Gamblers,
and most civilians as well, are continually confronted with predicaments
posed by uncertainty and chance. Yet, these phenomena are as elusive
as they are pervasive. At the root of the puzzlement is the discomfort
people experience with risk rather than assurance. Will it rain
tomorrow, or not? We're happier with yes or no than maybe, even
when the maybe is tagged with a level such as 4 on a scale of 17
where 1 means definite sunshine and 17 "Noah, launch the ark!"
Adding to the
aggravation, two different yardsticks are used to describe and measure
chance: probability and odds. More, within each category, numbers
are assigned in several alternate ways. So, when a figure ?? rough
or of great precision ?? is given for the chance of a proposition,
what does it tell you?
In the casino,
the most straightforward circumstances involve the chances associated
with individual bets. Here, values are found by counting the numbers
of ways different results can occur. As an illustration, say you're
betting a single spot at double-zero roulette. The ball can stop
in any of 38 distinctly numbered and colored but otherwise identical
pockets. Nothing favors one over another. You win with one and lose
with the remaining 37. Probability expresses chance by comparing
the number of ways you can win to the total range of possibilities.
In this example, it's one out of 38. Mathematically, this is the
fraction 1/38. If you have a calculator or remember long division,
you could reduce 1/38 to the decimal 0.0263 or the percentage 2.63
percent.
Odds quantify
chance by comparing the number of ways you can win to the number
of ways you can lose. The indicated roulette bet has one winner
and 37 losers. This can be stated as odds of 37?to-1 "against" the
wager. An alternate would be 1-to-37 "for" the bet or, dusting off
your arithmetic again, 0.027-to-1 for the proposition ?? obtained
by dividing 1 and 37, in turn, by 37.
These all describe
the same chance. And the samples above show how to convert from
one format to another within either category. How about switching
from probability to odds, and vice versa?
Assume the odds
of a bet are 9-to-4 against winning. This happens to describe "insurance"
at blackjack ?? assuming cards drawn from an infinite deck ?? since
nine (A through nine) lose while four (10, J, Q, and K) win. To
convert to probability, note there are four ways to succeed out
of four plus nine or 13 possible outcomes. This is 9/13, 0.6923,
or 69.23 percent.
Going the other
way is just as easy. Pretend the probability of an event is 40 percent.
This turns out to be the chance of winning a place bet on the five
at craps. What are the odds? A 40 percent probability is 40 ways
to win out of 100 possibilities. This means 100 minus 40 or 60 ways
to fail, so the odds are 40?to-60 for or 60?to-40 against the proposition.
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