feat(game): official first-move tile draw + admin step-by-step replay

Decide who moves first by the official rule: each seated player draws one
tile, the one closest to "A" leads (a blank beats every letter), ties
re-drawing until a single leader remains. Each draw uses honest per-draw
crypto/rand entropy (not the deterministic bag seed), so the recorded draw —
not a seed — is the only account of the outcome. The leader takes seat 0, so
the engine and journal replay are unchanged.

The draw is recorded with the game (game_setup_draws, migration 00013) for
future tournaments, designed as a discrete "player N draws a tile" step.
Friend/AI games draw at creation. Auto-match draws when the game opens,
against a synthetic uuid.Nil opponent whose draw rows (NULL account_id) are
back-filled to the real opponent on join — so the opener's seat is fixed up
front and the existing open-game pre-move is preserved with no reseating.

Admin /_gm/games/:id gains the recorded draw list and a simple step-by-step
board replay (game.ReplayTimeline + a vanilla-JS stepper): a board with
A-O/1-15 headers and highlighted premium squares, placed letters with their
tile value as a subscript, rack panels around the board (seat 0 top, 1
bottom, 2 left, 3 right) with the current player highlighted, and a per-move
log with the tiles drawn and the bag remainder.

Docs: ARCHITECTURE §6/§9, FUNCTIONAL (+_ru), PRERELEASE (FM row), design spec.

backend/internal/inttest/admin_test.go

@@ -206,6 +206,12 @@ func TestConsoleGameDetailRobotSchedule(t *testing.T) {
 	if !strings.Contains(body, "~40%") {
 		t.Error("robot play-to-win target caption missing")
 	}
+	if !strings.Contains(body, "First-move draw") {
+		t.Error("first-move draw section missing from the game detail")
+	}
+	if !strings.Contains(body, `id="replay-board"`) {
+		t.Error("replay board container missing from the game detail")
+	}
 }
 
 // TestConsoleThrottledViewAndFlagClear drives the rate-limit surface end to

backend/internal/inttest/dictionary_update_test.go

@@ -134,11 +134,13 @@ func TestDictionaryUpdateFlow(t *testing.T) {
 // newGameServiceOn builds a game service over the shared pool but a caller-supplied
 // dictionary directory, version and registry, for the isolated dictionary tests.
 func newGameServiceOn(dir, version string, reg *engine.Registry) *game.Service {
-	return game.NewService(
+	svc := game.NewService(
 		game.NewStore(testDB), account.NewStore(testDB), reg,
 		game.Config{DictDir: dir, DictVersion: version, TimeoutSweepInterval: time.Minute, CacheTTL: time.Hour},
 		zap.NewNop(),
 	)
+	svc.SetFirstMoveEntropy(seatZeroFirstMove)
+	return svc
 }
 
 // seedDawgs copies the committed DAWG of every variant from src into dst (flat).

