17 Nov 2009

WSJ Punts On Explaining Risk-Taking

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This article (HT2 Dan Simmons) is actually pretty good in explaining the logic behind Patriots’ coach Bill Belichick’s decision to go for it (rather than punt) on 4th down with the ball in his own territory and his team with a small lead. Since the Patriots were stopped and ended up losing the game, tons of people said Belichick was an idiot. You can read the article to see a defense of Belichick’s decision.

However, I want to quibble with what seems to be a mistake on the part of the WSJ writers:

[T]he essence of Mr. Belichick’s “crime” may be something simpler than all this: His decision went against the natural instincts of all human beings when they’re forced to make high-stakes decisions. In a recent study, researchers from Duke and UCLA found that when faced with a decision involving risk, people have an overwhelming tendency to make the supposedly safe choice—to err on the side of caution—even though doing so may lead to worse results.

By studying thousands of hands of blackjack played by random people, the researchers found that when they strayed from the “book” or the optimal strategy, those players who did something aggressive were more successful than those who did something passive.

In fact, the subjects made four times as many passive mistakes as they did aggressive ones. And these passive mistakes—holding on a 16 when the dealer has a king showing, for example—were more costly: They cost $2 for every $1 won, versus $1.50 for every $1 won on aggressive mistakes.

At issue, it seems, is the very idea of what constitutes gambling. If going for it gave the Patriots a statistically better chance of winning—and if aggressive deviations are often better than passive ones—then the gamble would have been to punt, even though that was the seemingly safe play.

In the part I’ve put in bold, I think the writes are mixing things up. First of all, the Blackjack deviations were from the correct play, so by definition, the deviation was a mistake. In contrast, the football statistician’s research (if correct) shows that Belichick deviated from the conventional wisdom but not from what the truly optimal play was.

Second of all, the WSJ writers are making it sound as if researchers have discovered some tendency that says, “If you’re going to deviate from tradition, better to err on the side of boldness–it will probably be better than if you err on the side of caution.”

But that’s not what the researchers found. No, they found that because people (apparently) have a predisposition to caution–they are afraid to hit and bust in Blackjack–you see them making relatively stupider moves when they err on the side of caution, compared to the times they err on the side of recklessness.

In other words, it’s not as if the researchers found that a “randomly generated mistake” is more likely to hurt you if the mistake is in refraining from taking a hit (when the optimal play is to take a hit), compared to a mistake when you hit and you really shouldn’t. Maybe that’s true and maybe it isn’t, but that’s not the question the researchers looked at.

In summary then, the safest (ha ha) thing to say would be: If you are stuck on a decision that’s really close, err on what seems to be the risky side, because your natural biases are already giving unwarranted appeal to the apparently safe side.

AN ASIDE: Blackjack is actually a very complex game, compared to something like Tic Tac Toe. I am pretty sure that when people refer to the “optimum play” they are actually relying on computer simulations. So for example, I don’t think it has actually been mathematically proven that you maximize your expected payout by hitting a 16 versus a Dealer’s face card. (Just think through how complicated that would get.) Instead, I think they just run through a bajillion computer simulations of a randomized deck (or maybe they model it with x decks), and then try different strategies and keep track of the outcomes.

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