Laravel - Session not transmitted

Why is the new session not being transmitted ?

class RandomController extends Controller
{
    public function one(Request $request) {
        $request->session()->put('game_token', csrf_token());
        // dd($request->session()->all() : 'game_token' is in.
        return redirect('/two');
    }

    public function two(Request $request) {
        dd($request->session()->all());
        return;
    }
}

(The dd don't show the new session)

I'm under Laravel 5.4, and the web middleware is apply on this controller.

via Thomas Petillot