class AppThreePlusThree extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    var game = new Game();
    var counter = 265;
    return new GameRedux(
      counter: counter,
      child: new MaterialApp(
        title: '3 + 3',
        theme: new ThemeData(
          primarySwatch: Colors.blue,
        ),
        home: new Scaffold(
     ...
     ...
     new Text('$counter'),
     ...

class AppThreePlusThree extends StatefulWidget {
  _AppThreePlusThreeState createState() => _AppThreePlusThreeState ();
}

class _AppThreePlusThreeState extends State<AppThreePlusThree> {
  var counter = 265;
  @override
  Widget build(BuildContext context) {
    var game = new Game();
    setState(() => counter = 265);//I seriously doesnt have any idea how you are going to change or update your counter variable. something like this should work
    return new GameRedux(
      counter: counter,
      child: new MaterialApp(
        title: '3 + 3',
        theme: new ThemeData(
          primarySwatch: Colors.blue,
        ),
        home: new Scaffold(
     ...
     ...
     new Text('$counter'),
     ...