Understanding Poker Errors Through Prospect Theory - Part 1

Player A makes the nut straight on the turn. One opponent probably has a flush draw, and another player has bet as if he were quite strong. Player A with the straight passes up the chance to raise on the theory that if a bad card comes on the river, he will have saved the money he would have "wasted" had he raised. Of course, he also passes up a chance to get more money in the pot when he holds the best hand and the percentages favor the raise. Why would someone play like this?



In another part of the cardroom, Player B holds pocket jacks and raises before the flop. A good player calls from the big blind, and the flop comes A-8-3 rainbow. The big blind checks, Player B bets, and the big blind check-raises. At this moment, Player B is pretty sure the big blind has an ace and is ahead, but Player B calls, hoping to hit his jack. When a jack fails to materialize on the turn, he folds to a bet. Most players know that the chances of hitting a jack on the turn are 22-1 against, and there are only seven and a half small bets in the pot when they call on the flop. No reasonable estimate of implied odds can make this call correct, yet people make this play almost routinely. Why do they make this error?



We can gain some insight from academics. People studying judgment and decision-making have documented a number of reliable errors that individuals make in risk-evaluation situations, in poker as well as away from the table. To help explain this, I have invited a noted researcher to join me in my next two columns. Her name is Dr. Rachel Croson, and she is an associate professor at the Wharton School of the University of Pennsylvania. She conducts research into why poker players (and others) think the way they do.



First, let's let Rachel introduce herself.



Rachel on Rachel: I started in this business because I was in love with Mr. Spock from Star Trek. All of my young girlfriends went gaga for Captain Kirk (of course), but I was enthralled with Spock's rationality. Even as a young girl, I didn't think that people (humans) actually acted in a rational way, and I wondered why.



My research is dedicated to describing how people act, primarily in strategic situations. I compare those actions to what would be rational and recommend strategies for moving decisions closer to rationality.



Among academics, Spock-like rationality is called normative decision-making, and what I do is descriptive (describing what people actually do) and prescriptive (designing strategies for overcoming their errors). My husband started playing poker in 1996 or so, and in watching behavior of the players, I recognized the very errors that researchers had documented in other areas. As a result, I started collecting data on poker players and their decisions, both at and away from the table.



I have documented a number of ways in which poker players are different from the general population, but also have found many in which they are the same. In this column, we'll discuss some of the ways that errors we see at the table are the same as errors that the general population makes in real life. We'll discuss some of the causes behind these errors, and will tell you how you can exploit them in others and overcome them in your own play.



Introducing Prospect Theory: Psychologists and economists study individual decision-making in a variety of settings, including large stakes (which person to marry) and small stakes (which brand of milk to buy), different areas (medical decisions, financial decisions, and so on), and by individuals, groups, and whole societies. But researchers especially love to study individuals in gambling and gaming situations. Studies from these different settings often lead to the same conclusions: People use the same processes to make decisions. And sometimes people make the same types of errors over and over again.



Three of the most important errors were formalized into Prospect Theory by Amos Tversky and Daniel Kahneman (Kahneman recently won the Nobel Prize in Economics for these contributions; Tversky would have, had he not passed away shortly before it was awarded). In this column, we describe those errors and provide examples of how they lead to common mistakes at the poker table.



The three errors that Prospect Theory formalizes are:

• Loss Aversion (the pain of a loss is about twice as much as the joy of a gain)

• Asymmetric Risk Preferences (preferring not to gamble when ahead, but to gamble more when behind)

• Misestimation of Probabilities (thinking that low-probability events are more likely to occur than they are)



Loss Aversion: To Mr. Spock, $100 is $100. It represents a value used to purchase goods and services. With humans, it is a different story. To most people, losing a fixed amount like $100 hurts more than gaining the same amount feels good. So, the subjective benefit of gaining $100 is less than the subjective pain of losing $100. In poker terms, people feel much worse (actually, about two to two and a half times as bad, according to Rachel) losing a bet than they feel good winning one.



Many experiments bear this out. For example, subjects were asked about a one-time fifty-fifty gamble between losing $10 and winning some amount. How large would the amount have to be in order to make this gamble just barely acceptable? Most people (not gamblers) require, on average, $25 to get them to take the bet. Thus, a loss of $10 is about equally painful as a gain of $25 is joyful.



At the poker table, loss-averse individuals act too timidly. In the introduction to this column, we saw Player A make a typical loss-averse play. He gave up expectation because he would have felt worse on those occasions when he lost a bet than he would have felt good when winning the extra bet or two. Another example of loss-averse play happens when players decline to value bet on the river. Again, if their bet gets called and they win, they feel OK, but they were getting the pot anyway ("It's big enough" can be heard in cardrooms across the country). But if their bet gets called and they lose, they feel bad and annoyed. So, they leave money on the table and wonder why they can't win.



Loss-aversion also happens when a player has a nut-flush draw on the flop against three opponents and fails to raise. He is getting an overlay for this bet, as he will win 33 percent of the time and is putting in only 25 percent of the money. But he knows he will lose two-thirds of the time, and feels bad when this happens. When he wins, he feels good anyway, and the extra few bets do not seem to matter as much.



Even players who read this and say, "Hey, I make that raise," typically will not raise on the turn in the same situation against six opponents. The issues are the same, but the player will lose two double bets four times out of five. Even though the play is a long-term winner, the frequent large loss hurts more than the gain feels good.



How you can use loss-aversion: When watching your opponents, look for signs of loss-aversion. Remember that loss-averse players rarely bet for value on the river and also bluff too infrequently. When a typical loss-averse player raises on the flop, he almost always has a real hand instead of a draw. He almost never makes semibluff raises on the turn. Understanding this can help your hand-reading skills and improve your folds.



You also need to monitor your own game. If you find yourself feeling that a bet lost hurts more than a bet (or even more) gained feels good, take a look and see how your feelings are affecting your play. You may be playing too passively, calling too much, checking too often on the river, and failing to make money-gaining raises in value situations.



In the next column, we will conclude this visit into Prospect Theory by looking at poker errors caused by asymmetric risk preferences and misestimation of probabilities. We also will tell you how to use this information to make more money at the tables.

Barry offers poker lessons tailored to each student's specific strengths and weaknesses. Please visit his website at www.barrytanenbaum.com or e-mail him at [email protected]. Rachel is always on the hunt for new sources of data regarding interesting gambling behaviors. Her website can be found at http://www.wharton.upenn.edu/faculty/crosonr.html, and she can be reached at [email protected]. You can write to her for detailed references regarding Prospect Theory.