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Best of Alan Krigman

Gaming Guru

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Think out Your Attitudes toward Uncertainty and Risk in Advance.

23 December 2003

Casino gambling entails far more than the mechanics of the games. It's a sophisticated exercise in managing uncertainty and risk. Many players are oblivious to the complexity this implies. So they push into the great punting palaces of the planet with only as much money as they can afford to lose, or maybe a bit more, and go hell bent for leather trying to win as much as possible.

The seemingly banal injunction to fix a loss limit and win goal offers some aid. Especially when the link is given between these amounts, parameters of particular games and betting strategies, and chances of success. But, uncertainty and risk go deeper. The bad news is they don't lend themselves to explicit sets of rules broadly applicable to situations solid citizens confront in the casino. The good news, as the late Professor Julian Simon noted, is that you can often devise puzzles involving basic choices, decide how you'd handle them, and find consistent patterns in your preferences that will guide you under real circumstances.

Pretend you're playing a hypothetical two-stage slot machine. A hit on the main game brings you to a screen with 10 buttons, some of which pay $100 and the rest $1,000. You're about to pick when someone offers you $550 to "buy" the gamble.

The information, as presented, gives you no "logical" basis for deciding. You'd accept or decline based on your attitude toward risk. Do you prefer a sure $550 to an unknown chance at $1,000 with the downside of $100. Neither is "right" or "wrong."

If you're analytically inclined, and have any insight at all into the way the bosses operate, you might guess that chances were much higher of winning $100 than $1,000. Say, 90 and 10 percent, respectively. Were this the case, you could figure the "expected value" of the gamble as 0.9 x $100 + 0.1 x $1,000 or $190. At this level, $550 is a better deal, mathematically. In fact, $550 is statistically superior to the gamble unless the odds drop to 50-50. That's when the decision becomes a wash because expected value is 0.5 x $100 + 0.5 x $1,000 or $550. Of course, you know this isn't about to happen since the idea of a slot machine is the carrot of big returns and the stick of low probabilities. Having thought this through, would you then accept the offer?

Assuming that the odds are indeed on the $100, you'd be going by "the book" to take the $550. The arithmetic book. But this presumes that you consider the "utility" of money purely a matter of its numerical value. It ain't necessarily so! As an extreme example, you may have to pay your landlord $1,000 the next day to stave off eviction; a lesser amount won't do. So $550 is worth no more to you at the moment than the $100 you'd get if you gambled and lost, while the $1,000 is a roof over your head.

Another theoretical situation that may help you reconcile your approach to risk might be a game where you could bet $100 on a 50 percent chance of finishing with $200 or a 0.5 percent shot at ending with $20,000. This is a "fair" bet with an expected value of $100 either way. You have three alternatives. You might elect not to play and have a certain $100. If you did bet, you'd be likely to view the two options as differing from each other, despite their equal expected values. The utility of the payoffs and the disappointment or regret or associated with the loss might be factors, as well as the prospects for one or the other result. How would you go: keep $100 or try for $200 or $20,000?

Change the conditions to a bonus round in a game with a "free" try at either a 50 percent chance of $200 or a 0.5 percent chance of $20,000. You don't have to bet, just pick one gamble or the other. Would you be more or less likely to take the longshot when the downside was money not gained as opposed to money lost?

These questions are simple to ask but tough to answer. Still, if you can't sort out your attitudes with dilemmas of this type, away from the heat of the action, how can you hope to make decisions you won't rue on the casino floor? The risky rhymer, Sumner A Ingmark, had just this in mind when he mused:

Gather rosebuds while ye may,
Before your money's put in play.
Time for strategy design,
Has passed when cash is on the line.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.