I haven't played by forum, I only play IRL. About remembering opponents teched cards etc, it helps make the game enjoyable. You can watch your opponent, see when he cycles, and although you don't get a perfect count of his discard pile in the back of your head you know 'I killed his taxman last turn, he could have it again in this hand or the next' or 'he played undo two turns ago, there's a good chance it's back in his hand' etc.
you can also read the opponent. And I admit, I'm very easy to read. The way I move my coins to count how much each action would take (2 for arg, 4 to maxband etc) prior to playing out my turn you can watch and then guess where I'm going with it. Or playing against @GRAG he had geiger out, and is flipping back and forth through his codex, you just know he's considering temporal distortion. He ended up playing it, so the secret was spoiled but if he decided against it, I would still know he had it teched in.
The problem with running formulas or working out exact probabilities is time. You've only got 25 minutes in a tournament game!