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Best of Alan Krigman

Gaming Guru

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Why It Helps to Know There's Math behind the Games

21 June 1999

My friend, Rick Z, says I sometimes go overboard with the math. Rick, who works in a casino and has vigorish in his veins, claims most players would be happy if I simply told them what to do.

Of course, Rick knows (at least, I think he does) that I don't just make all this stuff up. But the gambling world is rife with conflicting theories, systems and strategies we argue are valid because we badly want them to be, and liberal doses of myth and malarkey. Numbers are needed to give solid citizens clues about whom and what to trust, reasons why the unlikely happens so regularly, and help deciding what approaches are best for them.

Say someone presents an elaborate hedge to avoid being "hurt" by a seven at craps. Few players are so naive, nowadays, as to believe in secret loopholes the casino bosses don't want anyone to know. Still, based on your personal gambling goals, this strategy may be on target for you. Or, maybe not.

You could go by your gut, viewing the hedge as cheap insurance to minimize possible losses. You should realize that all hedges raise house advantage while moderating bankroll swings. To evaluate the impact of this particular hedge, you'd have to know how much extra edge the house "charged" you for it, what it does to your chances of surviving a session starting with a certain stake, and how it would influence the odds you'll reach a point where you'll be satisfied to quit before you go belly-up. Given the specifics of the hedge, these questions can be answered expressly and would let you decide rationally whether to use it.

Here's another situation. Pretend you always plays roulette with a $100 bankroll, betting $5 per spin on red or black. You find you can usually last long enough to rate a free meal for yourself and your spouse at the buffet, rarely depleting your stake, but hardly ever earning much of a profit. You buy a book explaining a progressive betting system in which you start with $5, raise your bet by some amount after each win, and return to $5 after a loss.

You try it for a while. Sure enough. You win $50, $250, $100 in your first three outings. In the next five games, you lose your $100. And, win or lose, your sessions are so short the pit boss won't "comp" your dinner. The math would have told you to expect a few big and fast wins offset by frequent and rapid wipe-outs. More, it would have helped you tune the system to your personal gambling goals. Perhaps you're willing to blow your whole bankroll in exchange for occasional healthy profits, provided you get enough playing time to qualify for free dining delights and to ignore the call of the Lorelei to the cash card machine in the lobby for more money to keep playing.

Here's an example involving fine distinctions between options, where the numbers are necessary to make proper distinctions. Some blackjack players stand on 16 versus 10-up. They're aware the experts say draw, assuming it has to do with 16 losing unless the dealer busts, while hitting offers a chance to win or push with totals from 17 to 21. But they remember breaking a lot by hitting 16, and the dealer sometimes busting with 10-up. So they question the "book," and follow what they consider experience. The dilemma can be resolved using statistics to show what's really going on.

If you're a purist, you may be surprised to learn that standing wins more often than hitting -- chance is over 23 percent compared to 20.5 percent. But standing also loses more often than hitting -- almost 77 percent as opposed to 74 percent. The key to the puzzle is that hitting yields pushes on 5.5 percent of all hands. Every $100 bet when the adverse 16-vs-10 occurs has a net expected loss of roughly $77 - $23 = $54 by standing, and about $74 - $20.50 = $53.50 by hitting. Expected loss is less when hitting, so "basic strategy" says it's the preferred decision.

It's fortunate for folks who flout the math that casinos use chips for anything more expensive than $0.50 slots. People surely wouldn't want to put real money at risk without understanding what they're doing. As the poet, Sumner A Ingmark, said:

Gambling need not be mysterious,
Secrets fade with study serious.
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.