Bluff, Bet, or Chase?
This subject seems to be winding down...but I will throw in my 2-cents worth.
First, I agree that this is one of those "rules" that seems to make no sense unless you understand the concept behind it. Checking down has only ONE purpose, to knock out the allin player. But, you also have to remember that you have another objective in the hand...win chips, if you can. So, here is what I do.
If I don't have a made hand AND one that I believe will win, I check it down. If I have a hand I believe will win (which can now meet BOTH my objectives), I will bet. Why check it down? If the allin beats me, he probably was gonna beat the other player also. I don't require the nuts to bet into this pot. But I do require a strong hand...at least TP/strong kicker.
I WOULD NEVER BLUFF OR BET A DRAW in this situation! That is just plain STUPID.
Okay, now what if my bet ran off the hand what would have won on the river and the allin ends up beating me? Well, first, I am not out any more chips for making my bet. Second, think about the odds of this happening. The opponent who folded had to fold the best hand or get lucky and draw the winner AND the allin has to beat my hand. I will take these odds when I have a good hand to bet on. Again, what am I out...no chips, just an opponent who got a second life in the tourney. But hey, he was in the game before this hand. Bummer, but not a big deal. IMO