We Make Implicit Bets Every Day

In last week’s column, I explored the possibility that calculating the payoff for making a bet is insufficient to decide whether or not it is in your best interest to take it. Even if the odds are heavily in your favor, other considerations might prohibit you from gambling. A common deterrence to taking a chance is the potential loss compared to your total holdings. This is often more important than your potential winnings. Since the odds of a wager are not dependent on your holdings, then knowledge of the odds is obviously insufficient to decide if the wager is a good one.

The example I used last week involved making a wager with odds favoring you winning when the minimum bet is either $1 or $1 million of your own money. Since most of us cannot afford to lose $1 million, we would not take the bet, but Bill Gates could take either bet without difficulty or second thought.

A similar issue arises when deciding to take chances. Suppose you have reason to believe that a potential sexual partner is unlikely to infect you with an STD, but you are not sure. You really like the person and the time is ripe, but neither of you has protection. What do you do? Assume the same thoughts are going through the potential partner’s mind. What happens? The event could be enjoyable and even meaningful, but it could also lead to a nasty disease and early death. Well, we don’t always behave either logically or in our own best interests. There are even times when we decide to ignore the warning signs. Such is life.

One common way to decide whether to take a bet or not is to go beyond the simple chances on winning or losing and look at the potential rewards and losses. This is normally done without reference to what fraction of your total wealth is represented by this calculation. In the examples above and last week, one probably does not take the bet for $1 million because we all have some net worth, which is a reasonable sum. But the logic of probability favors taking the bet. If you have net worth far greater than $1 million, either bet could simply be a pleasant diversion.

Consider a third scenario. Suppose you have very little cash and are allowed to make the $1 million bet on credit secured by your signature. Given your past earning record, suppose it is unlikely that you will earn enough to pay off the note if you lose. Also assume the lending institution is a legal one that does not contract for kneecaps. Does this situation change your betting strategy?

These artificial situations seem to be just that — artificial, but in fact, we make implicit bets every day. Should you cross the road in the middle of the block? What is the probability of getting hit? What is the probability of getting a jaywalking ticket? What is the cost of either loss and what is the benefit of taking the chance? What should you eat and how much?

In general, we make decisions considering what we have in resources, but often the decision theory problems are presented as though that were not an issue. An arbitrary situation is proposed and the probabilities and payoff matrix presented. Under those circumstances, we might derive a different result than would occur in real life.

In response to the interest my original tutorial generated, I have completely rewritten and expanded it. Check out the tutorial availability through Lockergnome. The new version is over 100 pages long with chapters that alternate between discussion of the theoretical aspects and puzzles just for the fun of it. Puzzle lovers will be glad to know that I included an answers section that includes discussions as to why the answer is correct and how it was obtained. Most of the material has appeared in these columns, but some is new. Most of the discussions are expanded compared to what they were in the original column format.

[tags]bet, gamble, decision theory, statistics[/tags]