learning to lay it down

I think making smart laydowns on the river is an over-rated concept, especially in a heads-up pot. Usually, if there has been any action, the money in the pot merits calling with almost any hand that has a legit shot to win.
But, making smart laydowns on the turn - that's a different story. First, the pot is smaller. Second, in order to show down your hand, you'll have to also call a river bet.

Here are two spots where this concept came up recently; I think I played one well, and the other poorly.

10/20 limit game, I held AKo in the small blind. An early position player opened with a raise, and a few players called; hoping to disguise my hand and possibly have a greater edge on a later street, I just called. The only player I figured to knock out of the hand with a raise was the big blind (in this game, in for a penny, in for a pound, so I knew my show of strength wouldn't get anyone to fold). With a slightly stronger hand (AA, KK, QQ, or AKs), I would be more inclined to raise. Another thought was that if I re-raised with AK, and hit the flop, a lot of hands would be getting the right odds to draw against me, whereas if I called, the pot would be smaller, perhaps making it easier to protect a potentially fragile holding (top pair, top kicker, etc).

The flop came A, rag, rag, with two spades. I checked, the big blind bet, and everyone called. I considered check-raising, but opted to wait until the turn. I was confident that the big blind had an ace, and would bet the turn, making it possible to check-raise on the more expensive street; I knew that a player must be on a flush draw, so I wanted to wait in order to reduce the odds that player would be getting; and I didn't have a spade.

A spade hit the board. I checked, the big blind checked, and a middle position player fired. Since I didn't have a spade (which would have set up re-draws on the river), I folded my top pair, top kicker hand. The big blind called, then check-called the river, and nodded, "Nice hand" when the player showed a queen-high flush. The big blind had an ace, with a worse kicker.

I was happy with my laydown.

A few hands later, holding 8,7o on the button, I limped behind 4 players. The big blind raised, and we all called.

The flop came 7, 6, 3. It was checked to me, I bet, and three players called. The turn brought a 3, and it was again checked to me. Thinking the 3 helped my hand, I bet, only to be check-raised! I called, then called the river, and my opponent showed 3,2s.

While I was a bit incredulous (he limped with 3,2s in middle position! he called the flop with bottom pair, no kicker!), paying him off was a mistake. I didn't want to believe that he was that bad a player that he could have a three, so I paid him off when he check-raised the turn (and I know that a check-raise on the turn means 'big hand').

I think I am giving away a lot of my profit by paying off hands when I feel I am beat. I think players pay off to feed their ego -- the attitude being, "I'm not going to get bluffed." That's an attitude that just costs money.