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What is probability? According to Webster’s Dictionary,
probability is
1. The quality or condition of being probable; likelihood.
2. A probable situation, condition, or event: Her election
is a clear probability.
3.
a. The likelihood that a given event will occur: little
probability of rain tonight.
b. A number expressing the likelihood that a specific
event will occur expressed as the ratio of the number of actual
occurrences to the number of possible occurrences.
The definition, number 3b will be used for charting players as
they are shooting craps. Success in
craps is the continued throwing of
more than six numbers before the seven is thrown. What’s happening at
this present time has no influence on what will happen in the future or
what happened in the past.
This first chart shows the result of the standard 36 possible ways
of setting the dice on the axle with the 16 possible faces of the two
dice. The total number possible throws are 576.
The seven would appear 96 times out of the 576 throws.
The two and twelve would appear 16 times out of 576 throws.
The three and eleven would appear 32 times out of 576 throws.
The four and ten would appear 48 times out of 576 throws.
The five and nine would appear 64 times out of 576 throws.
The six and eight would appear 80 times out of 576 throws.
|
576 percentage standard 2-12 |
|
Standard% 7 96/576 |
Standard% 2-12 16/576 |
Standard% 3-11 32/576 |
Standard% 4-10 48/576 |
Standard% 5-9 64/576 |
Standard% 6-8 80/576 |
|
16.67% |
2.78% |
5.56% |
8.33% |
11.11% |
13.89% |
The next chart divided the number of throws for each number into
576 total throws.
The seven would appear 1 time for every 6 throws.
The two and twelve would appear 1 time for every 36 throws.
The three and eleven would appear 1 time for every 18 throws.
The four and ten would appear 1 time for every 12 throws.
The five and nine would appear 1 time for every 9 throws.
The six and eight would appear 1 time for every 7.2 throws.
|
576 standard divided by count |
|
Seven |
Two |
Three |
Four |
Five |
Six |
Eight |
Nine |
Ten |
Eleven |
Twelve |
|
6 |
36 |
18 |
12 |
9 |
7.2 |
7.2 |
9 |
12 |
18 |
36 |
The next chart was created by throwing 576 throws.
Each of the 36
axel sets and the 16 faces of the two dice
were used to determine the
results.
The seven appeared 96 times verses the standard of
96 times out of
the 576 throws.
The two appeared 21 times verses the standard
16 times out of the 576
throws.
The three appeared 44 times verses the standard
32 times out of
the 576 throws.
The four appeared 46 times verses the standard
48 times out of the 576
throws.
The five appeared 69 times verses the standard
64 times out of the
576 throws.
The six appeared 79 times verses the standard
80 times out of the
576 throws.
The eight appeared 70 times verses the standard
80 times out of
the 576 throws.
The nine appeared 56 times verses the standard
64 times out of the
576 throws.
The ten appeared 54 times verses the standard
48 times out of the
576 throws.
The eleven appeared 33 times verses the standard
32 times out of
the 576 throws.
The twelve appeared 8 times verses the standard
16 times out of
the 576 throws.
|
576 percentage 2-12 |
|
2-12 |
Numbers thrown |
Percentages |
|
2 |
21 |
3.65% |
|
3 |
44 |
7.64% |
|
4 |
46 |
7.99% |
|
5 |
69 |
11.98% |
|
6 |
79 |
13.72% |
|
7 |
96 |
16.67% |
|
8 |
70 |
12.15% |
|
9 |
56 |
9.72% |
|
10 |
54 |
9.38% |
|
11 |
33 |
5.73% |
|
12 |
8 |
1.39% |
The next chart divided the number of throws for each number into
576 total throws.
The seven would appear 1 time for every 6 throws and the standard
is 6.
The two would appear 1 time for every 27.4 throws and the standard
is 36.
The three would appear 1 time for every 13.1 throws and the
standard is 18.
The four would appear 1 time for every 12.5 throws and the
standard is 12.
The six would appear 1 time for every 7.3 throws and the standard
is 7.2.
The eight would appear 1 time for every 8.2 throws and the
standard is 7.2.
The nine would appear 1 time for every 10.3 throws and the
standard is 9.