backend/internal/inttest/first_move_draw_test.go

@@ -0,0 +1,154 @@
+//go:build integration
+
+package inttest
+
+import (
+	"context"
+	"testing"
+	"time"
+
+	"github.com/google/uuid"
+
+	"scrabble/backend/internal/engine"
+	"scrabble/backend/internal/game"
+)
+
+// The first-move-draw suite covers the official seeding (docs/ARCHITECTURE.md §6): the draw is
+// recorded with the game, decides seat 0 (the first mover), and — in auto-match — runs against
+// a synthetic opponent at open time whose draw rows are back-filled when a real opponent joins.
+
+// TestCreateRecordsFirstMoveDraws checks a directly-seated game records the draw against the
+// real seated accounts and seats the drawn leader (the suite's deterministic draw elects the
+// first-listed account) at seat 0.
+func TestCreateRecordsFirstMoveDraws(t *testing.T) {
+	ctx := context.Background()
+	svc := newGameService()
+	a := provisionAccount(t)
+	b := provisionAccount(t)
+	g, err := svc.Create(ctx, game.CreateParams{Variant: engine.VariantEnglish, Seats: []uuid.UUID{a, b}, TurnTimeout: 24 * time.Hour, Seed: 1})
+	if err != nil {
+		t.Fatalf("create: %v", err)
+	}
+	if g.Seats[0].AccountID != a || g.Seats[1].AccountID != b {
+		t.Fatalf("seats = [%s %s], want [a b]", g.Seats[0].AccountID, g.Seats[1].AccountID)
+	}
+	draws, err := svc.SetupDraws(ctx, g.ID)
+	if err != nil {
+		t.Fatalf("setup draws: %v", err)
+	}
+	// seatZeroFirstMove resolves in one round: the first contender (a) draws a blank and wins.
+	if len(draws) != 2 {
+		t.Fatalf("draws = %d, want 2 (one round, two players)", len(draws))
+	}
+	if draws[0].Account != a || !draws[0].Blank {
+		t.Fatalf("draw[0] = %+v, want a having drawn a blank", draws[0])
+	}
+	if draws[1].Account != b {
+		t.Fatalf("draw[1] account = %s, want b", draws[1].Account)
+	}
+}
+
+// TestAutoMatchDrawBackfilledOnJoin checks an open auto-match game records the draw at open
+// time against the synthetic opponent (a NULL account) and back-fills those rows to the real
+// opponent when they join.
+func TestAutoMatchDrawBackfilledOnJoin(t *testing.T) {
+	ctx := context.Background()
+	clearOpenGames(t)
+	svc := newGameService()
+	starter := provisionAccount(t)
+	g := openGame(t, svc, starter, evenOpeningSeed(t))
+
+	draws, err := svc.SetupDraws(ctx, g.ID)
+	if err != nil {
+		t.Fatalf("setup draws: %v", err)
+	}
+	if len(draws) != 2 {
+		t.Fatalf("open draws = %d, want 2", len(draws))
+	}
+	var nullSeen, starterSeen bool
+	for _, d := range draws {
+		switch d.Account {
+		case uuid.Nil:
+			nullSeen = true
+		case starter:
+			starterSeen = true
+		}
+	}
+	if !nullSeen || !starterSeen {
+		t.Fatalf("open draws = %+v, want the starter and a NULL synthetic opponent", draws)
+	}
+
+	joiner := provisionAccount(t)
+	if _, joined, err := svc.OpenOrJoin(ctx, joiner, openParams(0), time.Now().Add(time.Minute), nil); err != nil || !joined {
+		t.Fatalf("join = (joined %v, err %v), want joined", joined, err)
+	}
+	after, err := svc.SetupDraws(ctx, g.ID)
+	if err != nil {
+		t.Fatalf("setup draws after join: %v", err)
+	}
+	for _, d := range after {
+		if d.Account == uuid.Nil {
+			t.Fatalf("draw still NULL after join: %+v", d)
+		}
+		if d.Account != starter && d.Account != joiner {
+			t.Fatalf("draw account %s is neither player", d.Account)
+		}
+	}
+}
+
+// TestReplayTimeline checks the admin replay timeline reconstructs the dealt racks and one
+// played move: the step count, the drawn tiles, the bag remainder, the running score and the
+// turn cursor.
+func TestReplayTimeline(t *testing.T) {
+	ctx := context.Background()
+	svc := newGameService()
+	a := provisionAccount(t)
+	b := provisionAccount(t)
+	seed := evenOpeningSeed(t)
+	g, err := svc.Create(ctx, game.CreateParams{Variant: engine.VariantEnglish, Seats: []uuid.UUID{a, b}, TurnTimeout: 24 * time.Hour, Seed: seed})
+	if err != nil {
+		t.Fatalf("create: %v", err)
+	}
+	hint, ok := newMirror(t, seed, 2).HintView()
+	if !ok || len(hint.Tiles) == 0 {
+		t.Fatal("no opening move for the seed")
+	}
+	if _, err := svc.SubmitPlay(ctx, g.ID, a, hint.Tiles); err != nil {
+		t.Fatalf("play: %v", err)
+	}
+
+	tl, err := svc.ReplayTimeline(ctx, g.ID)
+	if err != nil {
+		t.Fatalf("replay timeline: %v", err)
+	}
+	if len(tl.Steps) != 2 {
+		t.Fatalf("steps = %d, want 2 (deal + one move)", len(tl.Steps))
+	}
+	deal := tl.Steps[0]
+	if deal.Move != nil {
+		t.Fatalf("step 0 must be the deal, got move %+v", deal.Move)
+	}
+	rackSize := len(deal.Racks[0])
+	if rackSize == 0 || len(deal.Racks) != 2 || len(deal.Racks[1]) != rackSize {
+		t.Fatalf("deal racks = %v, want two equal full racks", deal.Racks)
+	}
+	move := tl.Steps[1]
+	if move.Move == nil || move.Move.Action != "play" {
+		t.Fatalf("step 1 move = %+v, want a play", move.Move)
+	}
+	if len(move.Drawn) != len(hint.Tiles) {
+		t.Fatalf("drawn = %v, want %d refilled tiles", move.Drawn, len(hint.Tiles))
+	}
+	if move.BagLen != deal.BagLen-len(hint.Tiles) {
+		t.Fatalf("bag after play = %d, want %d", move.BagLen, deal.BagLen-len(hint.Tiles))
+	}
+	if len(move.Racks[0]) != rackSize {
+		t.Fatalf("mover rack after refill = %d, want %d", len(move.Racks[0]), rackSize)
+	}
+	if move.Scores[0] <= 0 {
+		t.Fatalf("seat 0 score after play = %d, want > 0", move.Scores[0])
+	}
+	if move.ToMove != 1 {
+		t.Fatalf("to_move after seat 0 play = %d, want 1", move.ToMove)
+	}
+}

