feat(backend): per-tier, per-kind active-game limits with a guest funnel

Cap a player's simultaneous unfinished games per kind (vs_ai, random,
friends) with independent guest and durable-account tiers, held in a new
single-row backend.config table (-1 = unlimited) behind an in-memory cache
and editable live in the admin console (/_gm/limits). Each game is tagged
with games.game_kind on creation.

This replaces the earlier flat MaxActiveQuickGames=10 combined cap: the
per-tier/kind config is the single mechanism, enforced at the same handler
gate (ensureUnderGameLimit by kind on lobby/enqueue) plus the durable
friends cap in CreateInvitation. game.Service.AtGameLimit only resolves the
tier and counts; the limit policy stays at the request edge.

Guests are now refused friend requests, friend-code redemption,
befriend-in-game and invitation creation outright (403 guest_forbidden) --
previously only the UI hid these.

Admin: a kind column in both game lists and the config editor.

Defaults: guest 1 vs_ai / 1 random / 0 friends; durable 10 / 10 / 10.

backend/internal/game/service.go

@@ -17,6 +17,7 @@ import (
 
 	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/engine"
+	"scrabble/backend/internal/gamelimits"
 	"scrabble/backend/internal/notify"
 	"scrabble/backend/internal/payments"
 	"scrabble/backend/internal/session"
@@ -57,6 +58,9 @@ type Service struct {
 	// nil, only the free per-game allowance is served (no purchased hints). vs_ai hints are
 	// wallet-free and never touch it.
 	hintWallet HintWallet
+	// limits is the per-tier active-game cap config (cached). Set by SetGameLimits during wiring;
+	// when nil, no active-game limit is enforced (a game is always creatable).
+	limits *gamelimits.Service
 	// clearNudges, when set, marks the actor's pending nudges in a game read once they
 	// have committed a move (a nudge answered by moving stops counting as unread). It is
 	// best-effort and kept as a func so the game package never imports the social package.
@@ -126,6 +130,37 @@ func (svc *Service) SetHintWallet(w HintWallet) {
 	svc.hintWallet = w
 }
 
+// SetGameLimits installs the active-game limit config (cached), enabling the per-tier caps. When
+// unset (nil), a game is always creatable.
+func (svc *Service) SetGameLimits(l *gamelimits.Service) {
+	svc.limits = l
+}
+
+// AtGameLimit reports whether accountID has reached its tier's active-game cap for kind — the
+// per-tier, per-kind limits held in backend.config, read from the in-memory cache. It resolves
+// the caller's tier (guest vs durable) from the account, then counts its open+active games of that
+// kind. It reports false (not at the limit) when the limits config is not wired, the account is nil,
+// or the resolved cap is gamelimits.Unlimited. It backs the new-game gate (the handler aborts 409
+// game_limit_reached) and the lobby's at-limit flag.
+func (svc *Service) AtGameLimit(ctx context.Context, accountID uuid.UUID, kind gamelimits.Kind) (bool, error) {
+	if svc.limits == nil || accountID == uuid.Nil {
+		return false, nil
+	}
+	acc, err := svc.accounts.GetByID(ctx, accountID)
+	if err != nil {
+		return false, err
+	}
+	limit := svc.limits.LimitsFor(acc.IsGuest).Cap(kind)
+	if limit == gamelimits.Unlimited {
+		return false, nil
+	}
+	n, err := svc.store.CountActiveByKind(ctx, accountID, kind)
+	if err != nil {
+		return false, err
+	}
+	return n >= limit, nil
+}
+
 // walletContext resolves the payments gate inputs for an account on the current request: the
 // trusted execution context (from the session platform carried on ctx; absent ⇒ untrusted) and
 // the account's present identity sources (which chip/benefit segments are awake, §6).
@@ -338,6 +373,7 @@ func (svc *Service) Create(ctx context.Context, params CreateParams) (Game, erro
 		dropoutTiles:         params.DropoutTiles.String(),
 		multipleWordsPerTurn: params.MultipleWordsPerTurn,
 		vsAI:                 params.VsAI,
+		kind:                 params.Kind,
 	}
 	if err := svc.store.CreateGame(ctx, ins, seats, seeding.draws); err != nil {
 		return Game{}, err
@@ -401,6 +437,7 @@ func (svc *Service) OpenOrJoin(ctx context.Context, accountID uuid.UUID, params
 		multipleWordsPerTurn: params.MultipleWordsPerTurn,
 		status:               StatusOpen,
 		openDeadline:         &deadline,
+		kind:                 gamelimits.KindRandom,
 	}
 	// Decide the first move now by the official draw, with the not-yet-arrived opponent as a
 	// synthetic placeholder (uuid.Nil): the draw fixes who sits at seat 0 — and so moves
@@ -1386,14 +1423,6 @@ func (svc *Service) ListForLobby(ctx context.Context, accountID uuid.UUID) ([]Ga
 	return kept, nil
 }
 
