = max(bids), winners = { i : bids[i] == top }.
  6. If exactly one winner it gains prize; otherwise each tied seat gains prize / |winners|. Fractional scores are legal. (OpenSpiel's split convention: it keeps the pool constant at 91, which keeps the score formula exactly zero-sum.)
  7. Every seat removes its bid card from its hand - spent whether it won or not.
  8. margin = top - (highest bid strictly below top), and 0 when the top is tied. Emit reveal; if margin >= 6, emit overbid immediately after it.
  9. After the 13th prize: complete / prizes-exhausted.

Oshi-Zumo (mode "oshizumo", 2 seats, at most 20 rounds)

Buro's [N, K, M] parameterisation pinned to N = 20 coins, K = 3, M = 1.

• The field is 2K+1 = 7 cells, 0..6; the token starts at cell 3. Seat 0 pushes toward cell 6, seat 1 toward cell 0. The token is off the field at > 6 (seat 0 wins) or < 0 (seat 1 wins).
• A bid is an integer in [minBid_i, coins_i] where minBid_i = min(M, coins_i) - normally at least 1, but a seat holding 0 coins must bid 0. M = 1 makes the episode provably bounded by 20 rounds.
• Resolution order for round r:
  1. beginRound: publish the position and both purses (no prize event in this mode).
  2. Observations built; scripted seats inline; LLM seats in one parallel batch.
  3. Each seat returns one integer bid; same retry-then-fallback ladder as goofspiel.
  4. Bids locked, then revealed simultaneously.
  5. BOTH seats pay: coins[i] -= bids[i], unconditionally.
  6. bids[0] > bids[1] -> position += 1; bids[1] > bids[0] -> position -= 1; EQUAL BIDS DO NOT MOVE THE TOKEN, and both bids are still deducted (Buro 2004).
  7. Emit reveal, then overbid when margin = |bids[0] - bids[1]| >= 6, then push (carrying delta in {-1, 0, +1} and positionAfter).
  8. End checks, in this order: position > 6 -> complete/pushout, seat 0 wins; position < 0 -> complete/pushout, seat 1 wins; both purses 0 -> complete/coins-exhausted, scored by position; roundsPlayed == maxRounds -> complete/round-cap, scored by position.
• Scoring by position, used for every non-pushout ending including deadline: position > 3 seat 0 wins, position < 3 seat 1 wins, position == 3 is a draw.

Scoring

One scores array, same meaning in both modes, higher is better, and the array sums to 0.

• Goofspiel, N seats, pool = the prize value awarded so far (91 for a complete episode): share_i = points_i / pool, score_i = (N * share_i - 1) / (N - 1). At N = 4 that is (points_i - 22.75) / 68.25: +1 means "won every prize", 0 means "exactly the equal share".
• Oshi-Zumo: +1 for the winner, -1 for the loser, 0/0 on a draw.

Both scales top out at +1 deliberately, so a seat that dominates one variant and a seat that dominates the other look the same to the ladder. The league ranks by mean episode score, higher first.

Endings

results.reason has exactly two legal values, complete and deadline. The finer ending rides in results.ending:

deadline is an ACCEPTABLE ending for this coworld: the game is fully scored at the stop (goofspiel from the prizes already awarded, oshi-zumo by token position), so a deadline episode is a real result. The same settle(reason, ending) proc applies the ending on record and on playback, so a wall-clock stop re-derives identically in the wasm replay viewer.

The 'overbid' gasp

One predicate, both modes: overbid iff margin >= 6, where margin is the top bid minus the highest bid strictly below it (0 when the top is tied). It is its own event, its own feed line, its own scrub beat and its own banner.

Anti-collusion

Sealed bids server-side; anonymous cog aliases (no prompt ever contains a policy name); and a reported, never enforced bid-pattern audit: results.collusionIndex[i] is the share of goofspiel rounds in which seat i bid its lowest remaining card while the round's margin was >= 6 - it stood aside for someone else's blow-out. 0.5 is the threshold at which a human should look.

The meta

Every decision is made by Claude from a per-seat policy prompt plus the prize, every seat's remaining resource, the complete public bid history and the seat's own private notes. Prompts that price each prize against what it costs, track what rivals have already spent, and concede the prizes two rivals will fight over tend to score. The scripted baselines - match (bid the prize's rank, or the cheapest card above it) and hoard (dump the lowest card on small prizes, swing the highest on big ones) - fill seats without prompts and are fieldable policies in their own right.