A locus for eccentrics (hopefully)

Thursday, October 05, 2006

Freakonomics and poker

Steven Levitt, one of the Freakonomics authors, posted his strategy (on his blog) for a recent poker tourney. Obviously, I've been doing it all wrong this whole time. I know it's long, but I'm going to post it below:

I was in Las Vegas yesterday celebrating my 10 year anniversary with my wife Jeannette, who loves me but not nearly as much as she loves poker. So even though this blog is about my anniversary and about commitment, it is not about the sort of commitment you might suspect. Rather it is about what economists call a “commitment device,” which is when someone locks himself/herself into a course he/she wouldn’t otherwise want to have to follow, but as a result the person benefits.

The idea of a commitment device is counter-intuitive. How can it make you better off to lock yourself in so that you have fewer options to choose from? Aren’t more choices always better than fewer? If there is no strategic interaction, more is always better, but when you are competing against someone else, limiting your options can be helpful. A classic example is an attacking army burning the bridges behind them so that they have no easy way to retreat. It commits the army to fight harder and might lead the opponent to retreat, avoiding a battle altogether. In the famous criminal case of the nanny Louise Woodward (who was accused of killing the child she took care of in Boston), defense attorney Barry Scheck tried to use a commitment device on the jury. I don’t remember the exact details, but in Massachusetts the defense can elect not to allow the jury to settle on a lesser charge, forcing the jury either to find the accused guilty of murder, or finding the accused innocent, but not letting the jury give a verdict of guilty of some less serious charge like negligent manslaughter. (Maybe some lawyers who read this blog can spell out the details of this in the comments section.) The idea behind Scheck’s gambit is that the jury would be willing to find Woodward guilty of a lesser charge, but not the most serious charge. By taking the less serious charge away from them, he hoped she would be found innocent. In fact, though, it backfired and she was found guilty of the more serious charge, although the Massachusetts Supreme Court later overruled it.

Anyway, back to my 10 year anniversary. My wife wanted to spend our last hours in Las Vegas together playing in a poker tournament. Because I am a loyal husband, I agreed to do it. It was a $430 buy-in tournament at the Mirage and 20 players were entered. It started at 5 pm and we figured there was plenty of time to catch a flight at midnight. Since neither of us had ever played in a live tournament, we had no idea how long these take to complete. It took about three hours to narrow it down to a final table of ten players. I was still in the tournament at this point, although Jeannette got knocked out on a bad beat relatively early. Two hours later, there were still five players left, including me. I had about an average number of chips among the remaining players. I also had a dilemma. My flight left in two hours. It was the last flight of the night. I really wanted to catch it. On the other hand, having just played this tournament for five hours, I was hoping to get a nice payoff and maybe some bragging rights.

So it was 10:15 pm and I figured the latest I could leave for the airport and comfortably make my flight was 10:30 pm. I decided that I would go “all in” with any hand that was decent at all. This would give me a chance to either lose quickly or maybe win quickly. I didn’t announce this strategy to the table, I just adopted it. Over the next 12 hands I was “all in” about 6 times. Four times everyone else folded. I won one of the other two hands, and lost one against someone with fewer chips. That left me with a lot more chips than before, but no one had been knocked out.

It was now 10:30 pm. Much to the surprise of the people at the table, I said I had to catch a plane so I was only going to play one more hand. There was a player who had so few chips left that he was going to be eliminated any hand unless he won one, and I would get fourth place instead of fifth…that would be worth $300 to me. The people at the table were very happy—I was essentially giving away maybe $1,000 in expected value to them by quitting. Since it was my last hand, there was not really any reason to do anything but go all in. Any chips I had left were worth nothing to me since I was quitting anyway. The other players at the table were smart enough to understand that. So I look down at my cards and I have pocket aces! So I go all in like I would have with any two cards, and the guy next to me also goes all in with Ace-queen, thinking this is his lucky day. We turn over the cards and I beat him and I knock him out and now I have more chips than anyone. Which made leaving a lot harder because now I was the favorite to win the $3,000+ first prize.

So here is where the commitment device comes in. Everyone knew I really had to leave. So I announced that from here on out I was all in on every hand. Even if I had the worst possible hand, I was going all in. They may not have believed me initially, but when I went all-in four straight times, it started to seem credible. It was clear I was following a strategy that is generally not sound. It is valuable to have the option to fold bad hands. But, at the end of a poker tournament, most of the hands are won by someone betting a lot of money and everyone folding. There is a big advantage to being the first one to bet, since it is likely everyone else will fold rather than risk the whole tournament on a mediocre hand. Since I had more chips than anyone else and it was clear I would be all in every hand, any player who made any bet knew that if he lost he was out of the tournament. Furthermore, each player could see that there was a chance that if he was patient, there was a good chance I would knock out the other players at the table first since these all in moves are often like coin tosses in terms of who wins.

Consequently, because everyone knew I was commited to going all in and because I had so many chips, almost every hand involved me going all in and everyone else folding. This was doubly good for me because it meant the hands went very quickly, which helped my chances of making my plane. I never would have had the nerve to play this way if I didn’t have the constraint of the flight. Occasionally someone would call my all in or go all in themselves, and they won a couple of those, but since the blinds were so big and I had more chips I was still way ahead and I knocked out one person. When it was down to three of us the incentives for the other players to fold were even stronger because the difference between second and third place payoffs was much larger than between third and fourth place payoffs. Going all in against me only raised the chance of his finishing first a little because I was so far ahead, but made finishing third quite likely. So even though the two opponents collectively would have been much better off coordinating to try to go in against me and beat me, their individual incentives were at odds. They both tried to sit back and let the other one take all the risk. It didn’t take long before both were so weak that all they wanted to do was to outlast the other. With a little luck, I knocked them both out, grabbed my cash, and made a dash for a cab that just got me to my airplane on time.

Word to the wise: having seen how well it worked this time, if you ever sit across from me in a poker tournament and I say I have a flight to catch, don’t believe it.

1 Comments:

Blogger neill said...

He must have been playing against morons. Even if they bought his initial signal ("I have to catch a flight" + going all in on 4 out of 6 hands, or whatever it was), it sounded like he kept playing the game past 10:30. Knowing that he couldn't have had AA every hand (because of the deck being shuffled) or that he cared that much about the flight (more money on the table; sticking around in the first place), the last two guys' equilibrium strategies has to become calling down with any good (A-x, pairs) hands.

The last two guys bought into a cheap-talk equilibrium despite having thousands of dollars of incentive not to. That, as they say, is poker, but I don't see how that's the result of the initial announced commitment device.

10:33 AM

 

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