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/server/handlers.go

@@ -319,6 +319,8 @@ func statusForError(err error) (int, string) {
 		return http.StatusConflict, "request_declined"
 	case errors.Is(err, social.ErrFriendCodeInvalid):
 		return http.StatusUnprocessableEntity, "friend_code_invalid"
+	case errors.Is(err, social.ErrGuestForbidden), errors.Is(err, lobby.ErrGuestForbidden):
+		return http.StatusForbidden, "guest_forbidden"
 	case errors.Is(err, feedback.ErrGuestForbidden):
 		return http.StatusForbidden, "feedback_guest_forbidden"
 	case errors.Is(err, feedback.ErrBanned):

backend/internal/server/handlers_admin_console.go

@@ -70,6 +70,10 @@ func (s *Server) registerConsole(router *gin.Engine) {
 	gm.POST("/bans/unban", s.consoleUnban)
 	gm.GET("/games", s.consoleGames)
 	gm.GET("/games/:id", s.consoleGameDetail)
+	if s.gamelimits != nil {
+		gm.GET("/limits", s.consoleLimits)
+		gm.POST("/limits", s.consoleUpdateLimits)
+	}
 	gm.GET("/complaints", s.consoleComplaints)
 	gm.GET("/complaints/:id", s.consoleComplaintDetail)
 	gm.POST("/complaints/:id/resolve", s.consoleResolveComplaint)
@@ -1244,7 +1248,7 @@ func (s *Server) consoleUUID(c *gin.Context, back string) (uuid.UUID, bool) {
 
 // gameRow projects a game summary into its console row.
 func gameRow(g game.Game) adminconsole.GameRow {
-	return adminconsole.GameRow{ID: g.ID.String(), Variant: g.Variant.String(), Status: g.Status, Players: g.Players, UpdatedAt: fmtTime(g.UpdatedAt), VsAI: g.VsAI}
+	return adminconsole.GameRow{ID: g.ID.String(), Variant: g.Variant.String(), Status: g.Status, Players: g.Players, UpdatedAt: fmtTime(g.UpdatedAt), VsAI: g.VsAI, Kind: g.Kind.String()}
 }
 
 // trimForm returns the trimmed value of a posted form field.

backend/internal/server/handlers_admin_limits.go

@@ -0,0 +1,65 @@
+package server
+
+import (
+	"fmt"
+
+	"github.com/gin-gonic/gin"
+
+	"scrabble/backend/internal/adminconsole"
+	"scrabble/backend/internal/gamelimits"
+)
+
+// consoleLimits renders the per-tier, per-kind active-game limit form (backend.config), read from
+// the in-memory cache.
+func (s *Server) consoleLimits(c *gin.Context) {
+	cfg := s.gamelimits.Get()
+	s.renderConsole(c, "limits", "limits", "Game limits", adminconsole.GameLimitsView{
+		GuestVsAI:      cfg.Guest.VsAI,
+		GuestRandom:    cfg.Guest.Random,
+		GuestFriends:   cfg.Guest.Friends,
+		DurableVsAI:    cfg.Durable.VsAI,
+		DurableRandom:  cfg.Durable.Random,
+		DurableFriends: cfg.Durable.Friends,
+	})
+}
+
+// consoleUpdateLimits saves the active-game limits and refreshes the hot cache in place. Each
+// field is a per-kind cap: -1 is unlimited, 0 blocks the kind, a positive value caps concurrent games.
+func (s *Server) consoleUpdateLimits(c *gin.Context) {
+	cfg := gamelimits.Config{
+		Guest: gamelimits.Limits{
+			VsAI:    atoiForm(c, "guest_vs_ai"),
+			Random:  atoiForm(c, "guest_random"),
+			Friends: atoiForm(c, "guest_friends"),
+		},
+		Durable: gamelimits.Limits{
+			VsAI:    atoiForm(c, "durable_vs_ai"),
+			Random:  atoiForm(c, "durable_random"),
+			Friends: atoiForm(c, "durable_friends"),
+		},
+	}
+	if err := validateGameLimits(cfg); err != nil {
+		s.renderConsoleMessage(c, "Invalid", err.Error(), "/_gm/limits")
+		return
+	}
+	if err := s.gamelimits.Update(c.Request.Context(), cfg); err != nil {
+		s.consoleError(c, err)
+		return
+	}
+	s.renderConsoleMessage(c, "Saved", "game limits updated", "/_gm/limits")
+}
+
+// validateGameLimits rejects a limit below -1 (the unlimited sentinel); -1, 0 and any positive count
+// are valid. It mirrors the backend.config CHECK so a bad value is refused with a clean message
+// rather than a raw database error.
+func validateGameLimits(cfg gamelimits.Config) error {
+	for _, v := range []int{
+		cfg.Guest.VsAI, cfg.Guest.Random, cfg.Guest.Friends,
+		cfg.Durable.VsAI, cfg.Durable.Random, cfg.Durable.Friends,
+	} {
+		if v < gamelimits.Unlimited {
+			return fmt.Errorf("a limit must be -1 (unlimited), 0, or a positive count")
+		}
+	}
+	return nil
+}

