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Best of Alan Krigman

Gaming Guru

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Volatility: It'll Make or Break Your Day

10 July 2001

Everybody knows that casinos have an edge on bets they book against players. To some folks, this is enough reason to forego gambling altogether. To others, it's an incentive to find games and learn strategies that minimize the bite. And to a third group, arguably the largest, what or how people play makes no discernable difference in their chances of success or failure.

Edge matters. It's how the casinos win. So, by extension, it's how solid citizens lose. But the effect is a long-term phenomenon involving small influences on huge numbers of decisions. Like nearly imperceptible grains of sand, borne on prevailing breezes, that mold mountains over the eons.

Few bettors focus on the long haul. Most set their sights on a session, a few days' casino vacation, or maybe even a month or year. During such intervals, the inherent volatility of the games tends to swamp the edge. This, masquerading as luck, can put a person over the top or decimate a stake far more completely than the "expected loss" the experts invoke to evaluate options.

An example can afford some intuition about the relative impacts of edge and volatility. Compare $10 on one spot at a double-zero table with $1 on each of ten spots at the same game. Assume you have a $500 stake, want to win $500, and will be piqued at fate so foul as to deny you at least two hours of action ?? 100 spins.

For either alternative, edge is the same 5.26 percent. On $1,000 handle, 100 spins at $10 each, this gives the house an expected profit of $52.60. But you don't actually expect to lose $52.60. You hope to win $500 and fear you might drop the same amount.

Volatility, the mechanism that drives you to one or the other, is greater with the concentrated than the dispersed wagers. As a result, $10 on one spot yields 46 percent probability of doubling your money without first going broke, while $1 on each of ten spots offers only 11 percent likelihood of achieving this goal.

What if you bet $10 on one spot in a single-zero game? The edge shrinks roughly in half, to 2.7 percent. Expected loss in 100 spins is $27. Volatility stays almost the same. The chance of doubling before losing a $500 stake rises from 46 to 48 percent. The lower edge improves your short term lot, albeit marginally.

Does this imply that raising volatility can obviate edge over reasonable periods? Yes, but there's a catch. Higher volatility makes you more apt to bust any bankroll within a given time. At a double-zero game, switching from ten spots at $1 to one at $10 lowers the likelihood $500 will last for 100 spins from 99.5 to 58 percent. Halving the edge with $10 on one spot at single-zero roulette helps a bit, raising chances of survival to 59 percent.

Extending the perspective from 100 to 5,000 spins ?? from two to 100 hours ?? demonstrates how edge overtakes volatility in importance as the number of trials grows. Betting $1 on each of ten spots at a single-zero table offers an 8 percent shot at weathering 5,000 spins without a bankroll fix. Survival rate is low because edge alone projects a $1,350 loss (2.7 percent of $50,000), demanding an extraordinary compensatory upswing. A similar double-zero player has under one percent possibility that the original bankroll will last. Here, edge anticipates losing $2,630 (5.26 percent of $50,000) and relying on volatility for an even more phenomenal upswing. Neither outlook is promising, but fighting half the edge does lift prospects of survival tenfold.

You can see the problems. 1) Edge is only negative. You can check it, short term, with volatility. But volatility works two ways ?? the increasing fluctuations that overcome house advantage can also drive fortunes far below losses predicted by edge alone. 2) The effect of edge grows faster than that of volatility with extended play, so normal upswings ultimately aren't enough to surmount expected the downtrend. How to find a balance that's right for you?

Heed the bettors' bard, Sumner A Ingmark:

Though anyone can win, the real essence,
Of gambling is to play, and learn its lessons.

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.