The ten would appear 1 time for every 10.7 throws and the standard
is 12.
The eleven would appear 1 time for every 17.5 throws and the
standard is 18.
The twelve would appear 1 time for every 72 throws and the
standard is 36.
|
576 divided by count |
|
Sevens |
Two |
Three |
Four |
Five |
Six |
|
6 |
27.4285 |
13.0909 |
12.5217 |
8.3478 |
7.2911 |
|
576 divided by count |
|
Eight |
Nine |
Ten |
Eleven |
Twelve |
|
8.2285 |
10.2857 |
10.6666 |
17.4545 |
72 |
I threw using the same dice grips, table length and table position.
The closeness of the test results prove that the probability of
throwing close to the standard exists.
If the test was conducted throwing
ten times the amount,
the closer the results would be toward the
standard.
The game of craps is played with a relatively short amount of
throwing per person. The shortening
of the games could cause more
variable numbers being thrown than the standard.
The next chart is a standard chart for the six most favorite sets
used by most controlled throwers.
I look at the left face of each dice
as a determining way of setting the axels.
When I mention the 6 set, I am referring to the left dice axel
setting of a 6-1 and the right dice axel setting of a 6-1.
The 36 axel settings are:
6-1/6-1 --- 6-1/1-6 --- 1-6/6-1 --- 1-6/1-6
5-2/5/2 --- 5-2/2-5 --- 2-5/5-2 --- 2-5/2-5
4-3/4-3 --- 4-3/3-4 --- 3-4/4-3 --- 3-4/3-4
6-1/5-2 --- 6-1/2-5 --- 1-6/5-2 --- 1-6/2-5
5-2/6-1 --- 5-2/1-6 --- 2-5/6-1 --- 2-5/1-6
6-1/4-3 --- 6-1/3-4 --- 1-6/4-3 --- 1-6/3-4
4-3/6-1 --- 4-3/1-6 --- 3-4/6-1 --- 3-4/1-6
5-2/4-3 --- 5-2/3-4 --- 2-5/4-3 --- 2-5/3-4
4-3/5-2 --- 4-3/2-5 --- 3-4/5-2 --- 3-4/2-5
The six different sets that were thrown will be compared to the
standard.
The standard sets of the six set, five set and the four set offers four different ways of throwing
a seven. The other three sets only have
two ways of throwing a seven.
This chart displays four of the
major sets as a standard.
Set 6 the left dice axel setting and the right dice axel setting. 6-1
6-1
|
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12
|
| |
|
2-2 |
2-3 |
2-4 |
2-5 |
3-5 |
4-5 |
5-5 |
|
|
| |
|
|
3-2 |
4-2 |
5-2 |
5-3 |
5-4 |
|
|
|
| |
|
|
|
3-3 |
3-4 |
4-4 |
|
|
|
|
| |
|
|
|
|
4-3 |
|
|
|
|
|
Set 5 the left dice axel setting and the right dice axel setting. 5-2
5-2
|
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12
|
|
1-1 |
|
1-3 |
1-4 |
3-3 |
1-6 |
4-4 |
3-6 |
4-6 |
|
6-6 |
| |
|
3-1 |
4-1 |
|
6-1 |
|
6-3 |
6-4 |
|
|
| |
|
|
|
|
3-4 |
|
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| |
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4-3 |
|
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|
|
|
Set 4 the left dice axel setting and the right dice axel setting. 4-3
4-3
|
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12
|
|
1-1 |
1-2 |
2-2 |
|
1-5 |
1-6 |
2-6 |
|
5-5 |
5-6 |
6-6 |
| |
2-1 |
|
|
5-1 |
6-1 |
6-2 |
|
|
6-5 |
|
| |
|
|
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2-5 |
|
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|
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| |
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5-2 |
|
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Set 65 or V3 the left dice axel setting and the right dice axel
setting. 6-1 5-2
|
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12
|
|
|
2-1 |
3-1 |
2-3 |
2-4 |
3-4 |
2-6 |
3-6 |
4-6 |
5-6 |
|
| |
|
|
4-1 |
5-1 |
4-3 |
5-3 |
5-4 |
|
|
|
| |
|
|
|
3-3 |
|
4-4 |
|
|
|
|
Set 64 the left dice axel setting and the right dice axel setting.
