feat: playable arcade — rooms, identity, client, deployment

Round length is now bounded: the multiplier follows a hyperbolic curve
diverging at 60s, replacing an exponential one where a 275x crash point
produced a two-and-a-half minute round.

Fixes seed reveal, which silently failed every round because pgx cannot
encode a fixed-size byte array as bytea.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

docker-compose.yml

@@ -26,6 +26,19 @@ services:
       timeout: 3s
       retries: 20
 
+  arcade:
+    build: .
+    environment:
+      ARCADE_DSN: postgres://arcade:arcade_dev@postgres:5432/arcade
+      ARCADE_ADDR: ":8080"
+      # Development funding. Leave unset in any real deployment.
+      ARCADE_DEV_FAUCET: "${ARCADE_DEV_FAUCET:-0}"
+    ports: ["8080:8080"]
+    depends_on:
+      postgres: { condition: service_healthy }
+      redis:    { condition: service_healthy }
+    restart: unless-stopped
+
 volumes:
   pgdata:
   redisdata: