Player minimum of 3 to start a game or scene

Enforced server-side in lobby/start and confirm_scene_setup via
crud_base.has_min_players; Dev Mode bypasses it so local single-player
testing still works. Lobby and scene-setup UIs show a player-count
message instead of the start button when below the minimum.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

tests/test_game.py

@@ -1433,3 +1433,76 @@ def test_grant_and_revoke_admin():
         assert "admin_key" not in response.json()["game"]
     finally:
         app.dependency_overrides.clear()
+
+def test_player_minimum(session):
+    game = crud.create_game(session)
+    game.dev_mode = False
+    session.add(game)
+    session.commit()
+    crud.add_player(session, game.id, "P1", is_creator=True)
+    crud.add_player(session, game.id, "P2")
+    session.refresh(game)
+
+    # Two players can't start a scene
+    assert not crud.has_min_players(game)
+    ok, msg = crud.confirm_scene_setup(session, game.id)
+    assert not ok
+    assert "at least 3" in msg
+
+    # Dev Mode bypasses the minimum for testing
+    game.dev_mode = True
+    session.add(game)
+    session.commit()
+    assert crud.has_min_players(game)
+
+    # Three players is enough regardless
+    game.dev_mode = False
+    session.add(game)
+    session.commit()
+    crud.add_player(session, game.id, "P3")
+    session.refresh(game)
+    assert crud.has_min_players(game)
+
+def test_lobby_start_requires_min_players():
+    from fastapi.testclient import TestClient
+    from sqlalchemy.pool import StaticPool
+    from sqlmodel import SQLModel, create_engine, Session
+    from pirats.main import app
+    from pirats import crud
+
+    engine = create_engine(
+        "sqlite://",
+        connect_args={"check_same_thread": False},
+        poolclass=StaticPool,
+    )
+    SQLModel.metadata.create_all(engine)
+    session = Session(engine)
+
+    game = crud.create_game(session)
+    game.dev_mode = False
+    session.add(game)
+    session.commit()
+    crud.add_player(session, game.id, "P1", is_creator=True)
+    crud.add_player(session, game.id, "P2")
+
+    def get_session_override():
+        yield session
+
+    from pirats.database import get_session
+    app.dependency_overrides[get_session] = get_session_override
+    client = TestClient(app)
+
+    try:
+        response = client.post(f"/api/game/{game.id}/lobby/start")
+        assert response.status_code == 400
+        assert "at least 3" in response.json()["error"]
+        session.refresh(game)
+        assert game.phase == "lobby"
+
+        crud.add_player(session, game.id, "P3")
+        response = client.post(f"/api/game/{game.id}/lobby/start")
+        assert response.status_code == 200
+        session.refresh(game)
+        assert game.phase == "character_creation"
+    finally:
+        app.dependency_overrides.clear()