Linda Mae thrust herself in my direction muttering unpleasantries. Something upset her that winter's eve at her $4-8 Hold'Em table, and she wanted to get it off her rather bountiful chest. I took a deep breath, preparing myself for the calamitous tale to follow. She opened by saying, "How could he call when he knew he was beaten? I showed him my hand and he still called and then he rivered me! What an imbecile!" She told me that on the button she raised with [Ad]- [Kc] before the Flop. The Small Blind folded; the Big Blind called; three limpers called.
Five-handed they saw the dealer flop [Ah]-[3c]-[Kh]. They all checked to her; she bet $4. The Big Blind and two limpers folded; the other limper called. At that point, the pot held $46 after the house rake and badbeat drop.
The dealer turned the 3d, pairing the board. The limper checked. With [Ah]-[3c]-[Kh]-[3d] on the tableau, Linda Mae bet $8.
The limper asked for time. Ten seconds turned into twenty; twenty turned into thirty; and still the limper pondered. Impatient, Linda Mae said, "Here, I'll show you my hand," and did so, whereupon he quickly called. The River card, the 7a, made this board, [Ah]-[3c]- [Kh-][3d]-[7h.] The limper bet $8. After a bit, Linda Mae called. The limper showed down [Qh]-[Th]for the nut Flush and she went berserk.
"What did I think of that?" she asked. I asked her to point out the limper to me, because I wanted to put him on my danger list. I told her that he made a good play running her down. "What?" she exclaimed, "And you write articles for a poker magazine?"
"Not just any poker publication," I answered, "Poker Player newspaper, and anyway he made a good play. Here's why.
"He pondered whether you raised with pocket Aces or Kings, or just Ace-King. The average low-limit Hold'Em player automatically assumes that every raiser has A-K: an advanced player knows that those big pockets are almost equally likely. Actually, it's 57-43, so he studied you to see if he could tell whether you had the top Two Pairs, or a Full House."
If you already had a Full House, then he had only one out, the Ja. If you had only Two Pairs, then he had eleven outs: seven for a Flush; three for a Straight; and one for a Royal. When she asked why not eight outs for the Flush, I told her he wouldn't count the 3a, the only card that would make his hand and also improve hers. After you showed him your hand, he knew that he you didn't have a Full House.
Out of the hidden 44 cards, 11 cards would help him without helping you, exactly a 25% chance. The pot held 70 white chips and it cost him $8 to win $78, nearly 10 for 1 pot odds. The pot odds were much larger than the cards odds, so he had an easy call.
"I shouldn't've shown him my hand," she said, "because that removed all doubts he might have had." "Good thinking," I said.
Linda Mae, no longer so upset, was deep in thought. Then she asked, "I always put a raiser on A-K. Are you sure about those 57-43 chances?" I explained that there are 28 ways to deal two hole cards from the eight Aces and Kings: 16 ways for A-K; 12 ways for A-A or K-K. 16/28 equals .571; 12/28 equals 0.429.
Yes, I was sure.
