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.
