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Best of Alan Krigman

Gaming Guru

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Money Is Money. Or, Is It?

23 September 2003

Many casino buffs think in terms of "playing with the house's money." The idea is keep increasing bet size with gains from past winning rounds. Good luck escalates earnings faster and higher than they could go with bets based solely on their own initial bankrolls. An eventual loss, even in the limit of a parlay where no intermediate profits are held back, merely leaves players where they were when a series began. Those who espouse this philosophy argue that in games having neither extreme longshots, nor payout schedules in which modest wagers can deliver sizeable returns, it's the only way to pump a small stake up to big bucks.

Punting purists assert there's no such thing as the house's money. If you win a bet and are free to leave the game, it's your money. Not theirs. Strictly speaking, of course, this is true.

But strictly speaking, risking $1 million on a one-out-of-three shot at $2.5 million is quite favorable while $1 on one chance in five million to win the same amount is a sucker bet. Why? Because statistically, every dollar wagered has an expected value of roughly $1.17 the first way and $0.50 the second. Yet, few folks would take the good deal were it offered them, while gamblers galore buy lottery tickets exemplifying the poor proposition.

This isn't just the case in the casino. It also applies in the real world of business and finance. The reason can't simply be greed, unsophistication, desperation, a get-rich-quick mentality, or a potion they spray into the air. Something else must be going on that makes flouting the laws of probability so universal.

That "something else" has been studied in depth and is the essence of "game theory." This is a field which has claimed several Nobel Prizes in the recent past -- including one to John Nash, the mathematician in the book and movie "A Beautiful Mind." The relevant aspect of game theory involves "utility," the supposition that money has subjective as well as objective value.

In a business environment, one company may prudently invest $1 million with a 33 percent chance of earning $2.5 million while another may wisely decline to do so. Assuming the profit would be equally attractive to both, a possible distinction between the two might be that the former can afford to write off the $1 million while the latter will go bankrupt if the gamble fizzles. The front money would differ in utility in these instances.

In a casino or lottery, typical participants would consider a dollar bet to be chump change and a $2.5 million jackpot priceless, making the odds -- already unfathomable -- immaterial. But, how many players would bet $100 on one chance out of 50,000 or $1,000 on one chance out of 5,000 to win the $2.5 million? Would you? Much of the appeal of slot machines is that solid citizens perceive the amount at risk as what they bet on each round, not the total they might or do hazard in a session.

Similarly, bettors tend to assign different worth to money they bring into the casino and winnings they accumulate during the course of the action. Being $500 ahead at some point and dropping back to a $500 break-even bankroll isn't like losing that $500 stake. People may kick themselves for being ahead "and giving it back." But arriving on the deluxe motor coach with $500 and departing with an empty fanny pack is another story altogether. It can be downright depressing, notwithstanding the comp to the all-you-can-eat buffet and free casino-logo ice scraper.

Does this mean it's all right to bet when you're ahead as if you're really playing with the house's money? Or that it's OK to give back $500 you were winning but not to lose $500 you earned at your day job and used as a gambling stake? It doesn't mean things like this are right, but implies they're not necessarily wrong, either. It recognizes that money has a relative utility as well as an absolute value, and suggests that good gamblers recognize this factor -- intuitively if not explicitly -- and weigh it in deciding what's best for themselves. The parvenu's poet, Sumner A Ingmark, caught the concept in his canny couplet:

The value of money's not just what you get for it,
But also how badly you needed to sweat for it.

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.