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Best of Alan Krigman

Gaming Guru

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Betting Progressions Increase Your Bankroll Swings

5 May 2000

Some casino games let players with modest bankrolls feed their fantasies of fortune by thinking that the next round could be a big bonanza. The same games offer those who fall behind hope that one more spin, roll, or deal can get them out of trouble.

But what about games whose payoffs roughly match the amounts bet? How do players recover from cold streaks in such circumstances? Or multiply the money they can always scrape together into the kinds of cash they only dream about? Experienced gamblers often shoot for goals like these using betting progressions. Strategies for raising and lowering wagers during the course of the action.

Few aspects of gambling are more controversial than betting systems, even among solid citizens who otherwise agree on how best to play. Few are more poorly understood, even by those who are comfortable raising or lowering bets. And few are more apt to underlie "secrets the casino bosses don't want you to know," which appeal even to folks who should see through the hype.

Here's the single most important characteristic of betting progressions. They increase volatility -- the size swings players should expect their bankrolls to undergo relative to the average amount wagered per round. Big swings, of course, are mixed blessings. They make it more likely that players will either deplete their stakes or go over the top during a session.

I'll illustrate the effect with several alternate progressions involving the same average bet. Take blackjack at $10 per round as an example. The trend would be analogous for other averages. It would also be similar in other situations where progressions are widely used -- for instance bets on Banker and Player at baccarat, the outside at roulette, and the line or the numbers at craps. To do the comparisons, I'll convert representative progressions into their "even-money equivalents." These are hypothetical flat bets paying exactly 1-to-1, along with their probabilities of winning, which have the same house advantage and expected bankroll fluctuations as the actual series of wagers.

As a base, imagine a blackjack buff who slides out $10 on every round -- no more, no less. The even-money equivalent is a bet of $11.22 with a 49.66 percent chance of winning. The equivalent of the flat bet exceeds $10 because players can win $15 on naturals and can win or lose $20, $30, or more on splits and doubles.

Assume that instead of betting flat, a player wagers $5, $10, and $15, each a third of the time. The average is still $10. But the even-money equivalent is a bet of $12.12 with a 49.70 percent chance of winning. A steeper progression might mean betting $5 half the time, $10 a quarter of the time, and $15 and $25 each an eighth of the time. The average remains $10. But, the even-money equivalent is now $13.45 with a 49.72 percent chance of winning. A more aggressive player might bet 60 percent at $5, 25 percent at $10, 10 percent at $20, and 5 percent at $50. Although this progression again represents a $10 average bet, the even-money equivalent is $16.07 with a 49.77 percent chance of winning.

You get the idea. For the same average exposure, increasingly radical progressions are like betting substantially more money and having slightly greater chances of winning. From $11.22 at 49.66 percent with $10 flat bets, to $16.07 at 49.77 percent with the most aggressive progression cited.

These results suggest that progressions, like betting flat at higher levels, increase the bankroll swings in the game. So, why not just bet more? Because progressions also offer the chance to profile sessions according to personal preferences. Flat betting in games with short odds yields symmetrical up- and downswings. Raising bets when you're ahead tends to yield small chances of large profits. Increasing when you're behind offers high probabilities of small gains. The depletion of a given bankroll is the penalty for bad luck all three ways. The immortal poet, Sumner A Ingmark, described the opportunities to choose in verse:

Modest gains or profits glorious?
Different ways to be victorious.
 Different strategies laborious.

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.