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Game theory in the popular press.

How Winning and Losing Alters Our Perceptions of Risk

Poker Digest
Games People Play
Nolan Dalla
January 11, 2002
text is a cache of

Most poker players think of themselves as rational human beings. Most poker players believe they are fully capable of making sensible table decisions based on their knowledge of the game combined with a basic understanding of the laws of probability. But if this were really true, there would be no losing poker players - or winning poker players either, for that matter. In order for winning players to exist, there must also be losing players, those poor misfortunate souls who neither think nor act in their own best interest. In essence, all poker games need players who think irrationally, exercise poor judgment, and lack discipline.

Oddly enough, a strong argument can be made that all beings are inherently prone to these same human defects. At times, we are predisposed to irrational thought, bad judgment and poor discipline. Even a rational thought process does not necessarily beget consistent responses when it comes to decisions involving risk. The choices we make are often inconsistent (not to be confused with incorrect), no matter what our level of sophistication or naivete about the subject. Consider the following three alternatives which are intended to measure risk tolerance:

1. You own a house valued at $150,000. The house is yours clear of any debt. At a casino, you meet a gambler who offers an intriguing proposition. The gambler says he'll lay $300,000 in cash against your house on the honest flip of a coin. Heads means you win $300,000. Tails means you lose your house. Would you accept this proposition? (Note: The option of seeking out investors or backers shall be excluded.)

2. You own a car valued at $15,000. The car is yours clear of any debt. A gambler offers you a proposition. The gambler says he'll lay $30,000 in cash against your car on the honest flip of a coin. Heads means you win $30,000. Tails means you lose your car. Would you accept this proposition?

3. You have $150 in your pocket. A gambler offers you a proposition. The gambler says he'll lay $300 in cash against your $150 on the honest flip of a coin. Heads means you win $300. Tails means you lose the $150. Would you accept this proposition?

I suspect that most of you said "no" to proposition A, "maybe" to proposition B, and "yes" to proposition C. Those responses would be perfectly normal. If we conducted an extensive survey, the overwhelming majority of respondents would surely decline proposition A. A small percentage would accept proposition B. And almost everyone (especially gamblers) would accept proposition C.

What's revealing is that all three propositions offer the exact same odds with the same positive expectation. In each case, the gambler is offering a 2-to-1 payoff on a 50-50 proposition (we assume the coin to be legitimate). In A, B, and C, there is a 50 percent chance you'll lose your bet. But there's a 50 percent chance you'll win the 2-to-1 windfall. Why then, would most of us reject A and perhaps B, too, but accept A?

The inconsistency can be explained by weighing the emotional responses associated with each possible outcome.

For most people, the fear of losing $150,000 (the house) is much stronger than the temptation to risk it all for $300,000. Sure, a few hard-core gamblers (or very wealthy individuals) might be willing to risk their homes on a coin flip, but most of us would not risk beyond what we could not bear losing. This same rationalization applies to the risk of a $15,000 car, though to a lesser extent. In some cases, this fear of loss is so crippling that some people would not even risk losing $150, even if the favorable prospect of winning $300 is explained to them. People who are so risk-adverse usually don't go very far in life, for risk is a fundamental part of getting ahead.

Understanding human behavior and our perception of risk has been taken to new heights by each succeeding generation over the centuries. Scholars have gradually come to realize that the gambling world is the perfect laboratory to examine our responses to uncertain outcomes and how we make our choices in life. This is not meant to explain the reasons why people gamble, but to underscore the point that game theory has an unequivocal connection to more weighty topics than just cards or dice.

Twenty years ago, two psychologists, Amos Tversky and Daniel Kahneman, published a study they called Prospect Theory. The study matriculated from a lengthy collaboration between the two academics - one at Princeton and the other at Stanford - into researching human responses to uncertainty. In the seminal work, they designed a series of experiments which intended to determine common human responses and patterns of behavior when confronted with various risks.

