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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Saving a buck at the casino

21 October 2008

Sir William Thompson, aka Lord Kelvin, a 19th Century Scottish engineer, said, "When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind."

Few things are more definitively measured and expressed in numbers than money and probabilities. It turns out, though, that people routinely place surprisingly little stock on the numbers that are the sum and substance of either.

In gambling, for instance, the gurus commonly castigate solid citizens who go out of their way to save $20 on groceries but won't quit $20 ahead at the slots. Or, who'll blithely "give back" $50 playing long enough to earn two $15 comps to the buffet (comparable to $7.50 each at beaneries outside the casino).

The effect is more fundamental to human behavior than actions in the fantasy world of gambling, however. To illustrate, make believe that Larry and Harry operate electronics stores in your neighborhood. They obtain and sell identical items from the same suppliers. Larry's emporium is about a block north of your home on an upscale shopping boulevard. He pays high rent and charges a premium for his merchandise to cover it. Harry is about five blocks to the south in a seedy strip mall. His rent is low and he passes the savings on to the public.

You need a new calculator. Both outlets carry the model you want. Larry charges $20, Harry $15. Everything else is the same. Where do you buy it? Larry's store is closer and classy. Harry's is further away and shabby. You're in the minority if you believe the benefits of the shorter walk and posher ambience outweigh the lower cost. Therefore, barring unusual circumstances, you're most likely to go to Harry's to save the $5.

Say, instead, you're looking for a big flat-panel high-definition TV system. Again, both stores have the model you want. Larry sells it for $1,999.95. Harry's price is $1,994.95. Same system, warrantee, delivery, and installation. Would you go the extra few blocks to the less elegant store to save the $5?

You still might patronize Harry, but not to save the $5. This, despite what any economist would tell you. Namely, if the disadvantages are worth bearing to keep $5 in your pocket when you buy the calculator, ditto when you buy the TV: $5 is $5.

Almost nobody thinks like this, though. It's far more usual to reason relatively. In one case, the "discount" for shopping at Harry's rather than Larry's is $5 off $20. This seems like a big cut, even for those who don't do the arithmetic and find it's indeed substantial at 5/20 or 25 percent. In the other situation, it's $5 off $1,999.95, a seemingly insignificant savings that does happen to equal a low 5/1999.95 or 0.25 percent.

As for probabilities, the Martingale system provides a casino example. When you lose a round, double your bet for the next. The theory is that you'll eventually win and earn a one-unit profit. Pretend you try it with a $5 flat bet on Don't Pass at craps. You've heard the chance of losing 10 in a row is 0.1123 percent, which you figure is negligible. You stake yourself $5,115, enough for 10 coups. Only, 0.1123 percent isn't zero. Those 10 in a row can happen. And, when they do, it's a $5,115 disaster.

Alternately, maybe you play a slot machine with a $100,000 jackpot. You read that the chance it'll pay the bonanza is about one in a million. You spurn a game with a $10,000 biggie even though you've heard that the chance is roughly one in 100,000. These chances are almost the same, right? And, anyway, every bet is the same one pull away from a fortune, so what difference do the probabilities make?

The revered rhymster, Sumner A Ingmark, addressed these and similar questions, when he reflected:
When you can make a decision,
Based on what's known with precision,
Why is there a proclivity,
To invoke relativity?

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.