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Best of Alan Krigman

Gaming Guru

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Widen or Narrow Your Bankroll Swings with Your Betting Strategy

3 January 2001

Wishful thinking and that "system" you bought for $149.95 aside, you can't control or predict which cards will be drawn next, how dice will land, where balls or wheels will stop, or other events that decide games of chance. So you can't dictate casino triumphs by betting big when wins are sure and cutting or holding back when losses are unavoidable. But, this doesn't mean you can't use betting strategies to influence session results in helpful ways.

Betting options available to table players depend to a degree on game specifics. In cases such as craps and roulette, solid citizens can select one or more of a plethora of propositions on which to wager, each with its own odds of winning and payoff. And, in all table games, there's a choice of amount to be bet.

Varying bet sizes during games of independent trials can't alter house advantage. If the casino has 0.5 percent edge and you bet a total of $2,000 over 200 rounds, your expectation is to lose $2,000 x 0.005 or $10. It doesn't matter whether you bet exactly $10 per round, or vary the amount so the total is $2,000 and $10 just the average. This is how the casino earns its money -- as surely as in a coin flip or other 50-50 situation where you pay a nickel up front for every $10 bet, or risk $10.05 to win $9.95. And this is how it's resolved when the bosses tally the proceeds of billions bet in millions of rounds by thousands of players.

In a span of 200 rounds, though, few 50-50 gambles win and lose exactly 100 times each. So, even betting a steady $10 with a $0.05 fee up front, you'd be unlikely to finish precisely $10 in the hole. You'd probably show a profit, or a loss somewhat above or below the theoretical $10. Whether, or how, you vary your bets affects the range over which your fortune is apt to fluctuate.

You can picture the impact of bet sizing strategies on bankroll fluctuations using the notion of 50-50 equivalents. This is what you'd bet and what you'd win in a hypothetical 50-50 game having the same edge and volatility as your actual betting pattern. I'll spare you the arithmetic and simply illustrate the idea by citing examples based on alternate blackjack betting profiles.

Pretend you bet $10 flat. You know blackjack isn't an even-money game -- you may double or split and win or lose over $10, win $15 on a natural, or push and neither win nor lose. When all these factors are crammed into my Ignoble-prize-winning formula, what emerges is a bet of $11.35 with a 50-50 chance of winning $11.25.

What if you bet $5 on each of two spots, again on a constant basis, round after round? The house advantage is the same as for $10 flat on one spot so the casino's theoretical take remains $10 after 200 rounds at 0.05 percent. But the 50-50 equivalent is a bet of $9.48 to win $9.38. This is almost $2 per round less than for one spot at $10. You therefore expect to go less deeply down when the table is cold, and less far up when it's hot.

How about a strategy that ends up with you betting on one spot -- half the time at $5 and a quarter of the time each at $10 and $20? The edge is still 0.05 percent and you bet a total of $2,000 in 200 rounds so the casino figures your action is good for $10. But the 50-50 equivalent is $13.30 to win $13.20. Since the 50-50 equivalent amounts are almost $2 more, you can anticipate wider swings than by betting flat. You'll accordingly go broke faster when fate is cruel and get richer quicker when it's kind.

Varying both the size of your bets and the number of spots in play moves you back toward the middle. Say that half your bets are $5 on one spot and a quarter each are $5 and $10 on two spots. With this strategy, the 50-50 equivalent bet is $11.32 to win $11.22 -- almost the same as for $10 flat on one spot.

Which approach is best? Decide for yourself using -- as criteria -- factors such as your bankroll, tolerance for loss, and the profit that will make you happy. Just remember what the poet, Sumner A Ingmark, said about things tending to work both ways:

It's neither surprising, nor is it appalling,
That something fast rising, is also swift falling.

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.