use game start dto that i already defined

server.go

@@ -94,10 +94,9 @@ func (s *Server) joinAndServe(p person) {
 		go gameActor(ctx, g, p, other, nil)
 	}
 	// Reply with the game ID so they can share.
-	r := struct {
-		Game lobby.GameID `json:"game"`
-	}{
-		Game: id,
+	r := serve.GameStart{
+		ID:     id,
+		Dealer: deal,
 	}
 	if err := wsjson.Write(context.TODO(), p.conn, r); err != nil {
 		slog.WarnContext(ctx, "got a game but player dropped", "game", id, "player", p.id)