But the opponent can win by foreseeing what which value of i we're going to choose and which choice of representatives we'll make. I suppose we would ban foresight of i? – Alexander Pruss Dec 19, 2013 at 21:25

yes the order would be: 1)describe the probabilistic strategy 2)opponent choses a sequence 3)probabilistic variable i is instanciated – Denis Dec 19, 2013 at 23:02