backend/internal/server/handlers_game.go

@@ -10,6 +10,7 @@ import (
 
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/game"
+	"scrabble/backend/internal/gamelimits"
 )
 
 // The handlers below cover the game and chat operations the UI needs. They follow
@@ -46,10 +47,11 @@ type historyDTO struct {
 }
 
 // gameListDTO is the caller's games (active and finished) for the lobby. AtGameLimit
-// reports whether the caller has reached the simultaneous quick-game cap
-// (game.MaxActiveQuickGames); while it is true the lobby disables "New Game" and shows a
-// notice. It rides the lobby response — which the lobby re-fetches on every game event —
-// instead of a separate request.
+// reports whether the caller has reached its tier's active-game cap for the random
+// (quick auto-match) kind (the per-tier, per-kind limits in backend.config); while
+// it is true the lobby disables "New Game" and shows a notice. It rides the lobby
+// response — which the lobby re-fetches on every game event — instead of a separate
+// request.
 type gameListDTO struct {
 	Games       []gameDTO `json:"games"`
 	AtGameLimit bool      `json:"at_game_limit"`
@@ -395,23 +397,13 @@ func (s *Server) handleSaveDraft(c *gin.Context) {
 	c.JSON(http.StatusOK, okResponse{OK: true})
 }
 
-// atGameLimit reports whether uid already holds the maximum number of simultaneous
-// quick games (game.MaxActiveQuickGames). It backs both the lobby's at_game_limit flag
-// and the new-game gate; friend games created by invitation are not counted.
-func (s *Server) atGameLimit(ctx context.Context, uid uuid.UUID) (bool, error) {
-	n, err := s.games.CountActiveQuickGames(ctx, uid)
-	if err != nil {
-		return false, err
-	}
-	return n >= game.MaxActiveQuickGames, nil
-}
-
-// ensureUnderGameLimit aborts the request with 409 game_limit_reached when uid is at the
-// simultaneous quick-game cap, and reports whether the caller may proceed. It guards
-// every new-game entry point — quick auto-match/AI and invitation creation; accepting an
-// incoming invitation is deliberately exempt.
-func (s *Server) ensureUnderGameLimit(c *gin.Context, uid uuid.UUID) bool {
-	atLimit, err := s.atGameLimit(c.Request.Context(), uid)
+// ensureUnderGameLimit aborts the request with 409 game_limit_reached when uid has reached its
+// tier's active-game cap for kind (the per-tier, per-kind limits in backend.config), and reports
+// whether the caller may proceed. It guards the quick new-game entry points — auto-match (random)
+// and AI (vs_ai). Friend-invitation limits are enforced in the lobby's CreateInvitation, and
+// accepting an incoming invitation is deliberately exempt.
+func (s *Server) ensureUnderGameLimit(c *gin.Context, uid uuid.UUID, kind gamelimits.Kind) bool {
+	atLimit, err := s.games.AtGameLimit(c.Request.Context(), uid, kind)
 	if err != nil {
 		s.abortErr(c, err)
 		return false
@@ -437,7 +429,7 @@ func (s *Server) handleListGames(c *gin.Context) {
 		s.abortErr(c, err)
 		return
 	}
-	atLimit, err := s.atGameLimit(c.Request.Context(), uid)
+	atLimit, err := s.games.AtGameLimit(c.Request.Context(), uid, gamelimits.KindRandom)
 	if err != nil {
 		s.abortErr(c, err)
 		return

