finding the outs

I didn't play this hand, but found it interesting.

In a 3/6 game at the Mirage, the player in the big blind held A,8, suited in hearts. Six players limped, and she raised (a questionable play, but not the crux of the story). Everyone called, and they took the flop seven handed.

The flop came 8,8,2, rainbow, and she bet. One player called, the button raised, and everyone else folded. She re-raised, the limper cold-called, and the button raised again (cap). Everyone called.

The turn was a queen, putting four suits on board, and the big blind bet out. The middle player called, and the button raised. The big blind, feeling good about three-of-a-kind with top kicker, re-raised (VERY questionable raise), the middle player again cold-called, and the button again capped the action.

The river was an ace, and she bet, the middle player again called, the button again raised, she re-raised, the middle player called, the button capped, and everyone called.

The button -- of course -- held 2,2, and had flopped a full-house.

The middle player, one can assume from the action, held the case 8.

The loser of the pot, in telling me how bad the winner played, almost screamed, 'She only had 3 outs! 3 outs!'

Well, no. And, while her reckless raising ended up costing him a lot of money, it would be impossible to expect that any player in a limit game is going to fold three-of-a-kind with top kicker.

On the flop, she had 4 outs (the case 8 and any ace). On the turn, she picked up three more outs (any queen that pairs the board gives her eights full of queens, which beats twos full of eights), for a total of 7 outs. Even if she was positive that the button held pocket twos, she would have been right to call him down. If the button would be aggressive with an eight or an over-pair, she has to call.

14 small bets went in pre-flop. Another 15 small bets went in on the flop. That's 14.5 big bets.
On the turn, with 7 outs, the odds against improving are better than 6 to 1, making it an easy call. Actually, raising is OK, especially if there's any chance trips with top kicker is good. The big blind bet, the limper called, the button raised. Now, there's 18.5 big bets, and she's 6 to 1 against making her hand. She's getting 18.5 to 1 on a call, or better than 9 to 1 on a raise, a clear overlay. If she checks, the pot would be laying 15.5 to 1 on a call, or almost 8 to 1 on a raise, still a clear overlay.

Finding 'hidden' outs is a key concept. Given the excessive flop action, it's reasonable to assume that no one had a queen, so when the queen hit the turn, it created an additional three outs, making it clearly correct to continue with the hand.