-// CountActiveQuickGames reports how many in-progress quick games the account holds —
-// the count the simultaneous-game limit (MaxActiveQuickGames) is checked against. It
-// counts active and still-open quick games (including honest-AI ones) and excludes
-// friend games created by invitation and finished games. See Store.CountActiveQuickGames.
-func (svc *Service) CountActiveQuickGames(ctx context.Context, accountID uuid.UUID) (int, error) {
-	return svc.store.CountActiveQuickGames(ctx, accountID)
-}
-
 // HideGame hides a finished game from accountID's own lobby (it stays visible to the other
 // players); it is irreversible by design. Only a player of a finished game may hide it
 // (ErrNotAPlayer / ErrGameActive otherwise); hiding an already-hidden game is a no-op.

backend/internal/game/store.go

@@ -15,6 +15,7 @@ import (
 
 	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/engine"
+	"scrabble/backend/internal/gamelimits"
 	"scrabble/backend/internal/postgres/jet/backend/model"
 	"scrabble/backend/internal/postgres/jet/backend/table"
 )
@@ -45,6 +46,8 @@ type gameInsert struct {
 	multipleWordsPerTurn bool
 	// vsAI marks an honest-AI game (games.vs_ai).
 	vsAI bool
+	// kind tags the game's origin (games.game_kind) for the active-game limits.
+	kind gamelimits.Kind
 	// status is the lifecycle state to create the game in: StatusActive for a normal
 	// seated game, StatusOpen for an auto-match game still awaiting an opponent. An
 	// empty string defaults to StatusActive.
@@ -138,6 +141,20 @@ func (s *Store) CreateGame(ctx context.Context, ins gameInsert, seats []seatInse
 	})
 }
 
+// CountActiveByKind counts the account's active (open or in-progress) games of the given kind — the
+// per-tier active-game limit is checked against it before a new game of that kind is created.
+func (s *Store) CountActiveByKind(ctx context.Context, accountID uuid.UUID, kind gamelimits.Kind) (int, error) {
+	var n int
+	if err := s.db.QueryRowContext(ctx,
+		`SELECT count(*) FROM backend.games g
+		   JOIN backend.game_players p ON p.game_id = g.game_id
+		  WHERE p.account_id = $1 AND g.game_kind = $2 AND g.status IN ('open', 'active')`,
+		accountID, int16(kind)).Scan(&n); err != nil {
+		return 0, fmt.Errorf("game: count active by kind %s: %w", accountID, err)
+	}
+	return n, nil
+}
+
 // insertGameTx inserts the games row and one game_players row per seat (seat 0
 // first) on tx, stamping each seat's display-name snapshot. A seat whose account id is
 // uuid.Nil is written with a NULL account_id (and an empty snapshot) — the still-empty
@@ -155,9 +172,9 @@ func insertGameTx(ctx context.Context, tx *sql.Tx, ins gameInsert, seats []seatI
 		table.Games.GameID, table.Games.Variant, table.Games.DictVersion, table.Games.Seed,
 		table.Games.Status, table.Games.Players, table.Games.TurnTimeoutSecs,
 		table.Games.HintsAllowed, table.Games.HintsPerPlayer, table.Games.OpenDeadlineAt,
-		table.Games.DropoutTiles, table.Games.MultipleWordsPerTurn, table.Games.VsAi,
+		table.Games.DropoutTiles, table.Games.MultipleWordsPerTurn, table.Games.VsAi, table.Games.GameKind,
 	).VALUES(ins.id, ins.variant, ins.dictVersion, ins.seed, status, ins.players,
-		ins.turnTimeoutSecs, ins.hintsAllowed, ins.hintsPerPlayer, deadline, ins.dropoutTiles, ins.multipleWordsPerTurn, ins.vsAI)
+		ins.turnTimeoutSecs, ins.hintsAllowed, ins.hintsPerPlayer, deadline, ins.dropoutTiles, ins.multipleWordsPerTurn, ins.vsAI, int16(ins.kind))
 	if _, err := gi.ExecContext(ctx, tx); err != nil {
 		return fmt.Errorf("insert game: %w", err)
 	}
@@ -501,28 +518,6 @@ func (s *Store) ListGamesForAccount(ctx context.Context, accountID uuid.UUID) ([
 	return out, nil
 }
 