backend/internal/server/handlers_invitations.go

@@ -133,9 +133,6 @@ func (s *Server) handleCreateInvitation(c *gin.Context) {
 		}
 		inviteeIDs = append(inviteeIDs, id)
 	}
-	if !s.ensureUnderGameLimit(c, uid) {
-		return
-	}
 	inv, err := s.invitations.CreateInvitation(c.Request.Context(), uid, inviteeIDs, settings)
 	if err != nil {
 		s.abortErr(c, err)

backend/internal/server/handlers_user.go

@@ -8,6 +8,7 @@ import (
 	"github.com/google/uuid"
 
 	"scrabble/backend/internal/engine"
+	"scrabble/backend/internal/gamelimits"
 )
 
 // The /api/v1/user/* endpoints require X-User-ID (RequireUserID middleware). The
@@ -189,13 +190,15 @@ func (s *Server) handleEnqueue(c *gin.Context) {
 	if !s.ensureVariantAllowed(c, uid, variant.String()) {
 		return
 	}
-	if !s.ensureUnderGameLimit(c, uid) {
-		return
-	}
+	kind := gamelimits.KindRandom
 	enter := s.matchmaker.Enqueue
 	if req.VsAI {
+		kind = gamelimits.KindVsAI
 		enter = s.matchmaker.StartVsAI
 	}
+	if !s.ensureUnderGameLimit(c, uid, kind) {
+		return
+	}
 	res, err := enter(c.Request.Context(), uid, variant, req.MultipleWordsPerTurn)
 	if err != nil {
 		s.abortErr(c, err)

backend/internal/server/server.go

@@ -25,6 +25,7 @@ import (
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/feedback"
 	"scrabble/backend/internal/game"
+	"scrabble/backend/internal/gamelimits"
 	"scrabble/backend/internal/link"
 	"scrabble/backend/internal/lobby"
 	"scrabble/backend/internal/notify"
@@ -100,6 +101,10 @@ type Deps struct {
 	// console routes are registered when the wallet surface lands. A nil Payments
 	// omits them.
 	Payments *payments.Service
+	// GameLimits is the per-tier, per-kind active-game limit config, cached in memory. The
+	// game domain reads it through game.Service (SetGameLimits) for the new-game gate; the admin
+	// console reads and edits it here. A nil GameLimits omits the limits console section.
+	GameLimits *gamelimits.Service
 	// Notifier publishes live-event intents — here the banner-eligibility re-poll
 	// signal the banner/hint/role console actions emit. A nil Notifier discards
 	// them (notify.Nop).
@@ -140,6 +145,7 @@ type Server struct {
 	banview     *banview.View
 	ads         *ads.Service
 	payments    *payments.Service
+	gamelimits  *gamelimits.Service
 	robokassa   robokassa.Config
 	notifier    notify.Publisher
 	console     *adminconsole.Renderer
@@ -194,6 +200,7 @@ func New(addr string, deps Deps) *Server {
 		banview:       deps.BanView,
 		ads:           deps.Ads,
 		payments:      deps.Payments,
+		gamelimits:    deps.GameLimits,
 		robokassa:     deps.Robokassa,
 		notifier:      notifier,
 		renderer:      deps.Renderer,