> Player 1 should only bluff at the optimal rate if player 2 punishes them for deviating from this rate by changing the frequency that they call when holding th

> Player 1 should only bluff at the optimal rate if player 2 punishes them for deviating from this rate by changing the frequency that they call when holding the king. Otherwise, Player 1 gains more on average by bluffing with the queen more frequently. So, how should Player 2 figure out if Player 1 is actually bluffing at the optimal rate (and not higher)? You're describing exploitative strategies - that's the kind of circular thinking of "if he knows that I know what he knows...". In a Nash equilibrium neither side has an incentive to change their strategy even if they know what their opponent is doing. If you're betting at the optimal frequency, there is nothing that your opponent can do to counterexploit your strategy. If you're deviating from the optimal frequency, your opponent can adjust, you can adjust in return and so on.