-// CountActiveQuickGames counts the account's in-progress quick games — the ones the
-// simultaneous-game limit (MaxActiveQuickGames) is checked against. It includes both
-// active and still-open (awaiting-opponent) games, the honest-AI ones among them, and
-// excludes friend games (those linked to a game_invitations row) and finished games.
-// A hidden game still occupies a slot, so this is a dedicated count rather than a
-// filter over ListGamesForAccount (which drops hidden games). Joining on the account's
-// own seat counts each game once (an open game's empty opponent seat has no account).
-func (s *Store) CountActiveQuickGames(ctx context.Context, accountID uuid.UUID) (int, error) {
-	// The status literals are game.StatusActive / game.StatusOpen, matching the
-	// games.status CHECK in the baseline migration.
-	const q = `
-SELECT COUNT(*) FROM backend.games g
-JOIN backend.game_players gp ON gp.game_id = g.game_id
-LEFT JOIN backend.game_invitations gi ON gi.game_id = g.game_id
-WHERE gp.account_id = $1 AND g.status IN ('active', 'open') AND gi.game_id IS NULL`
-	var n int
-	if err := s.db.QueryRowContext(ctx, q, accountID).Scan(&n); err != nil {
-		return 0, fmt.Errorf("game: count active quick games: %w", err)
-	}
-	return n, nil
-}
-
 // HideGame hides a game from the account's own lobby list (idempotent). The caller validates the
 // game is finished and the account is a player.
 func (s *Store) HideGame(ctx context.Context, accountID, gameID uuid.UUID) error {
@@ -1361,6 +1356,7 @@ func projectGame(g model.Games, seats []model.GamePlayers) (Game, error) {
 	}
 	out.MultipleWordsPerTurn = g.MultipleWordsPerTurn
 	out.VsAI = g.VsAi
+	out.Kind = gamelimits.Kind(g.GameKind)
 	if g.EndReason != nil {
 		out.EndReason = *g.EndReason
 	}

backend/internal/game/types.go

@@ -7,6 +7,7 @@ import (
 	"github.com/google/uuid"
 
 	"scrabble/backend/internal/engine"
+	"scrabble/backend/internal/gamelimits"
 )
 
 // Status values persisted in the games.status column.
@@ -94,15 +95,6 @@ const DefaultTurnTimeout = 24 * time.Hour
 // one of AllowedTurnTimeouts (never offered in the creation UI).
 const AIInactivityTimeout = 7 * 24 * time.Hour
 
-// MaxActiveQuickGames is the cap on a player's simultaneous quick games (human
-// auto-match and honest-AI), counting both in-progress (StatusActive) and
-// still-open, awaiting-opponent (StatusOpen) games. Friend games created by
-// invitation are not counted. At the cap the backend refuses to create a new game
-// of any kind — quick or by invitation — and the lobby disables "New Game";
-// accepting an incoming invitation is always allowed. See
-// Store.CountActiveQuickGames.
-const MaxActiveQuickGames = 10
-
 // aiPlayerName labels the robot seat in an honest-AI game's GCG export, so a downloaded
 // game file shows a clean "AI" rather than the robot's human-like pool name (the in-app
 // UI shows 🤖 from the game's vs_ai flag).
@@ -125,6 +117,10 @@ type CreateParams struct {
 	// robot is seated at once, the move clock is AIInactivityTimeout, and chat/nudge
 	// and finish-time statistics are suppressed. Set by the lobby's AI-match path.
 	VsAI bool
+	// Kind tags the game's origin (games.game_kind) for the active-game limits: vs_ai / random /
+	// friends. The lobby sets it; a zero (unknown) kind is never gated. The active-game limit itself
+	// is enforced at the new-game handler (Server.ensureUnderGameLimit), not here.
+	Kind gamelimits.Kind
 }
 
 // Game is the persisted state of a match: the games row joined with its seats.
@@ -151,6 +147,9 @@ type Game struct {
 	// VsAI is true for an honest-AI game (games.vs_ai): the opponent is a robot the
 	// player knowingly chose, shown as 🤖, with chat/nudge disabled and no statistics.
 	VsAI bool
+	// Kind is the game's origin tag (games.game_kind) for the active-game limits: vs_ai / random /
+	// friends, or unknown for an untagged game. Read-only projection; set once on creation.
+	Kind gamelimits.Kind
 }
 
 // Seat is one player's standing in a game.