backend/internal/inttest/helpers.go

@@ -26,9 +26,10 @@ import (
 // assembly, and the stats reader. Helpers used by a single test file stay in
 // that file; everything reused across files lives here.
 
-// newGameService builds a game service over the shared pool and registry.
+// newGameService builds a game service over the shared pool and registry, with a
+// deterministic first-move draw so the suite keeps a stable turn order.
 func newGameService() *game.Service {
-	return game.NewService(
+	svc := game.NewService(
 		game.NewStore(testDB),
 		account.NewStore(testDB),
 		testRegistry,
@@ -40,6 +41,39 @@ func newGameService() *game.Service {
 		},
 		zap.NewNop(),
 	)
+	svc.SetFirstMoveEntropy(seatZeroFirstMove)
+	return svc
+}
+
+// seatZeroFirstMove is a first-move-draw entropy factory that always elects the first
+// listed account as the leader, keeping the integration suite's turn order stable
+// despite the real draw's randomness: the first contender draws a blank — the best
+// possible tile — and wins outright, the rest draw the first remaining tile. It is a
+// factory so each game restarts the one-shot "blank" pick.
+func seatZeroFirstMove() func(n int) (int, error) {
+	first := true
+	return func(n int) (int, error) {
+		if first {
+			first = false
+			return n - 1, nil // a blank sits last in the bag → best rank
+		}
+		return 0, nil
+	}
+}
+
+// seatOneFirstMove is a first-move-draw entropy factory that elects the second contender (in
+// auto-match, the synthetic opponent) as the leader, so the caller is seated at seat 1: the
+// first contender draws the first remaining tile and the second draws a blank, winning.
+func seatOneFirstMove() func(n int) (int, error) {
+	pick := 0
+	return func(n int) (int, error) {
+		i := 0
+		if pick == 1 {
+			i = n - 1 // the second contender draws a blank → best rank
+		}
+		pick++
+		return i, nil
+	}
 }
 
 // newSocialService builds a social service over the shared pool, reading game

backend/internal/inttest/open_match_test.go

@@ -18,8 +18,9 @@ import (
 // The open-game suite covers an auto-match game that a player enters immediately and
 // waits inside (status 'open', the opponent seat empty) until a human or a robot joins.
 
