1.THE BASIC TOOLS In order to really understand the game of craps, you must be able to
calculate the odds of different possible events occurring in the rolls
of
the dice. In most cases, this is extremely easy to do. The fundamental
tool
in doing so is a knowledge of how many ways each of the different
numbers at
craps can be rolled. Although there are eleven possible numbers that
can be
rolled with two dice (anywhere from a total of 2 to a total of 12),
there
are actually 36 different possible combinations that can come up on the
two
dice. This is because each die has six sides and each of the six sides
on
the first die can come up in combination with any of the six sides on
the
other die: six times six gives us thirty-six combinations.
The number 2, the lowest total, can only be rolled with one combination
(1-1). This is also true of 12, the highest total, which can only be
rolled
with 6-6. By contrast, the number 3 can be rolled with two combinations
(2-1
or 1-2). Similarly, the number 11 can be rolled with two combinations
(5-6
or 6-5). The number 4 can be rolled three ways (1-3, 2-2, 3-1), and the
number 10 can also be made three ways (4-6, 5-5, 6-4). The number 5 can
be
rolled with four combinations (1-4, 2-3, 3-2, 4-1), and the number 9
can
also be rolled with four combinations (3-6, 4-5, 5-4, 6-3). The number
6 can
be made five ways (1-5, 2-4, 3-3, 4-2, 5-1), and the number 8 can also
be
rolled five ways (2-6, 3-5, 4-4, 5-3, 6-2). Finally, the number 7 can
be
rolled with any of six different combinations (1-6, 2-5, 3-4, 4-3, 5-2,
6-1). Obviously, the more combinations that a number can be rolled
with, the
more frequently that umber will come up. So it is no accident that the
number 7 is the central number at craps. It was chosen because it is
the
most frequently rolled number.
All of this may seem very simple, and it is. But if you plan to play
much
craps, I urge you to memorize the contents of the above paragraph. You
will
constantly use that information in calculating various odds and
probabilities in the game. Remember that there are a total of
thirty-six
possible combinations. Remember how many ways each number can be
rolled,
Take particular note of the symmetry between the number 2 and 12, 3 and
11,
4 and 10, 5 and 9, and 6 and 8. This means that any odds that apply to
the
number 6 will also apply to the number 8. Similarly, any calculations
you
make concerning the number 5 will be just as valid for the number 9.
This
symmetry is graphically illustrated in the illustration below.
You will note that all the paired numbers add up to 14. This is because
any
tow opposite sides of a pair of dice must always add up to 14. Every
time
you roll a pair of dice and get a 6 on top of the dice, you have also
gotten
and 8 on the bottom of the two dice. If follows, therefore, that 8 can
be
made with exactly the same number of combinations as 6 can. The same is
true
of 5 and 9, 4 and 10, 3 and 11, and also 2 and 12. As soon as you get
accustomed to thinking in terms of these pairings, you will find that
you
have, in effect, only half as much to remember about the various bets,
payoffs, odds, and percentages at craps.
What throws some people is the notion that a combination like 4-3 is
different from 3-4. To them, they are the same combination and should
not be
counted twice. This is an understandable but dangerous fallacy. Someone
who
thinks this way will believe that 6 can be rolled three ways (1-5, 2-4,
3-3)
and that 7 can also be rolled three ways (1-6, 2-5, 3-4). He will
therefore
believe that a wager that a 6 will be rolled before rolling a 7 is an
even-money bet since either number is equally likely to come up. In
fact,
someone betting that he can roll a 6 before a 7 should be getting 6 to
5
odds in order for the bet to be a fair one (six ways of rolling a 7
versus
five ways of rolling a 6). Anyone who takes that bet at even money will
soon
be bankrupt.
You can prove this to yourself by getting two dice of different colors,
for
example, one green die and one white die. Start rolling the dice. One
time
you may roll a 7 with 4 on the green die and 3 on the white die. Later
you
may roll a 7 with a 3 on the green die and 4 on the white die. Clearly,
these are two different ways of rolling a 7. The two die faces that
combined
to produce the first 7 are completely different from the two die faces
that
combined to make the second 7. They must be counted as two different
combinations in order to correctly calculate dice odds. By contrast,
you may
roll a 6 with a 3 on the green die and a 3 on the white die. This is
the
single combination that will give you a total of 6 with two3s. That is
why
you cannot equate a reversible combination like 3-4 with one like 3-3. see more > > >
