Assumption: We have a machine that plays games perfectly.
The machine plays a game of Chess. Chess is a game of perfect information and complete information. We (assuming we have enough computational power for that) build the complete game tree for a game of chess and show that every move the machine made was minimizing the possible loss for the worst case scenario (comparison to minimax) and as a result, prove that it was playing perfectly.
The machine plays a game of Backgammon. Backgammon is a game of imperfect information, but still complete information since both players have the same amount of information available to them. We do the same thing as with chess, including the dice rolls and probabilities for every possible outcome and show that every move that the machine made was, once again, minimizing the possible loss for the worst case scenario (comparison to expectiminimax) and as a result, prove that it was playing perfectly.
Now the machine plays a game of Poker. Poker is a game of imperfect information and also incomplete information. Once we're reviewing the game, can we mathematically prove that the moves the machine made were perfect? Or is the fact that bluffing as a concept exists already means that it's sometimes impossible to compare two moves with each other and decide if there was anything better that could've been done?
If not, does that also mean that the assumption is wrong and it's impossible to play perfectly with incomplete information?