As the dealer shuffles the cards and flings two to each player around the table, we each in turn look down at our hand and assess our chances to win the hand. The first several players fold, but the lady sitting directly to my right makes a large raise. I look down at my hand and like my chances, so I call. After the first three cards are dealt, she bets again. I look at the table, reach down to grab chips, and raise. She thinks for a second and discards her hand.
“How did you know I was bluffing?” she asks.
I respond, “From watching your past play, I knew that when you raised before the flop, you had two face cards or a pocket pair. On the flop, there was just one face card, an Ace. I calculated that of the 18 possible hands you might hold, you had only made a pair with 4 of them, so my raise makes you fold 77% of the time. From there I calculated that with what I stood to risk and what I stood to win, I would earn, in the long run, $4 by raising. To bet there, you would have to expect me to fold at least 35% of the time, but since I would have raised your bet no matter what my two cards were, you made a mistake by betting.”
“I wouldn’t even know where to start,” she responds.