The paradox of making money from opponents mistakes

[Xhad]

You're missing the point. You are trying to minimize mathematical mistakes by playing correctly. However, since you can't see anyone's cards, you can't eliminate them altogether.

You're right that you can't know that betting the AJ is a mathematical mistake this time. But the reason you bet it is that it is less likely to be a mathematical mistake than checking based on the limited information that you have.

Again, strategically correct plays are the plays that reduce the likelihood and impact of your mathematical mistakes while increasing the likelihood and impact of your opponents'.