> But you're telling me that the concept of subgame applies in both directions (not only imperfect information by my opponent's perspective, but also imperfect

> But you're telling me that the concept of subgame applies in both directions (not only imperfect information by my opponent's perspective, but also imperfect information in my perspective). So when I say "my opponent's presumed range is X", that sentence doesn't describe 1 subgame, that sentence actually describes multiple subgames. Yes; consider a chess move, every move is a subgame - a subtree of that game. He just can't safely say tree, because there are games that are better described as a graph than a tree. Actually, Two Envelope is such a game. The action switch, in Two Envelope, leads to the subgame in which you are at I[null] and need to decide whether to keep or switch - the same situation as you started in. Switch again and you arrive at the subgame I[null]. It contains itself. > If the opponent's strategy is fixed, then our optimal strategy is to play 100% exploitative. If the opponent's strategy is not fixed, then the optimal strategy will be a mix with elements from both exploitative and GTO strategies. (Again, note that this only makes sense if the opponent is not playing perfect GTO. If the opponent is playing perfect GTO, then obviously the optimal strategy is to also play GTO.) I agree.