 The proponent wins this play. But one may wonder if there is not something that the opponent could do in order to win. In fact, this question arises quite naturally if one is curious about the relationship between winning a play and proving the validity of a thesis in a dialogical setting. In the play above, the proponent happens to win a play for a formula that is clearly not valid. Now, it is quite easy to see that, in fact, the opponent had a way to win by making another choice at move 3: