I don't understand the final river bet, though. I understand the theory behind it, it's just that the players I'm used to don't play the way the theory says they will.

If they're behind, they won't know or care, and having bet the flop and turn, they'll bet the river too if I were to check it. If I bet, they'll call, unless they have no pair and were completely bluffing or on a draw that didn't come through. Or they might raise, if the hand they're behind with seems good enough to them.

If they're ahead, they will probably raise my river bet. Or maybe they'll just call.

Since I'm gonna have to put in a bet to see the showdown one way or another, I might as well just check it, and call the bet which they are 90% likely to make after I check.