Use Game Theory as a Tool to Make Decisions

There's nothing worse for a poker player than going broke during the World Series of Poker. When my friend Doc tapped out during last year's tournament, he figured he could salvage the trip by taking in some of the beautiful scenery around Las Vegas. Perhaps because he felt sorry for him, Jake, a tough-as-nails poker player who had contributed to Doc going broke, agreed to go for a hike with him in the mountains near Lake Mead. It was 98 degrees, but they didn't bother taking any water along.

Four hours into their hike, the desert sun had taken its toll and they were both on the verge of dehydration. Thankfully, they found a vending machine that sold 16-ounce bottles of water for $1. The only problem was that the machine took only coins. Jake reached into his pocket and, aside from his wad of cash, all he had was a nickel. Doc did the same and counted out 95 cents.

Before they combined their money and put it in the machine, Doc pondered the situation. Since he had 95 percent of the funds, he should get 95 percent of the water. They were still probably two hours away from their car, so it wasn't just a matter of being greedy; he was concerned for his health. When he said this, Jake replied, "The way I see it, we need each other equally. Without your money, we can't buy the water, and without mine, we can't, either."

"You're right, Jake," said Doc, "and you are certainly entitled to your share; 5 percent entitles you to 5 percent of the water. Give me your nickel, and let's get this over with."

Jake decided to wait it out. The game was on.

Game theory is a field that combines psychology and math to work out ways to solve games based on how strategies are formed when people interact. With the success of the movie A Beautiful Mind, it's becoming a more mainstream way of solving problems. The primary insight of game theory is the importance of putting yourself in the shoes of the other player to see the situation from all angles. It's nothing new to poker players.

As David Sklansky writes in Hold'em Poker for Advanced Players, "First, think about what your opponent has. Second, think about what your opponent thinks you have. And third, think about what your opponent thinks you think he has."

I was playing $20-$40 hold'em and played pocket eights on the button in a capped pot with seven-way action. The flop came 7-3-2 rainbow, and when the first player bet out, a solid player named Michelle raised. Just about the whole field called, and even though I figured to be up against a set or a bigger overpair, I called for the size of the pot. When the initial bettor reraised and Michelle made it four bets, I was all but certain that she had flopped a set.

The turn paired the deuce and the first player led at it again, except Michelle flat-called this time. Several other players called, and even though I was drawing to only two cards, the pot was well over a grand – making it correct to draw for a 22-to-1 shot.

The river brought an 8!

Even better, the first player led again, only to be raised by Michelle. All the other players folded and I had a decision to make. As Sklansky advises, I thought about what my opponent had. I put her on a set on the flop. Had she turned threes full or sevens full, with the pot as big as it was, she probably would have raised to get rid of any overpairs (like mine) that could outdraw her. If, however, she had made four deuces on the turn, she probably would have flat-called to keep everyone in.

So, when my best card hit on the river and Michelle raised, I read her as having four deuces. I walked in her shoes and thought about how she would have played four deuces, and it seemed to fit. Don't get me wrong – I didn't fold. I only wish I was that good! Instead, I called the bet with the rationale that I was probably beat, and even if I wasn't, just calling would probably keep the other player in for one more bet.

Sure enough, Michelle had the four deuces and a $1,500 pot, while I walked away with only a moral victory for making a good read and the $80 that I saved from not raising (and paying off her reraise). Even so, applying the principles of game theory and seeing things from my opponent's perspective saved me $80 on that hand and countless amounts in other hands.

As for Doc and Jake, the lesson from game theory is that there isn't a set answer to any given problem. On one hand, they need each other equally and should split the water. On the other, each should receive an amount of water equal to his contribution. The genius of game theory is that it takes into account the human side of decisions. It's the makeup of the characters, sometimes more so than the numbers, that influences the outcome.

Jake reasoned that given the choice of no water or some water, Doc would choose the latter. By the time Doc was licking the salt that had hardened on his body, he gave up and handed Jake his change. The power had suddenly shifted.

Jake's fortitude to wait out Doc was more instrumental in the outcome of this game than how much money he had. Because Jake now controlled the money, he also controlled the water. One would think that Jake would have at least split the water evenly with Doc. But as thinking poker players and game theorists, you have to see the situation from how Jake, a tough-as-nails poker player, would act – not how you would act, or how a rational person would act.

Jake guzzled most of the water, and only because Doc was on the verge of passing out, he saved him the last sip.

Ever used lessons from poker to succeed in business? E-mail your stories to [email protected], and I will share them in my next column. The three best will receive an advanced reader's copy of my book entitled The Poker MBA: Winning in Business No Matter What Cards You're Dealt, which will be published by Random House's Crown Business imprint in April.