WOLFRAM NOTEBOOK

Dice Probabilities

​
number of dice
6
number of sides
2
4
6
8
10
12
20
tablestart
roll
chances
chance
freq.
24
25927.
2.59
38.6
25
30492.
3.05
32.8
26
35127.
3.51
28.5
27
39662.
3.97
25.2
28
43917.
4.39
22.8
29
47712.
4.77
21.0
30
50877.
5.09
19.7
31
53262.
5.33
18.8
32
54747.
5.47
18.3
33
55252.
5.53
18.1
34
54747.
5.47
18.3
35
53262.
5.33
18.8
36
50877.
5.09
19.7
37
47712.
4.77
21.0
38
43917.
4.39
22.8
39
39662.
3.97
25.2
total chances:
1000000
This table and graph show the chances for each outcome of a number of
n
-sided dice. The chances column lists chances out of total chances. The % chance column is 100 × probability. The frequency is the inverse of probability; that is, the odds are 1 in
x
of a given outcome.

Details

Chances are calculated by representing an
n
-sided die as the polynomial (
1
x
+
2
x
+...+
n
x
), and then multiplying the dice together. The chances can be directly read off the coefficients of the expanded result.

External Links

Permanent Citation

Jonathan Wooldridge
​
​"Dice Probabilities"​
​http://demonstrations.wolfram.com/DiceProbabilities/​
​Wolfram Demonstrations Project​
​Published: August 29, 2008
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