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Best of Alan Krigman

Gaming Guru

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How to Use the Volatility Choices Offered by the New Slot Machines

30 March 2005

Everyone knows that casinos have an edge on every bet they book. Yet, this isn't the whole story of gambling. Players can win despite the edge. Or lose but get enough play making bets of moderate size, starting with affordable stakes, to deem their dough well spent. And when luck is bad, they can also go bust in much shorter order than the erosive effect of edge would imply.

These conditions result because bets have volatility as well as edge. Edge is familiar but often poorly understood; picture it as an average commission or fee casinos levy on bets. Volatility is less readily recognized; think of this parameter, commonly measured by what math mavens call "standard deviation," as akin to the average fluctuations bankrolls undergo per decision.

Solid citizens can rarely do much about the edge, once they've chosen a game and in some instances learned the optimal strategy. Table players, however, have traditionally had means to raise or lower volatility. The new breed of multi-line, multi-coin slots now affords machine aficionados a similar opportunity.

To see how this works, and what you can do with it, envision a set of hypothetical 10-line, 10-coin-per-line slot machines that look alike but differ internally. In all cases, pretend that bets on any line result only in losses or even-money wins. Also, that the feature distinguishing the machines is the chance of winning.

The edge on any particular setup will be the same regardless of how solid citizens concentrate or spread their bets with respect to the lines. Imagine, for example, that a person picks a game with 45 percent chance of winning on any bet. Edge will then be 10 percent whether this player risks $1.00 on a single line or $0.10 on each of 10 lines; either way, the bosses will figure they're netting an average of $0.10 per pull. Similarly, at a device with 47 percent chance of winning, the house will estimate a "take" of $0.06 on the dollar regardless of its distribution.

In contrast, volatility depends on how funds are apportioned. When a dollar is bet on a single line, bankroll fluctuations are the maximum $1.00 up or down per pull. When the bet is a dime on each of 10 lines, a round might yield bankroll changes of $1, $0.80, $0.60, and so forth, up or down. It could also break even, producing no change. The standard deviation, which accounts for the amounts and their probabilities, is between $0.31 and $0.32.

An important ramification of volatility is the impact it has on players' confidence about the action they can get for their money. Win or lose, folks want their cash to buy entertainment time and, of course, a comp to the all-you-can-eat buffet.

You can put the effect of volatility into perspective. Consider how apt someone with a $100 buy-in is to be in action at one of these hypothetical slots for two and three hours of betting $1.00 per round, all on one line or $0.10 on each of 10 lines. Assume 667 spins in two hours and 1,000 in three.

Of 1,000 players betting $1.00 on a single line at the machine with 45 percent chance of winning, 876 should persist for at least two hours and 438 for three. By reducing the volatility with bets of $0.10 on each of 10 lines, 999 should be in there trucking for two hours and 500 for three. With a less severe edge, for instance on a machine with 46 percent chance of winning, the one-line bet should find 952 in contention after two hours and 681 after three, compared with 999 and 978 survivors, respectively for the 10-line alternative.

The flip side of these factors, to be sure, is that trimming volatility to limit cumulative negative losses during downswings also puts a ceiling on aggregate profits during upswings. So the flexibility offers gamblers the opportunity to trade-off trying to stay in the game for extended periods on their hard-earned dough versus going for broke. Only bezonians think they can have it both ways, or don't think about it at all. As the volatile versifier, Sumner A Ingmark, veritably verbalized:

Of compromises, life is full,
For every push there'll be a pull,
So seek a mean that's sensible.

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.