Tversky and Kahneman drew several conclusions from the study (and subsequent follow-ups), which were groundbreaking at the time and resonate with us to this day. Their findings are echoed, even at the poker table. Here are a few of the key points (Note: For more detail, see the chapter titled, "The Failure of Invariance," in Against the Gods, by Peter L. Bernstein):

Where significant sums are involved, most people
will reject a fair gamble in favor of a certain gain.
In one study, people were asked to choose between two options: an 80 percent chance of winning $4,000 and a 20 percent chance of winning nothing versus a lump sum of $3,000. Even though taking the gamble had a higher expected value (80 percent of $4,000 equals $3,200), 80 percent of respondents chose the sure thing (to receive $3,000). Other experiments were conducted with similar test questions. In each case, the results were the same. Most people prefer to protect what they have already won.

People are less likely to accept a loss.
People prefer to gamble rather than accept a loss.
The same test group was offered a similar proposition to the one previously described. They were asked to choose between gambling on the prospect of an 80 percent chance of losing $4,000 and a 20 percent chance of breaking even versus a 100 percent chance of losing $3,000. Interestingly enough, the researchers found that 92 percent of the respondents chose to gamble! Even though the mathematical expectation is the same as in the first question (80 percent of $4,000 is $3,200), we become risk takers when the prospect includes the possibility of taking a loss.

Combining the results of both tests indicates that most people prefer to lock up a win (not to gamble) when they're ahead, but will take risks (to gamble) when confronted with a loss. But if this is really true, why would anyone ever play a casino game? Why play games of chance, which are known to be losing propositions for the player? The conclusions cited above seem inconsistent with our daily observations of tourists stampeding into casinos ready to throw their money away on games they know little or nothing about.

Another researcher, Richard Thaler, conducted a study which addresses, in part, this apparent contradiction. Thaler identified what he described as a "house money" effect.

Two experiments were conducted. In the first experiment, a group of people were each given $30, then were subsequently offered a coin flip where heads meant a loss of $9 and tails meant a win of $9. The choice was between: (Option 1) to gamble or (Option 2) not to gamble. Seventy-five percent chose to gamble.

In the second experiment, respondents were offered an identical option - but it was posed in a slightly different manner. Each person had the choice between: (Option 1) flipping a coin and getting $39 for heads and $21 for tails or (Option 2) taking $30 and not flipping the coin at all. Although the expectation is exactly the same as in the first experiment, this time, only 43 percent chose to gamble. Fifty-seven percent preferred the sure thing (receiving $30).

Thaler concluded that once the respondents had $30 in their possession, they were more willing to gamble, but they were not inclined to take the same risk until the $30 was tangible. In a sense, the promise of something is not as effectual as the real thing. Cash is more meaningful than a check.

Gamblers enter a casino with a tangible number of dollars they are willing to put at risk. Poker players who sit in a poker game have a tangible number of dollars they are willing to put at risk. Almost everyone that enters a casino or a poker room goes in with a specific figure in mind - the amount of money they are willing to gamble with. But once money is either won or lost, the attitude toward that money changes. Losers are inclined to begin taking more risks. Winners are inclined to be protective of what they have won.

There's nothing new about the idea that people resort to more desperate measures when they're losing. Anyone who has ever seen a player go on tilt at a poker table understands this wholeheartedly. By the same token, people become increasingly protective of a win (whether it's a house, a car or chips won in a poker game). The bigger the win (in other words, the more they now have to lose), the less risk-tolerant most people become. Once they've locked up a sure thing, they're reluctant to risk losing it. Finally, most people are risk-tolerant when the stakes are not too high. They will take a gamble if the stakes are within reason and they perceive they have a fair chance of winning. But they will also decline a wager if the stakes get too high, even if offered favorable odds.

In bringing up these studies, it's only fair to point out that these results may be skewed to a certain extent since a broad spectrum of the general population was measured. If these same test questions were posed to gamblers, or poker players, the percentages of those favoring "risk" to "no action" would likely be much higher than normal. Nevertheless, the responses of gamblers are likely to be consistent with the general population when it comes to taking big risks. Just as most people want to protect winnings but abandon that self-control when they lose, most poker players behave much the same way.

Copyright © 2001 CJPG.