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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Which is preferable: High or low volatility?

7 September 2009

Many solid citizens view casino gambling as mainly a matter of luck. As in: one game is more or less the same as any other. If these folks make any distinctions, they're that some tables or machines require bets too high for their budgets, are too complicated, or have payoffs worth or not worth the risks.

More polished players recognize that the house's edge varies among games and wagers. Edge, also referred to as "advantage," is the average fraction of a bet the house earns as a result of the disparity between the odds of winning and the payoff. Edge is the engine that moves money into the casino coffers. It accordingly stands to reason that higher edge pumps up profits for the bosses and leads to larger corresponding losses for the bettors. Not necessarily individually, but for gaming buffs as a whole.

Were edge the whole story, nobody would gamble. Using wagers on Player at minibaccarat as an illustration, it would mean that a person betting $10 per round for about an hour roughly 200 hands would always lose between $26 and $27. This would be an unattractive prospect, even with the $8 or $9 "reward" credit "earned." The same applies to other games, adjusting the figures for the total bet during a session and the edge on the action.

Punters almost always come out ahead of, or go deeper into a hole than, what's predicted purely on edge. This shows the impact of volatility the bankroll swings occasioned by the payoffs or losses on every decision. Volatility is generally measured with a quantity the math mavens call "standard deviation," which you can envision as a representative bankroll jump up or down.

Volatility dominates specific sessions or casino visits; edge governs extended periods. To see this, consider one and a million hands of minibaccarat with $10 on Player. In one hand, a bankroll rises or falls by $10. Edge amounts to $0.13. But it's invisible, buried in the lower probability of winning than losing. In a million hands, volatility has about 95 percent chance of inducing swings as much as $20,000 up or down while edge causes over $130,000 loss; $10 players, as a group, consequently lose between $110,000 and $150,000 in 95 percent of all million-round series.

Bettors have some control over edge. Sophisticated video poker fans, for instance, can deduce the value from the payout display and therefore find the most favorable games. As another example, Basic Strategy keeps edge below 0.5 percent in blackjack; playing by guess and by gosh can give away two to four times this much.

Volatility can also be managed to a certain extent. One approach is by choosing the games and particular propositions on which to wager. Higher payoffs signal greater volatility. A $1 outside bet at single-zero roulette, which returns 1-to-1, has a standard deviation close to $1.00. A $1 bet on a single spot in the same game, paying 35-to-1, has a volatility of $5.84. Another way is to vary bets. With $25 on Player at minibaccarat on every hand, standard deviation is just under $25. Alternately, the following yield an average of $25 per hand: $10 56.6 percent, $25 20,2 percent, $50 14.0 percent, $75 7.6 percent, and $100 1.6 percent. The standard deviation for this spread is $33.44.

In principle, you'd like the lowest possible edge. In practice, you may want to balance edge against factors such as partiality to games, how much homework is needed to learn the optimum strategy, the sizes of bets the casino requires, and the payoffs offered. Volatility adds another dimension of choice. High volatility improves chances of reaching a desired profit before going bust, but lowers the outlook of a stake being enough to outride the normal downswings of a game for as long a session as desired. Conversely for low volatility.

Wouldn't it be nice to have a hard and fast set of gambling guidelines that works for everybody under all circumstances? The same could be asked about everything we do. Is the lack of such rules to be lamented or celebrated? Here's what the immortal inkslinger, Sumner A Ingmark, asserted:

Some prefer a life robotic,
Others opt for the chaotic.

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.