Craps
Craps - Casino Edge - Crapshooters
| by Larry Edell, published on Wednesday,
October 3 2001 |
| |
| You are probably aware that a pair of dice has 36
combinations. The 2 and 12 can roll one way, the 3 and 11 two ways, the
4 and 10 three ways, the 5 and 9 four ways, the 6 and 8 five ways, and
the ubiquitous 7 can roll six ways. On the pass line, you can win with
the seven or eleven. The seven can be rolled six ways, and the eleven
two ways, so you will win 8 of 36 times on the pass line, or, 2/9 of the
time. You will lose on the pass line with a 2, 3 (twice) or 12, so you
lose 4 of 36 times, or 1/9 of the time. This means that 1/3 of the time,
the bet is decided without a point, as 1/9 (losing) plus 2/9 (winning)
equals 3/9 or 1/3. The other 2/3 of the time a point is established.
There are six points - the 4, 5, 6, 8, 9 and 10, with twenty four
possible point rolls. If the point is 4 (or 10), as an example, there
are 3 ways to roll a 4 (or 10) but 6 ways to roll a 7. Thus, a four (or
10), which rolls three times, compared to the seven, which rolls six
times, will roll 3/9 (or 1/3) of the time a seven does. Similarly, with
the five and nine, rolling four times, each is 4/10 (or 2/5) as likely
to roll as the seven. The six and eight, rolling five times, is 5/11 as
likely to roll as the seven. To get the winning percentage then, we
simply have to take how often you can possibly win with each point, and
multiply it by how often each point occurs. The casino's edge is the
losing percentage minus the winning percentage. After the come-out,
there are six point numbers which can be rolled twenty four possible
ways (4-3,5-4, 6-5, 8-5, 9-4, 10-3). The four or ten will roll 3/24 (or
1/8) of the time. The five or nine will roll 4/24 (or 1/6) of the time.
And the six or eight will roll 5/24 of the time. The chance of winning
the four or ten, then, is 1/3 of the time, but only comes up 1/8 of the
time. The chance of winning the 5 or 9 is 2/5 of the time, and comes up
1/6 of the time. And, the chance of winning the 6 or 8 is 5/11 of the
time, and comes up 5/24 of the time. So, for the 4 and 10, we multiply
1/3 x 1/8 x 2. For the five and nine, we multiply 2/5 x 1/6 x 2. And for
the six and eight, we multiply 5/11 x 5/24 x 2. All this adds up to
67/165. However, we know from before that an actual point is established
only 2/3 of the time. 1/3 of the the time you will win or lose without
the point being established. And, when no point is established, you'll
win 2/3 of the time and lose 1/3 of the time. So, we need to take 2/3 of
67/165 and add it to 1/3 of 2/3, which is 244/495, or the winning
percentage, which is 49.3%, or .493. Since the winning percentage is
49.3%, the losing percentage is 50.7% (or .507). We can now finally find
the house edge, in percentage, by subtracting the winning percentage
(49.3%) from the losing percentage (50.7%). This is 1.4%, the house edge
for the pass line with no odds. It's not important that you know how
this 1.4% figure was calculated, but at least now you know! Next time
you play, you'll have just a little more knowledge than the next guy!
And, as always, don`t forget to tell your friends about this article on
Craps - Casino Edge - Crapshooters |
|
|
