The Art of Strategy
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You Gotta Know When to Hold ’Em

In February 2002, a young assistant professor at INSEAD was trying his hand at poker. Randy Heeb had entered the World Heads Up Championship, held at the Aviation Club de France, a luxurious club well situated on the Champs Elysees in Paris. Heeb was a recent economics Ph.D. from the University of Chicago who had done well in several European tournaments, but was still relatively unknown.

Thomas Preston, Jr., aka Amarillo Slim, was the defending champion. Slim was also the 1972 World Champion and one of the more colorful players on the circuit. A repeat victory would bring him a 40,000 Euro prize.

Under the rules of Texas Hold’em, each player is dealt two cards face down. There is a round of betting and then three more cards are exposed (the flop). After the flop, there is a second round of betting, followed by another card (the turn), a third round of betting, and finally the fifth card is dealt (the river) with its final round of betting. The player with the best five-card hand using any of his two and the five community cards wins.

Slim and Heeb faced off in round one of the match play event. Slim was leading the pack with 4,200 chips and Heeb was next with 3,800. Heeb was dealt a pair of 9s. That's a good hand, but not a great one. Played to the end, it has just over a 50% chance of winning. Based on his pair, Heeb bet 175, Slim raised him to 500 and Heeb called. Given the nature of the pre-flop bidding, Heeb was convinced that Slim had either an Ace or a King, but not both. (Expert poker players really can get to this level of precision.)

Heeb had decided that he would fold if either an Ace or King showed up on the flop. The reason is that a pair of 9s loses to either a pair of Kings or Aces, and the chance of getting three of a kind (or a full house) on the next two draws was under 10%. If Slim had either a King or an Ace as one of his hidden cards, the chance that he would be holding a pair was too high for Heeb to stay in the hand.

At the flop, the three cards turned over were 2 of spades, 3 of diamonds, and then a K of hearts. Damn. When Heeb saw the King, he knew he was out. But Slim was looking at Heeb, not the cards. Their eyes met and Heeb realized that he had shown a look of resignation. He saw Slim recognize that look and then instantly push a large pile of chips on the table. Slim had bet 1,700.

It was decision time. Based solely on probability, the King on the table meant that there was 3/7th chance that Slim had a pair of Kings and 4/7th chance that he held a hidden Ace. Those weren't good enough odds to call. What made the odds even worse for Heeb was the eagerness of Slim's bet—he would undoubtedly have bet if he had the pair of Kings.

But Slim had made his bet based on Heeb's eyes, not just the cards. If Slim had a pair of Kings, he wouldn't have needed to interpret Heeb's look, the cards would have justified the bet all on their own. Heeb realized that Slim had given away his own strategy. Heeb went all in, 3,300. Slim called. The final two cards came up as an 8 of clubs and 4 of hearts. Heeb's pair of 9s beat Slim's single Ace.*

In strategy, your best move depends not just on your own strengths and weaknesses, but also on what you think the other players will do. And their best moves generally depend on what they think you will do. Thus you want to get inside their heads to understand what they are thinking you'll do. With that understanding, you may also want to influence what they think you'll do.

 

* While Randy didn't end up winning the Heads Up tournament, later that year he went on to win a World Series of Poker No Limit Hold’em championship (and $367,240).

 

 

Copyright © 2008 by Avinash Dixit and Barry Nalebuff