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# Why gamblers can win with systems that don't work

15 March 2010

Aren't they maddening? Those slick pitches for gambling systems guaranteed to beat the house, with "bogus" written all over them? You'll be glad to know that few system touts get many takers.

You might be surprised, though, to learn that folks who do buy or devise their own systems are often content with them. Sometimes, although the systems lose, they leave the impression of almost winning, just needing a little adjustment. More often, because systems with no redeeming value send players home with profits.

Normally, in casino games, payoffs are less than the odds which must be overcome to win. The offset between the two gives the house its edge. As an example, the odds against winning a Place bet on the four at craps are 2-to-1; a "fair" return on a \$5 bet would be \$10, but there's a \$1 offset and the house only pays \$9.

To circumvent or overcome edge, a system would have to indicate or create conditions where payoffs exceed the odds against winning. This can happen. Blackjack card counters and shuffle trackers can monitor when probabilities change because ranks about to be dealt deviate from full deck proportions. Astute video poker buffs can spot games where features like progressive jackpots or bonuses push payoffs above break-even. And highly-skilled craps shooters can set and throw dice in a manner that influences the likelihood some faces will show more than others, not with equal probability. These effects can all be proven with mathematics, computer simulations, or repeatable experiments.

Systems involving such things as detecting patterns, betting on combinations of wagers all of which give the house an edge, varying bet sizes, and spotting dealers who do things like shuffle cards or release roulette balls in certain ways are spurious. They can't be shown analytically or experimentally to indicate or cause appropriate changes in payoffs or odds.

Players may win using these systems, anyway. They got lucky. Another follows from the edge on individual bets being low compared to the actual win or loss in a given round or session of reasonable duration. Pretend you're in an even money game with odds against winning of 51-to-49. Edge turns out to be 2 percent. On a \$1 bet, edge theoretically gives the house \$0.02, but volatility raises or lowers your bankroll by \$1. The \$0.02 falls out of the bet losing marginally more often than winning.

In one round of this game, you have a decent shot at earning a buck no matter how you decide what to do. As more rounds are clocked, the impact of edge grows faster than and eventually outweighs that of volatility. Solid citizens may not reach this point in one or even a series of sessions, so volatility dominates amounts won or lost by individuals. The casino relies on the net from many players for edge to give it a profit.

There's another reason systems seem to work. Commonly tossed in gratuitously after the gobbledygook is an admonition not to be greedy but shoot for frequent small wins. Regardless of what a system purports to do, the chance of reaching profit P before exhausting Bankroll B is related to B divided by B plus P.

Absent edge, the probability would equal this ratio precisely. To illustrate, say you play a fair game starting with a \$90 bankroll and quitting when you earn \$10. Your chance of success is \$90/\$100, that's nine out of 10. On the average, in 10 sessions, you'll come out even with nine \$10 wins and one \$90 loss. When the house has an edge, the probability decreases. But a \$90 stake and \$10 goal still give a strong chance of success, maybe eight out of 10. But that's \$80 minus \$180, a \$100 beating.

Anyone can win at a casino without knowing anything. So any system can be successful in the short term regardless of its validity. But, unless it truly improves your odds or payoff, a system doesn't enhance and may, instead, diminish your prospects. Here's how the poet, Sumner A Ingmark, put the phenomenon.

Don't think you can hold your own,
Winning games by chance alone.

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Best of Alan Krigman
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.