Originally Posted by PokerToad
Out of position in LHE I most likely check-call on the river - there is no way in hell I fold the 2nd nuts on the river for one bet.
Not seeing a showdown is definitely awful. However, checking and calling is almost certainly not the way to go. Betting and calling a raise is better. Much, much better.
Out of position (in LHE), you only need to have the best hand more than 50% in order for bet/calling to be the best move if he will call with any worse hand. And we can be very certain that he isn't folding anything at this point.
position this changes. If your opponent checks, he now has to have the ace of hearts only 34% of the time for you to be wrong to bet (since he will checkraise).
The problem with being out of position is that when you check he won't bet his whole range, just the really strong hands. His weakest hands, he's going to check behind and then you've lost a bet those times. In other words, you allow him to play the river perfectly. This is not good.
If you bet, he can only play perfectly if he has the ace of spades, which is going to be a minority of the times. Therefore, you're forcing him to make the mistake of calling (or better, raising without the ace of hearts) the majority of the time.
Specifically, it's the fact that it's 50% that's required to bet out, but it's actually 34% required to bet in position.
(However, and this is of course also an important perspective, if he has the ace of hearts he's somewhat unlikely to check the river when you're in position. So if he checks to you, his likelyhood of having the Ah goes down some and you are still probably correct to bet when checked to)