“Never Bet More Than You Can Afford To Lose.”

A recent exchange of emails with Jeff Partridge about my last couple of columns suggests that I should take time to explore the functions of “bet,” “wager,” or “gamble” as used in examples of decision making as opposed to their use in common langu. In the previous columns I presented a situation where a wager would pay off much better than even odds, but a reasonable person would not take that bet because it required putting on the line a large fraction of the bettor’s net worth.

Jeff quotes the old rule, “Never bet more than you can afford to lose.”

That is a good rule which we could quantify a bit more. Decide how much you are comfortable in losing. Know the probabilities such that you can compute the long-term expected return on your gamble. This can help you estimate how long you can survive. In the example I gave, the probability is that in the long run your profit would be positive. However, the problem is that if you go broke in the short run, you never get to the long run. It does not matter how much the odds favor you if you lose everything on the first event. A similar calculation shows that on the average if equally skilled poker players compete, the one who starts with the most money will win all of it. Of course this assumes each hand depletes only a small part of each player’s holdings otherwise someone could go bust before the long-term effects of probability kick in.

All these considerations contain a hidden assumption that is probably not justified. We have assumed that people place bets to win and increase their wealth. While that might be a motivation of some mathematicians who really know they have an edge, it in not the motivation for most people. Most people seem to gamble at games, love, and business for much the same reason people go to horror shows or bungee jump — they relish the adrenaline rush. That is, the gambling as an activity is an end in itself. Starting a business might make money, but a true entrepreneur gets satisfaction from the effort.

All this is well and good unless the addiction to the rush requires betting enough at a time that losing really hurts.

That fact is that using wagers and bets as examples in discussing rational decision theory, statistics, and probability is convenient, but artificial. Very few people will go to Las Vegas with a book on the theory of probability in their suitcase. That does not mean that the gambling exercises are invalid. The puzzle of the Sultan’s daughter was completely artificial but illustrated an advanced concept in a way that made learning it more fun than wading through several pages of mathematics.

Decision theory is a powerful tool when combined with an understanding of statistics and how probabilities are reliably derived from them, but like any tool, garbage in means garbage out. If you attempt to extend the definition of gambling to include the psychological aspects, then the computations get a whole lot more complex.

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]wager, bet, gamble, probability, statistics[/tags]