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Playing It Smart: Does edge really make a difference for the average gambler?25 March 2008
Casinos earn their money by means of the statistical advantage they hold on the bets they book. And, whatever the casinos take to the bank is nothing more or less than the amount bettors leave behind. So this edge is also the mechanism by which players lose.
But the effect is a matter of averages over many coups. In the relatively brief span of a single gambling session, or even of an extended casino visit, an individual bettor may finish ahead of the game perhaps way ahead or may lose lots more than edge alone would suggest. The reason is that the normal fluctuation of the game, the volatility, swamps edge when numbers of trials are small. As the duration of play increases, however, the impact of edge rises faster than that of volatility and overtakes it.
On the bright side, slot devotees depend on volatility to feed their fantasies of riches in a few hours of action even though edge on the machines tends to be high. Conversely, blackjack or craps buffs may lose their shirts in comparable time frames despite giving the bosses what seems like a negligibly low edge.
So, how much should you heed house advantage when you're deciding how or what to play? Examining a few alternate bets at single- and double-zero roulette may help provide some answers. For this purpose, consider wagers on columns (12 numbers) paying 2-to-1, and splits or lines (two numbers) paying 17-to-1.
Edge on either bet at a single-zero table is 2.70 percent; in a double-zero game it's almost twice as much, 5.26 percent. Volatility is measured by what the math mavens call "standard deviation;" think of this as the average multiple of the amount you bet by which your bankroll jumps up or down from round to round. For columns, this is 1.40 units in single-zero and a close 1.39 units in double-zero games. Standard deviations for splits are about triple those for column; however, they're similar in single- and double-zero games, 4.07 and 4.02 units, respectively.
Here's how to get a perspective on the way edge, in and of itself, affects a game. Determine how much you play, on the average, before the edge accounts for a loss equal to one bet. Find this simply by dividing edge expressed as a percent into 100. For the single-zero wagers, it's 100/2.70 which equals 37 rounds; the double-zero figure is 100/5.26, or 19 rounds.
The action you can get for the theoretical cost of a single bet is a good benchmark. But it's a long term average that doesn't tell much about your prospects for a particular session of any reasonable duration. For this, volatility also has to enter the equation. And the results aren't so easily calculated.
One good indication is the probability your bankroll will be enough to carry you for some given number of coups making bets of a constant size. For this purpose, pretend you have $200 and want to bet $10 per spin on one or the other of the proposed propositions. You might want to know the chance your money will last through normal downswings for at least two hours. With a proficient dealer, this will be about 100 spins. The results are presented in the accompanying table.
Chance that a $200 bankroll will be enough for 100 rounds betting $10 at a time on splits and columns in single- and double-zero roulette bet single-zero double-zero splits 35.6% 34.1% columns 80.1% 75.2%
These figures show that edge does have an influence. Chances are lower in the higher-edge double-zero situations. But, in practical terms for the kinds of action solid citizens typically encounter, such as the likelihood a stake will suffice for a game, it's less than you're apt to think. Nearly doubling the edge cuts the likelihood of survival by only roughly 4 percent in the cases cited. Increasing the volatility by a factor of four, on the other hand, more than halves the chances of survival under the same conditions. Which illustrates what Sumner A Ingmark, that optimus urbicus poeta (as the peripatetic punter, V P Pappy, has deferentially dubbed him), meant when he mused:
Gamblers can increase their pleasures,
Maybe even augment their treasures,
Gauging bets with proper measures.
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