Stereotypes And Base Rates

A complete stranger just shoved all in. The bet was three times the medium-sized pot. It’s your first hand at the final table of a small tournament. There are ten players left, and only six will cash. Your stack is above-average, and your opponent has you covered.

If you call and lose, you’re busted. If you win, you’ll become the chip leader. You’ve got the number two flush, and there isn’t a pair on the board. There’s only one critical question: What’s the probability that your opponent doesn’t have the nut flush?

Since you’ve never seen this opponent play, your decision will certainly be influenced by your beliefs about certain kinds of people. For example, you believe – correctly – that a tattooed young man with green hair is much more likely to shove than a conservatively-dressed, 75-year-old woman. But how much weight should you give to that difference?

Daniel Kahneman, a Nobel Laureate, describes how we make this kind of judgment in Thinking Fast and Slow. All the quotations are from that book. We often rely on stereotypes. We see people as representatives of types such as reckless gamblers or hyper-conservative rocks.

The more closely someone represents our image of these types, the more likely we are to overvalue the stereotypes and undervalue the base rate. It’s the percentage of people who have certain qualities or take certain actions.

Stereotypes are generally based on facts such as: “People with a Ph.D. are more likely to subscribe to The New York Times than people who ended their education after high school. Young men are more likely than elderly women to drive [or bet] aggressively…
“One sin of representativeness is an excessive willingness to predict the occurrence of unlikely (low base-rate) events… You see a person reading The New York Times on the New York subway. Which of the following is a better bet about the reading stranger? She has a Ph.D. She does not have a college degree.”

The stereotype “would tell you to bet on the Ph.D., but this is not necessarily wise. You should seriously consider the second alternative, because many more nongraduates than Ph.Ds. ride in New York subways.” (pp. 151-152)

Kahneman urges us to “Discipline Intuition… You should not let yourself believe whatever comes to your mind. To be useful, your beliefs should be constrained by the logic of probability.” (p. 153)

“There are two ideas to keep in mind… The first is that base rates matter, even in the presence of evidence about the case at hand. This is often not intuitively obvious. The second is that intuitive impressions of the diagnosticity [predictive value] of evidence are often exaggerated…” (p. 154)

“Some people ignore base rates because they believe them to be irrelevant in the presence of individual information.” (p. 152)

He recommends: “Anchor your judgment of the probability of an outcome on a plausible base rate. Question the diagnosticity of your evidence.” (p. 154)

Not taking these steps can cause us to “keep making the same mistake: predicting rare events from weak evidence. When the evidence is weak, one should stick with the base rates.” (p. 155)

Alas, many people ignore base rates and may completely ignore logic. In one experiment subjects read a description which included these words: “Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy… she was deeply concerned with issues of discrimination and social justice.”

They then ranked the probability of eight choices, including “bank teller” and “bank teller active in the feminist movement.”

“89 percent of the undergraduates in our sample violated the logic of probability.” They believed that it was more likely that someone was a ‘feminist bank teller’ than a ‘bank teller…’ The set of feminist bank tellers is wholly included in the set of bank tellers, as every feminist bank teller is a bank teller. Therefore, the probability that Linda is a feminist bank teller must be lower than the probability of her being a bank teller.” (p. 157)

Even people trained in statistics and probability can make this mistake. Kahneman repeated the experiment with Stanford University doctoral candidates who had studied statistics, probability, and decision-making. They weren’t much better. “85 percent of these respondents also ranked ‘feminist bank teller’ as more likely than ‘bank teller.’” (p. 158)

These surprising results caused him to “make ‘increasingly desperate’ attempts to eliminate the error.” Instead of ranking eight choices, “we introduced large groups of people to Linda and asked them this simple question: Which alternative is more probable? Linda is a bank teller. Linda is a bank teller and is active in the feminist movement…”

“About 85 percent to 90 percent of undergraduates at several major universities chose the second option, contrary to logic. Remarkably, the sinners seemed to have no shame. When I asked my large undergraduate class in some indignation, ‘Do you realize that you have violated an elementary logical rule?’ someone in the back row shouted, ‘So what?’ and a graduate student who made the same error explained herself by saying, ‘I thought you just asked for my opinion.’ (p. 158)

Perhaps it’s OK to be illogical when you’re just expressing an opinion, but poker decisions determine whether you win or lose money. You can’t afford to be illogical, especially not when your tournament life is at stake.

The central poker decision rule is maximize your EV. Busting out costs you much more EV than you gain by becoming chip leader. Unless you believe there’s a very high probability that your opponent would shove without the nut flush, it’s much higher EV to fold.

You most definitely don’t have enough evidence to be confident that anyone would bet without the nut flush. The young man is much more likely than the older women to shove without it, but not many young men will do it. Since the costs of a bad call are far greater than the benefits or a good one, you should fold.

The tendency to ignore or minimize base rates is closely related to people’s cognitive style. My previous articles described what Kahneman called System 1 and System 2 thinkers. Most people call them “intuitive” and “logical.”

Intuitive thinkers are much more likely than logical thinkers to ignore base rates. “Your System 1 will automatically process the information available as if it were true.” (p. 153) A few intuitive thinkers have too much confidence in their “feel.” These few just “know” that this young kid doesn’t have the nut flush.

Sometimes they are right, make “heroic” calls, and win tournaments. When they’re wrong and bust out, they generally don’t realize they were illogical. They just believe, “I was terribly unlucky.”

Recommendations

Accept that you’re not immune to this type of mistake. We all occasionally make it, but you’ll make it less often if you accept your vulnerability.

Unless you have very good evidence that the base rate is unimportant, put greater weight on it than on the stereotype.

Don’t let egotistical beliefs about your wonderful people-reading skills cause illogical decisions. ♠

Dr-Al-Schoonmaker.net. After publishing five expensive poker books, Dr. Al, [email protected], now writes inexpensive eBooks. How to Beat Small Poker Games, Stay Young; Play Poker, How to Beat Killed Hold’em Games, and Competitive Edge Strategies For Poker And Business Winners cost only $2.99 at Amazon.com.