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GAMBLING
ESSENCE
Events
or outcomes that are equally probable have an equal chance of occurring in each instance.
In games of pure chance, each instance is a completely independent one; that is, each play
has the same probability
as each of the others of producing a given outcome. Probability statements apply in
practice to a long series of events but not to individual ones. The "law of large numbers"
is an expression of the fact that the ratios predicted by probability statements are
increasingly accurate as the number of events increases; but the absolute number of
outcomes of a particular type departs from expectation with increasing frequency as the
number of repetitions increases. It is the ratios that are accurately predictable, not the
individual events or precise totals. The
probability of a favourable outcome among all possibilities can be expressed: probability
(p) equals the total number of favourable outcomes (f ) divided by the total
number of possibilities (t), or p = f/t. But this holds only
in situations governed by chance alone. In a game
of tossing two dice,
for example, the total number of possible outcomes is 36 (each of six sides of one die
combined with each of six sides of the other), and the number of "ways to make,"
say, a seven are six (made by throwing 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6
and 1); therefore, the probability of throwing a seven is 6/36, or 1/6 (or approximately
.167). In
most gambling games it is customary to express the idea of probability in terms of
"odds against winning." This is simply the ratio of the unfavourable
possibilities to the favourable ones. If the probability of throwing a seven is 1/6, then
in every six throws, "on the average," one throw would be favourable and five
would not; the odds against throwing a seven are therefore 5 to 1. The probability of
getting "heads" in a toss of a coin is one-half; the odds are 1 to 1, called
"even." Care must be used in interpreting the phrase "on the average."
Again it applies most accurately to a large number of cases and is not useful in
individual instances. A common gamblers' fallacy called "the doctrine of the maturity
of the chances" (or "Monte Carlo fallacy") falsely assumes that each play
in a game of chance is not independent of the others and that a series of outcomes of one
sort should be balanced in the short run by the other possibilities. A number of
"systems" have been invented by gamblers based largely on this fallacy; casino
operators are happy to encourage the use of such systems and to exploit any gambler's
neglect of the strict rules of probability and independent plays. In
some games an advantage may go to the dealer, banker (the individual who collects and
redistributes the stakes), or some other participant. Therefore, not all players have
equal chances to win or equal payoffs. This inequality may be corrected by rotating the
players among the positions in the game. Commercial gambling operators, however, usually
make their profits by regularly occupying advantaged positions; or they may charge money
for the opportunity to play or subtract a proportion of money from the bank on each play.
In the dice game of craps--which, of the major casino games, offers the gambler the
most favourable odds--the casino returns to winners from Many
gambling games include elements of physical skill or strategy as well as of chance. The
game of poker,
like most other card games, is a mixture of chance and strategy. Betting on horse racing
or athletic contests involves the assessment of a contestant's physical capacity and the
use of other evaluative skills. In order to assure that chance is allowed to play a major
role in determining the outcomes of such games, weights, handicaps, or other correctives
may be introduced in certain cases to give the contestants approximately equal
opportunities to win, and adjustments may be made in the payoffs so that the probabilities
of success and the magnitudes of the payoffs are put in inverse proportion to each other. Pari-mutuel
pools in horse-race betting, for example, reflect the chances of various horses to win as
anticipated by the players. The individual payoffs are large for those bettors whose
winning horses are backed by relatively few bettors and small if the winners are backed by
a relatively large proportion of the bettors; the more popular the choice, the lower the
individual payoff. The same holds true for betting with bookmakers on athletic contests
(illegal in most of the United States but legal in England). Bookmakers ordinarily accept
bets on the outcome of what is regarded as an uneven match by requiring the side more
likely to win to score more than a simple majority of points; this procedure is known as
setting a "point spread." In a game of United States or Canadian football, for
example, the more highly regarded team would have to win by, say, more than 10 points to
yield an even payoff to its backers. Unhappily,
these procedures for maintaining the influence of chance can be interfered with; cheating
is possible and reasonably easy in most gambling games. Much of the stigma attached to
gambling has resulted from the dishonesty of its promoters, and a large proportion of
modern gambling legislation is written to control cheating. More laws have been oriented,
however, to efforts by governments to derive tax
revenues from gambling than to control cheating. (Taxes can be levied against the incomes
of the promoters or players or of the turnover [bank, pool] itself.)
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