Since by definition σ * 2 always chooses an entropy maximizing segment, for player 1 to choose a non-entropy maximizing segment (more or less than half the length) amounts to yielding the round to player 2, which is equivalent in terms of the resulting accepted frame to a situation where player 1 chooses an entropy maximizing segment -the same one chosen by player 2.
we need to consider only deviations with entropy maximizing frames.