Are casino gamblers anxious about edge too smart by a half?

Edge in the various games tops the list of factors that drive revenue into casino coffers. Conven-tional wisdom says this should be critical to solid citizens as well. But, is it?

The bosses make their money on long-term averages involving tens or hundreds of thousands of patrons and untold millions of bets. Conversely, individual players tend to focus on the results of single rounds, sessions usually of at most a few hours, and – occasionally – casino visits lasting one or several days. Some folks indulge frequently enough so they're less attentive to the ups and downs they encounter in particular instances than with what happens over weeks, months, or years; however, these gamblers are far more the exception than the rule.

Roulette offers insights into the impact of edge on prospects for the short spans on which players typically judge success or failure. This applies within games, where edge is constant but bettors can manipulate the size of bankroll fluctuations by the way they wager. And it also holds between double- and single-zero versions of the game, where house advantage on nominally-equivalent propositions differs by a factor of nearly two – 5.26 and 2.70 percent in the former and latter, respectively.

Pretend you bet $10 on one spin. Here are some ways you can make the wager, how much you're up to earn, and the chance you'll win.

*	$10 on one spot: chance of winning $350 is 2.6 percent double-zero, 2.7 percent single-zero;
*	$10 split between two spots: chance of winning $170 is 5.3 percent double-zero, 5.4 percent single-zero;
*	$10 on the corner of four spots: chance of winning $80 is 10.5 percent double-zero, 10.8 percent single-zero;
*	$5 on Black and $1 on each of five Red spots: chance of winning $26 is 25 percent double-zero (value differs under Atlantic City rules), 26.3 percent single-zero.

Cutting edge almost in half does have an effect. Prospects of joy for the same earnings or losses are greater at single- rather than double-zero tables. But the gain is small, reflecting the house's theoretical monetary take of roughly $0.53 and $0.27 on the $10 wagers rather than the 2-to-1 reduction in percentage.

Imagine you'd like an hour's action on a $100 stake, betting $10 in one of the indicated ways. Figure about 45 spins in the hour. Sure, you'd like to finish the session with a profit. But you wouldn't cry with a loss, provided you didn't bust out within the hour. What would be your outlook for survival making these bets?

*	$10 on one spot: 19.2 percent double-zero, 19.5 percent single-zero;
*	$10 split between two spots: 26.6 percent double-zero, 27.4 percent single-zero;
*	$10 on the corner of four spots: 37.0 percent with double-zero, 38.6 percent with single-zero;
*	$5 on Black and $1 on each of three Red spots: 72.5 percent with double-zero (value differs under Atlantic City rules), 76.8 percent with single-zero.

Again, edge introduces a bias. The repercussions are greater than on individual bets, mainly because the edge acts on a larger gross wager. Betting on 45 spins puts a total of $450 at risk, theoretically siphoning off 5.3 and 2.7 percent of this figure. The equivalent losses would be approximately $24 and $12 in the double- and single-zero implementations, respectively. Still, deviations across two games are small, compared not only to the substantial change in edge but to the divergences within each game caused by alternate choices of how to wager the same $10.

These illustrations show that edge does impair short-term performance. But the blow is negligible for individual bets and relatively small for sessions of reasonable duration, especially compared with the influence exerted by the volatility of the game. And volatility, which you can picture as the average magnitude of bankroll changes when rounds are resolved, is something you can manage by your choice of bets. So, in deciding on personal criteria for gambling, remember this rhyming recommendation by that odester of options, Sumner A Ingmark:

To dwell on the immutable, ignoring what you can control, Is tactically unsuitable, and may not help you reach your goal.