-// evenOpeningSeed returns an even seed (so OpenOrJoin seats the starter at seat 0, which
-// moves first) whose fresh two-player English opening rack has a legal move.
+// evenOpeningSeed returns a seed whose fresh two-player English opening rack (seat 0) has a
+// legal move, for tests that drive or attempt an opening play. It scans even seeds; seat
+// order no longer depends on the seed — the first-move draw decides it (docs/ARCHITECTURE.md §6).
 func evenOpeningSeed(t *testing.T) int64 {
 	t.Helper()
 	for seed := int64(2); seed <= 400; seed += 2 {
@@ -59,9 +60,9 @@ func openGame(t *testing.T, svc *game.Service, starter uuid.UUID, seed int64) ga
 	return g
 }
 
-// TestOpenGameStarterMovesThenWaits checks the starter (seat 0) may move on their turn
-// while the game is open, after which it is the empty opponent seat's turn and the
-// starter just waits.
+// TestOpenGameStarterMovesThenWaits checks the starter may move on their turn while the game
+// is open (the first-move draw, run when the game opened, put them at seat 0), after which it
+// is the empty opponent seat's turn and the starter just waits.
 func TestOpenGameStarterMovesThenWaits(t *testing.T) {
 	ctx := context.Background()
 	clearOpenGames(t)
@@ -89,28 +90,30 @@ func TestOpenGameStarterMovesThenWaits(t *testing.T) {
 	}
 }
 
-// TestOpenGameStarterWaitsWhenOpponentMovesFirst checks that when the starter is seated
-// at seat 1 (odd seed), the still-empty seat 0 is to move, so the starter cannot act.
+// TestOpenGameStarterWaitsWhenOpponentMovesFirst checks that when the first-move draw seats
+// the starter at seat 1 (the synthetic opponent won the open draw), the still-empty seat 0 is
+// to move, so the starter cannot act until an opponent fills it.
 func TestOpenGameStarterWaitsWhenOpponentMovesFirst(t *testing.T) {
 	ctx := context.Background()
 	clearOpenGames(t)
 	svc := newGameService()
+	svc.SetFirstMoveEntropy(seatOneFirstMove) // the synthetic opponent wins → the caller sits at seat 1
 	starter := provisionAccount(t)
 	g, _, err := svc.OpenOrJoin(ctx, starter, openParams(1), time.Now().Add(time.Minute), nil)
 	if err != nil {
 		t.Fatalf("open: %v", err)
 	}
 	if g.ToMove != 0 || g.Seats[0].AccountID != uuid.Nil {
-		t.Fatalf("odd-seed open game: to_move %d seat0 %s, want the empty seat 0 to move", g.ToMove, g.Seats[0].AccountID)
+		t.Fatalf("opponent-won open draw: to_move %d seat0 %s, want the empty seat 0 to move", g.ToMove, g.Seats[0].AccountID)
 	}
 	if _, err := svc.Pass(ctx, g.ID, starter); !errors.Is(err, game.ErrNotYourTurn) {
 		t.Fatalf("starter acting on the empty seat's turn = %v, want ErrNotYourTurn", err)
 	}
 }
 
-// TestOpenGameJoinAfterStarterMoved checks a second human joins an open game even after
-// the starter has already made their first move, landing on the board mid-opening and
-// able to act on their turn.
+// TestOpenGameJoinAfterStarterMoved checks a second human joins an open game even after the
+// starter has already made their first move: the seats were fixed by the draw at open, so the
+// joiner takes the empty seat without disturbing the journal, and can act on their turn.
 func TestOpenGameJoinAfterStarterMoved(t *testing.T) {
 	ctx := context.Background()
 	clearOpenGames(t)