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# Betting Systems May Not Deliver What You Think They Promise

27 February 1995

ay I advertised a betting "system" offering over a 50-50 chance of winning, which paid more than even money. Say I asserted any solid citizen could use it, making \$1 table bets even when the posted minimum was \$5 or \$10. And, say I guaranteed double your money back if you could show my figures were wrong, the bets weren't allowed by the casinos, or the system depended on factors like unlimited playing time and bankroll.

You'd wonder why I'd sell this super system, not just soak up the centavos using it myself. But, wouldn't you be tempted to buy it?

There's good news, better news, and bad news.

The good news: I've developed such a system.

The better news: I'm gonna give it to you free.

The bad news: I've told you the truth, but not the whole truth, and the system doesn't work.

Here's what's behind it. Practically speaking, every casino bet has a fixed chance to win on any try. No matter how many times you've won or lost before, the probability of scoring on the next try is always the same. Keep playing, though, and the likelihood you'll win at least once goes up as the number of tries increases.

Imagine a dollar slot machine having one 10-position reel with a single winning stop and nine losers. A hit pays \$9 and returns your buck. This constitutes a bet with a 10 percent (1 out of 10) probability of winning and a 9-to-1 payoff. The accompanying table gives the chance of at least one win in various numbers of tries. It shows that the probability of collecting at least \$9 within seven tries is 52 percent.

Think of a "hand" as comprising seven tries. You have a 52 percent chance of this hand's earning a profit, from \$3 for winning just once to \$63 for hitting seven times, against only 48 percent chance of losing \$7. Compare this with a \$7 even-money bet on a single flip of a coin. Here you have a 50 percent chance of winning \$7 against a 50 percent chance of losing \$7.

Apply the idea in a real game to \$1 wagers on two or 12 at craps, bets any casino will book on \$5 or \$10 tables. The probability of winning each individual bet is 2.8 percent (1 out of 36) and the payoff is 30-to-1. But the probability of collecting \$30 and getting back your \$1 at least once in twenty-six tries is 52 percent. So now think of a hand as comprising twenty-six tries. You have a 52 percent chance of coming out ahead on this hand by \$5 to \$780, against a 48 percent chance of losing \$26.

You could also use the system betting \$1 at a time on your lucky number at double-zero roulette. The probability of winning on any try is 2.6 percent (1 out of 38) and the payoff is 35-to-1. The probability of collecting \$35 and recovering your \$1 bet at least once during a hand of twenty-eight tries is 52.6 percent. The bottom line is that the hand affords a 52.6 percent chance of making from \$8 to \$980 profit, against a 47.4 percent chance of losing \$28.

Why doesn't this work? You think about it, as you should if you were considering buying and trying the system with real money. I won't spoil your fun by spelling out the answer. I'll help by mentioning three things, though.

All the numbers I've given are correct.

In comparing the imaginary one-reel slot machine and the flip of the coin, you can expect to break even over a long period of play either way.

No matter how often or how much you bet on two or 12 at craps or your lucky number at roulette, the house edge doesn't change.

While you're puzzling over the pith of the problem, inundate your intellect with this inspiring injunction of Sumner A Ingmark, songster of the system seeker:

Casinos aren't impervious to
Math governing the universe,
So pause before you dare pursue
A system that could make things worse.

TABLE

Chance of at least one hit in multiple tries
when the probability of winning on a single try is 10 percent

 Number of tries Probability 1 10% 2 19 3 27 4 34 5 41 6 47 7 52 8 57 9 61
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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.