Stage 17 round 5 (L2): robot play-to-win intent + next-move ETA in the admin game card

The admin game detail now shows, per robot seat, the game's deterministic play-to-win
decision (from the bag seed) and — while it is that robot's turn — its scheduled next-move
ETA (sampled think-time delay, deferred past the sleep window), plus a caption with the
~40% global target. Wiring: robot.PlayToWin/NextMoveAt/PlayToWinTargetPercent exports,
account.IsRobot, game RobotSchedule (seed + turn-start). Tests: NextMoveAt invariants
(never early, never in the sleep window), PlayToWin export, and an admin render integration
test asserting the intent + ETA + target appear.

backend/internal/game/service.go

@@ -220,6 +220,12 @@ func (svc *Service) GameVariant(ctx context.Context, gameID uuid.UUID) (engine.V
 	return svc.store.GetGameVariant(ctx, gameID)
 }
 
+// RobotSchedule returns a game's bag seed and turn-start time, for the admin console's
+// robot-schedule panel (the deterministic play-to-win intent and next-move ETA).
+func (svc *Service) RobotSchedule(ctx context.Context, gameID uuid.UUID) (seed int64, turnStartedAt time.Time, err error) {
+	return svc.store.RobotSchedule(ctx, gameID)
+}
+
 // transition validates the actor and turn, applies op under the per-game lock and
 // commits the result.
 func (svc *Service) transition(ctx context.Context, gameID, accountID uuid.UUID, op engineOp) (MoveResult, error) {