feat(rules): forbid repeating a word already on the board in Erudit

Russian "Эрудит" treats a word laid on the board as belonging to the
game: it cannot be laid again. Neither the solver, the backend nor the
offline JS port knew the rule, so a player (and the robot) could replay a
word freely. Official Scrabble places no such restriction, so both
Scrabble variants keep playing unrestricted.

The rule applies in two ways. A play whose main word is already on the
board is illegal, and is neither accepted nor generated. A play whose
perpendicular cross-word is already there stands — that word is
incidental to laying the main word — but scores nothing. The set of
played words is the game's own move journal, main words and cross-words
alike, compared decoded, so a word spelled with a blank is the same word.

It lives in the game layer, not the solver: only a game knows its
history, and the solver stays stateless and standard-rules. The backend
applies it at submit, at the move preview and over generated moves
(filtering and re-ranking them, so neither the robot nor the hint can
offer a play the engine would then refuse); the client port does the same
for the offline engine and for the on-device preview of an online game.

The rule is pinned per game (games.no_repeat_words, set from the variant
at creation) rather than keyed on the variant, because a game is replayed
from its journal on every open. Applied retroactively it would make an
already-played repeat illegal — closing that game as a draw — and would
rescore a play whose cross-word repeats an earlier word, shifting a live
game's totals. Games created before the rule keep playing without it. The
flag rides the wire as a trailing field because the client's preview must
score the way the server does, and offline games pin the same answer in
their own record.

backend/internal/game/eventwire.go

@@ -57,6 +57,7 @@ func gameSummary(g Game, names []string) notify.GameSummary {
 		EndReason:            g.EndReason,
 		Seats:                seats,
 		LastActivityUnix:     last.Unix(),
+		NoRepeatWords:        g.NoRepeatWords,
 	}
 }
 

backend/internal/game/replay_timeline.go

@@ -60,6 +60,7 @@ func (svc *Service) ReplayTimeline(ctx context.Context, gameID uuid.UUID) (Repla
 		Seed:                 seed,
 		DropoutTiles:         pre.DropoutTiles,
 		MultipleWordsPerTurn: pre.MultipleWordsPerTurn,
+		NoRepeatWords:        pre.NoRepeatWords,
 	})
 	if err != nil {
 		return ReplayTimelineView{}, err

backend/internal/game/service.go

@@ -284,6 +284,13 @@ func (svc *Service) versionResident(version string) bool {
 	return false
 }
 
+// noRepeatWordsFor reports whether a game of variant v is created with the no-repeat-words rule
+// (see engine/norepeat.go): a word already on the board cannot be laid again. It is a rule of
+// Russian "Эрудит" alone — both Scrabble variants let a word be played as often as a player can
+// manage. The answer is pinned into games.no_repeat_words at creation and read back from there
+// afterwards, never re-derived, so games created before the rule existed keep their own answer.
+func noRepeatWordsFor(v engine.Variant) bool { return v == engine.VariantErudit }
+
 // Create starts and persists a new game seating the given accounts in turn order
 // (seat 0 first), deals the racks, and warms the live-game cache. It validates
 // the player count (2–4), the move clock, the hint allowance and that every seat
@@ -359,6 +366,7 @@ func (svc *Service) Create(ctx context.Context, params CreateParams) (Game, erro
 		Seed:                 seed,
 		DropoutTiles:         params.DropoutTiles,
 		MultipleWordsPerTurn: params.MultipleWordsPerTurn,
+		NoRepeatWords:        noRepeatWordsFor(params.Variant),
 	})
 	if err != nil {
 		if errors.Is(err, engine.ErrUnknownVariant) || errors.Is(err, engine.ErrUnknownVersion) {
@@ -382,6 +390,7 @@ func (svc *Service) Create(ctx context.Context, params CreateParams) (Game, erro
 		hintsPerPlayer:       params.HintsPerPlayer,
 		dropoutTiles:         params.DropoutTiles.String(),
 		multipleWordsPerTurn: params.MultipleWordsPerTurn,
+		noRepeatWords:        noRepeatWordsFor(params.Variant),
 		vsAI:                 params.VsAI,
 		kind:                 params.Kind,
 	}
@@ -445,6 +454,7 @@ func (svc *Service) OpenOrJoin(ctx context.Context, accountID uuid.UUID, params
 		hintsPerPlayer:       params.HintsPerPlayer,
 		dropoutTiles:         params.DropoutTiles.String(),
 		multipleWordsPerTurn: params.MultipleWordsPerTurn,
+		noRepeatWords:        noRepeatWordsFor(params.Variant),
 		status:               StatusOpen,
 		openDeadline:         &deadline,
 		kind:                 gamelimits.KindRandom,
@@ -1584,6 +1594,7 @@ func (svc *Service) replay(ctx context.Context, pre Game) (*engine.Game, error)
 		Seed:                 seed,
 		DropoutTiles:         pre.DropoutTiles,
 		MultipleWordsPerTurn: pre.MultipleWordsPerTurn,
+		NoRepeatWords:        pre.NoRepeatWords,
 	})
 	if err != nil {
 		return nil, err

backend/internal/game/store.go

@@ -44,6 +44,8 @@ type gameInsert struct {
 	dropoutTiles    string
 	// multipleWordsPerTurn false selects the single-word rule for the game.
 	multipleWordsPerTurn bool
+	// noRepeatWords true forbids laying a word that is already on the board (games.no_repeat_words).
+	noRepeatWords 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.
@@ -173,8 +175,10 @@ func insertGameTx(ctx context.Context, tx *sql.Tx, ins gameInsert, seats []seatI
 		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.GameKind,
+		table.Games.NoRepeatWords,
 	).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, int16(ins.kind))
+		ins.turnTimeoutSecs, ins.hintsAllowed, ins.hintsPerPlayer, deadline, ins.dropoutTiles, ins.multipleWordsPerTurn, ins.vsAI, int16(ins.kind),
+		ins.noRepeatWords)
 	if _, err := gi.ExecContext(ctx, tx); err != nil {
 		return fmt.Errorf("insert game: %w", err)
 	}
@@ -1355,6 +1359,7 @@ func projectGame(g model.Games, seats []model.GamePlayers) (Game, error) {
 		UpdatedAt:      g.UpdatedAt,
 	}
 	out.MultipleWordsPerTurn = g.MultipleWordsPerTurn
+	out.NoRepeatWords = g.NoRepeatWords
 	out.VsAI = g.VsAi
 	out.Kind = gamelimits.Kind(g.GameKind)
 	if g.EndReason != nil {

backend/internal/game/types.go

@@ -144,6 +144,10 @@ type Game struct {
 	FinishedAt     *time.Time
 	// MultipleWordsPerTurn true selects standard Scrabble; false the single-word rule.
 	MultipleWordsPerTurn bool
+	// NoRepeatWords true forbids laying a word that is already on the board (the "Эрудит" rule,
+	// see engine/norepeat.go). It is pinned at creation from the variant rather than derived on
+	// read, so a game started before the rule existed keeps replaying and scoring unchanged.
+	NoRepeatWords bool
 	// 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