2d20 Math Probabilities

Aluman · Admin Posts: 45 Join date: 2008-08-25

2d20 has an average of 21, a low of 2 and high 40

Code:

Number Raw Chance Percentage
2 1/400 .25
3 2/400 .5
4 3/400 .75
5 4/400 1
6 5/400 1.25
7 6/400 1.5
8 7/400 1.75
9 8/400 2
10 9/400 2.25
11 10/400 2.5
12 11/400 2.75
13 12/400 3
14 13/400 3.25
15 14/400 3.5
16 15/400 3.75
17 16/400 4
18 17/400 4.25
19 18/400 4.5
20 19/400 4.75
21 20/400 5
22 19/400 4.75
23 18/400 4.5
24 17/400 4.25
25 16/400 4
26 15/400 3.75
27 14/400 3.5
28 13/400 3.25
29 12/400 3
30 11/400 2.75
31 10/400 2.5
32 9/400 2.25
33 8/400 2
34 7/400 1.75
35 6/400 1.5
36 5/400 1.25
37 4/400 1
38 3/400 .75
39 2/400 .5
40 1/400 .25

squarecircle · Subject: Re: 2d20 Math Probabilities Mon Aug 25, 2008 5:30 am

So this means, rolling 2d20 without modifiers and trying to hit a target number:

Code:

Target
Number Raw Chance Percent Chance
2 400/400 100%
3 399/400 99.75%
4 397/400 99.25%
5 394/400 98.5%
6 390/400 97.5%
7 385/400 96.25%
8 379/400 94.75%
9 372/400 93%
10 364/400 91%
11 355/400 88.75%
12 345/400 86.25%
13 334/400 83.5%
14 322/400 80.5%
15 309/400 77.25%
16 295/400 73.75%
17 280/400 70%
18 264/400 66%
19 247/400 61.75%
20 229/400 57.25%
21 210/400 52.5%
22 190/400 47.5%
23 171/400 42.75%
24 153/400 38.25%
25 136/400 34%
26 120/400 30%
27 105/400 26.25%
28 91/400 22.75%
29 78/400 19.5%
30 66/400 16.5%
31 55/400 13.75%
32 45/400 11.25%
33 36/400 9%
34 28/400 7%
35 21/400 5.25%
36 15/400 3.75%
37 10/400 2.5%
38 6/400 1.5%
39 3/400 0.75%
40 1/400 0.25%

Is the math right? I based it on yours.

Aluman · Admin Posts: 45 Join date: 2008-08-25

Yup, that looks right at least.

which means 21-22 will be the half way mark (like 11 in D20)

Aluman · Admin Posts: 45 Join date: 2008-08-25

So working from that:
21 is a simple diffculty (roughhly 50% chance of success)
27 is a medium diffculty (roughly 25% chance of success)
35 is a hard diffculty (roughly 05% chance of success)

If we have +1 /2 levels like 4E
21 for level 1
25 for level 10 (1/3ish chance at level 1)
30 for level 20 (1/6 chance at level 1)
35 for level 30 (1/20ish chane at level 1)

squarecircle · Subject: Re: 2d20 Math Probabilities Tue Aug 26, 2008 7:25 am

Wouldn't a 50% chance of success be a moderate difficulty? I think of a "simple" difficulty as something that any ordinary person can pull off with relative ease, and a "moderate" difficulty as something a skilled person can pull off with relative ease (whereas an unskilled person would struggle but have perhaps still a decent chance of success).

10 very easy
17 easy
21 moderate
27 hard
35 very difficult

I'm not sure about the +1/2 levels. I'm not even sure we should have "true" levels per se, but I'll explain that in another thread.