6-1 4-3
|
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12
|
| |
2-1 |
3-1 |
3-2 |
4-2 |
2-5 |
2-6 |
3-6 |
4-6 |
5-6 |
|
| |
|
2-2 |
4-1 |
5-1 |
5-2 |
3-5 |
5-4 |
5-5 |
|
|
Set 54 or 6H6 the left dice axel setting and the right dice axel
setting. 5-2 4-3
|
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12
|
|
1-1 |
1-2 |
3-1 |
3-2 |
1-5 |
1-6 |
3-5 |
3-6 |
4-6 |
6-5 |
6-6 |
| |
|
|
4-1 |
4-2 |
6-1 |
6-2 |
4-5 |
|
|
|
Let's compare the
difference between the throws and the standard
Home
|
66 set count and % |
|
Percentage |
2-12 |
Count totals |
|
37.50% |
3 |
6 |
|
12.50% |
5 |
2 |
|
18.75% |
6 |
3 |
|
12.50% |
7 |
2 |
|
6.25% |
8 |
1 |
|
6.25% |
10 |
1 |
|
6.25% |
11 |
1 |
The seven appeared 2 times verses the standard of 4 times out of
the 16 throws.
The two appeared 0 times verses the standard 0 times out of the 16
throws.
The three appeared 6 times verses the standard 0 times out of the
16 throws.
The four appeared 0 times verses the standard 1 time out of the 16
throws.
The five appeared 2 times verses the standard 2 times out of the
16 throws.
The six appeared 3 times verses the standard 3 times out of the 16
throws.
The eight appeared 1 time verses the standard 3 times out of the
16 throws.
The nine appeared 0 times verses the standard 2 times out of the
16 throws.
The ten appeared 1 time verses the standard 1 time out of the 16
throws.
The eleven appeared 1 time verses the standard 0 times out of the
16 throws.
The twelve appeared 0 times verses the standard 0 times out of the
16 throws.
|
55 set count and % |
|
Percentage |
2-12 |
Count totals |
|
6.25% |
2 |
1 |
|
12.50% |
4 |
2 |
|
6.25% |
5 |
1 |
|
6.25% |
6 |
1 |
|
12.50% |
7 |
2 |
|
18.75% |
8 |
3 |
|
18.75% |
9 |
3 |
|
18.75% |
10 |
3 |
The seven appeared 2 times verses the standard of 4 times out of
the 16 throws.
The two appeared 1 time verses the standard 1 time out of the 16 throws.
The three appeared 0 times verses the standard 0 times out of the
16 throws.
The four appeared 2 times verses the standard 2 times out of the 16
throws.
The five appeared 1 time verses the standard 2 times out of the 16
throws.
The six appeared 1 time verses the standard 1 time out of the 16
throws.
The eight appeared 3 times verses the standard 1 time out of the
16 throws.
The nine appeared 3 times verses the standard 2 times out of the
16 throws.
The ten appeared 3 times verses the standard 2 times out of the 16
throws.
The eleven appeared 0 times verses the standard 0 times out of the
16 throws.
The twelve appeared 0 times verses the standard 1 time out of the
16 throws.
|
44 set count and % |
|
Percentage |
2-12 |
Count totals |
|
6.25% |
3 |
1 |
|
12.50% |
5 |
2 |
|
6.25% |
6 |
1 |
|
18.75% |
7 |
3 |
|
25.00% |
9 |
4 |
|
18.75% |
10 |
3 |
|
12.50% |
11 |
2 |
The seven appeared 3 times verses the standard of 4 times out of
the 16 throws.
The two appeared 0 times verses the standard 1 time out of the 16
throws.
The three appeared 1 time verses the standard 3 times out of the
16 throws.
The four appeared 0 times verses the standard 1 time out of the 16
throws.
The five appeared 2 times verses the standard 0 times out of the
16 throws.
The six appeared 1 time verses the standard 2 times out of the 16
throws.
