Wiki · rules

Rules

Last edited by David Bloomin · 2d ago ·

Matrix Games — rules

The yard

One fixed arena, 24 cells wide by 14 tall, rendered at 40 px per cell (a 960 x 560 board). It is the same map in every variant, mirror-symmetric left-right and top-bottom, fully connected, with 216 free cells. # is wall, . is floor:

########################
#....##..........##....#
#..........##..........#
#.##....#......#....##.#
#.##................##.#
#......##......##......#
#..##..............##..#
#..##..............##..#
#......##......##......#
#.##................##.#
#.##....#......#....##.#
#..........##..........#
#....##..........##....#
########################

Eight cogs play, always: Ash Birch Cedar Dune Elm Fern Gorse Holly, one per slot, each in a fixed livery. In bach-or-stravinsky slots 0-3 are the row (blue) camp and slots 4-7 the column (orange) camp; in every other variant every cog is eligible against every other.

One episode is 12 beats of 50 ticks = 600 ticks. Playback is 24 fps, so a full replay is 25 seconds of video.

Tokens

The variant fixes K (2 or 3) and the token names. Spawners are fixed cells that hold at most one token, drawn once at episode start from the seeded RNG: 16 in zone A (type 0, top left), 16 in zone B (type 1, top right), 16 in zone C (type 2, centre bottom, K = 3 only), and a 12-spawner mixed scatter across the centre band whose n-th spawner carries type n mod K.

Stepping onto a spawner that holds a token collects it unless that type is already at tokenCap = 8. A collected spawner refills 45 ticks later. Zone token counts are public, so camping a zone to starve a rival is visible to everyone as a falling counter.

Every cog starts, and after every resolution resets to, the ENDOWMENT: one token of each type. Maximum purity is 8/9 (K = 2) or 8/10 (K = 3): commitment is expensive and never total.

Inventory mix IS strategy. A cog's strategy at the moment of an interaction is the rational vector x_i = n_i / N.

One intent per beat

At each beat boundary every seat submits ONE intent, which a deterministic per-tick kernel then executes for the next 50 ticks.

intent	argument	what the kernel does
`gather`	`token`	path to the nearest cell holding a token of that type and collect it; at the cap, hold at the type's zone centre. Never fires.
`deny`	`token`	take the token of that type nearest to the nearest other cog. Never fires.
`hunt`	`target`	path toward that cog's last known cell; fire the first tick it is in the ray and the beam is ready.
`avoid`	`target`	move away and never enter a cell within 2 of it. Never fires.
`hold`	—	stand still, re-face the nearest cog within 6 cells every 4 ticks, fire when one is in the ray.

Pathing is a breadth-first search over free cells with ties broken in the direction order N, E, S, W. A cog with no legal step waits.

The ten numbered tick rules

Timers. freeze, stepCd, beamCd and immune each tick down to 0.
Token respawn. Every spawner whose refillAt == t gets its token back.
Intent evaluation. Each unfrozen cog produces one micro-action: step(dir), turn(dir), fire or wait. Frozen cogs produce wait.
Movement, seats in ascending slot order. A cog with stepCd == 0 moves one cell if it is floor and currently unoccupied, sets its facing and takes stepCooldownTicks = 3. turn(dir) costs nothing.
Pickup, ascending slot order.
Beam fire, ascending slot order. Range 4 cells along the facing, stopped by the first wall; the first cog in the ray is the target. No target, or a frozen / immune target, or (in bach-or-stravinsky) a same-camp target, is a miss or a no-contest and costs beamMissCooldown = 6.
Resolution. The row player is the shooter, except in bach-or-stravinsky where it is the row-camp participant regardless of who fired. With the row inventory n (N = sum n) and the column inventory m (M = sum m):
```
rowPayCp = ( sum_i sum_j  n_i * rowPay[i][j] * m_j * 100 ) div (N * M)
colPayCp = ( sum_i sum_j  n_i * colPay[i][j] * m_j * 100 ) div (N * M)
```
div truncates toward zero. Payoffs are in centipoints. The cell the viewer pops is (argmax n, argmax m), ties to the lowest index.
Reset. Both participants reset to the endowment, freeze = 12, immune = 12, beamCd = beamResetCooldown = 25.
Indices. The convention histogram, the cooperation accumulator, the per-seat exploitability accumulators and the leader check.
Record. One state frame, its events and two series rows.

Scoring

scores[i] is the sum of the payoffs seat i collected, in points. Higher is better. In running-with-scissors the scores are zero-sum and negatives are normal. A cog that never resolves an interaction scores exactly 0: there is no participation bonus and no penalty for hiding.

The episode ends at the first of: 12 beats played (complete / full_match); the play deadline, 60 % of episodeTimeoutSeconds, crossed between beats (deadline); or no seat socket connected within 180 s (forfeit). Those three are the only legal results.reason values.