When the Numbers Say Go Nuts

After explaining what I do for a living, I've had several people ask if I just play "solid poker." What they seem to mean is playing what could be called an honest strategy: betting or raising good cards, checking or folding weak cards.

I'm not sure how I would define "solid poker," but a reasonable definition might be playing in a way that is difficult to exploit. In this sense an honest strategy is not solid because it's very easy to exploit. When they bet or raise, you fold unless you have a very strong hand. When they check, you bet. Their actions translate to reliable information about their hand that you can then act upon.

So while honest play isn't really solid, the association between the two ideas is common and stretches beyond poker. After Bill Belichick went for a controversial and risky fourth down conversion, Tony Dungy criticized the call on ESPN by saying "you have to play the percentages"...even though analysis of the percentages showed that Belichick made the right call by going for it. But to Dungy and many other commentators, "playing the percentages" was synonymous with playing conservatively. The numbers, they felt, would always point to conservative options, while aggressive strategies could only be motivated by emotion.

In poker the opposite often holds true: the numbers suggest a highly aggressive approach, but many players play too conservatively for emotional reasons. In The Mathematics of Poker by Bill Chen and Jerrod Ankenman, the authors find that a "high level of aggression is supported by analysis. When we study toy games [simplified games similar to poker] we are often surprised at how aggressive [the optimal] strategies are." While No Limit Hold'em has not been solved, analysis suggests that a mathematically "correct" strategy would appear to most players to be psychotically aggressive. Nonetheless, many players are reluctant to push their aggression because they're uncomfortable with the risk involved in going for a big bluff. In other words, emotional hangups prevent them from going for the mathematically correct play.

So why the persistent association between analysis and conservative approaches? It may be because the most visible and disastrous examples of under-analysis are often over-aggressive. In poker this would be the "maniac," a player who bets and raises compulsively with too many hands. Not only does this type of player often go broke, he does so with the full attention of everyone at the table. From the analytical point of view, an overly cautious approach is no more correct than a maniacal one, but it's far less conspicuous.