The eight appeared 0 times verses the standard 2 times out of the
16 throws.
The nine appeared 4 times verses the standard 0 times out of the
16 throws.
The ten appeared 3 times verses the standard 1 time out of the 16
throws.
The eleven appeared 2 times verses the standard 2 times out of the
16 throws.
The twelve appeared 0 times verses the standard 1 time out of the
16 throws.
|
65 set and count % |
|
Percentage |
2-12 |
Count totals |
|
12.50% |
4 |
2 |
|
25.00% |
5 |
4 |
|
18.75% |
6 |
3 |
|
12.50% |
7 |
2 |
|
25.00% |
8 |
4 |
|
6.25% |
9 |
1 |
The seven appeared 2 times verses the standard of 2 times out of
the 16 throws.
The two appeared 0 times verses the standard 0 times out of the 16
throws.
The three appeared 0 times verses the standard 1 time out of the
16 throws.
The four appeared 2 times verses the standard 1 time out of the 16
throws.
The five appeared 4 times verses the standard 2 times out of the
16 throws.
The six appeared 3 times verses the standard 3 time out of the 16
throws.
The eight appeared 4 times verses the standard 3 times out of the
16 throws.
The nine appeared 1 time verses the standard 2 times out of the 16
throws.
The ten appeared 0 times verses the standard 1 time out of the 16
throws.
The eleven appeared 0 times verses the standard 1 time out of the
16 throws.
The twelve appeared 0 times verses the standard 0 time out of the
16 throws.
Home
|
64 set count and % |
|
Percentage |
2-12 |
Count totals |
|
6.25% |
2 |
1 |
|
6.25% |
3 |
1 |
|
6.25% |
4 |
1 |
|
6.25% |
5 |
1 |
|
6.25% |
6 |
1 |
|
12.50% |
7 |
2 |
|
12.50% |
8 |
2 |
|
18.75% |
9 |
3 |
|
12.50% |
10 |
2 |
|
12.50% |
11 |
2 |
The seven appeared 2 times verses the standard of 2 times out of
the 16 throws.
The two appeared 1 time verses the standard 0 times out of the 16
throws.
The three appeared 1 time verses the standard 1 time out of the 16
throws.
The four appeared 1 time verses the standard 2 times out of the 16
throws.
The five appeared 1 time verses the standard 2 times out of the 16
throws.
The six appeared 1 time verses the standard 2 times out of the 16
throws.
The eight appeared 2 times verses the standard 2 times out of the
16 throws.
The nine appeared 3 times verses the standard 2 times out of the
16 throws.
The ten appeared 2 times verses the standard 2 times out of the 16
throws.
The eleven appeared 2 times verses the standard 1 time out of the
16 throws.
The twelve appeared 0 times verses the standard 0 times out of the
16 throws.
|
54 set count and % |
|
Percentage |
2-12 |
Count totals |
|
18.75% |
4 |
3 |
|
6.25% |
5 |
1 |
|
6.25% |
6 |
1 |
|
31.25% |
7 |
5 |
|
18.75% |
8 |
3 |
|
6.25% |
9 |
1 |
|
6.25% |
10 |
1 |
|
6.25% |
11 |
1 |
The seven appeared 5 times verses the standard of 2 times out of
the 16 throws.
The two appeared 0 time verses the standard 1 time out of the 16 throws.
The three appeared 0 times verses the standard 1 time out of the
16 throws.
The four appeared 3 times verses the standard 1 time out of the 16
throws.
The five appeared 1 time verses the standard 2 times out of the 16
throws.
The six appeared 1 time verses the standard 2 times out of the 16
throws.
The eight appeared 3 times verses the standard 2 times out of the
16 throws.
The nine appeared 1 time verses the standard 2 times out of the 16
throws.
The ten appeared 1time verses the standard 1 time out of the 16
throws.
The eleven appeared 1 time verses the standard 2 times out of the
16 throws.
The twelve appeared 0 times verses the standard 1 time out of the
16 throws.
As you can see the skewing occurred more on
shorter throwing.
The testing will continue shooting 96 times to see what the
relationship would be compared
to the standard.
Meyer Bendavid
Craps Coach
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