[cbloom]

I think the phrasing of the fundamental theorem is really strange. If they're a bad player there could be cases where if they knew your cards they'd actually play *worse* because they make bad decisions (eg. if you have a good hand, they might fold even though they have pot odds to call, etc.). I think it's better to think just in terms of your own play, and thinking of their exact cards is silly too.

Any time you make a play which is not optimal against their correct Bayesian card range (the best knowable card range given their action), you lose (compared to optimal).

If you play such that your cards are obvious, it allows them to play optimally against you (if they're capable of that).