In an imperfect information game this is no longer true. Now you need to consider counterfactuals --- how would the opponent have played if I had done something different earlier?
They illustrated with a toy game they called "Coin Toss". The idea is that Player A flips a coin, but Player B doesn't get to see the result. Player A then gets to choose whether to end the game there or continue playing. If they end the game, they get $1 from Player B if the coin is heads and lose $1 from Player B if the coin is tails. If they decide to continue playing, then Player B gets to guess whether the coin is heads or tails. If Player B guesses correctly, they get $2 from Player A, and otherwise lose $2.
If you spend some time thinking about the strategy, you can figure out that the best strategy for Player B is to guess heads 25% of the time and tails 75% of the time. But if you change the rules to the game for Player A, so that they get $1 if it's tails and lose $1 if it's heads, then the best strategy for Player B reverses as well --- now Player B should guess heads 75% of the time and tails 25% of the time. Yet nothing about Player B's situation has changed --- the only change happened prior to Player B's involvement. Yet this nevertheless changes Player B's strategy because Player B must consider how Player A would have acted given that the coin landed heads vs. tails.
So to solve these imperfect information games, you have to be very careful to model these sorts of counterfactuals. If you mess up you will leave yourself with an exploitable strategy --- that is, someone can devise a strategy that causes you to lose the game.
Link to the paper here: