Friday, September 2, 2016

A quick diversion on probabilities

Over on the RPGSite a poster named Cave Bear asked about probabilities for adapting from 2d6 to 2d12. I couldn't easily post the numbers on the forum, so as a temporary measure I'm putting that here. And since H+I uses a 2d6 system it is at least somewhat relevant.

The system in question uses range bands with associated probabilities of

Range Band 2d6 P(iin Range)
6~8 for an easy action 44.4%
9~11 for a doable action 25.0%
12~15 for a hard action 2.8%
16+ for a nearly impossible action 0.0%


Probabilities for 2d6
N on 2d6 Freq(N) P( N) P(≤N) P(≥N)
2 1 2.8% 2.8% 100.0%
3 2 5.6% 8.3% 97.2%
4 3 8.3% 16.7% 91.7%
5 4 11.1% 27.8% 83.3%
6 5 13.9% 41.7% 72.2%
7 6 16.7% 58.3% 58.3%
8 5 13.9% 72.2% 41.7%
9 4 11.1% 83.3% 27.8%
10 3 8.3% 91.7% 16.7%
11 2 5.6% 97.2% 8.3%
12 1 2.8% 100.0% 2.8%
16+ 0 0.0% 100.0%

Probabilities for 2d10

N on 2d10 Freq(N) P( N) P(≤N) P(≥N)
2 1 1.0% 1.0% 100.0%
3 2 2.0% 3.0% 99.0%
4 3 3.0% 6.0% 97.0%
5 4 4.0% 10.0% 94.0%
6 5 5.0% 15.0% 90.0%
7 6 6.0% 21.0% 85.0%
8 7 7.0% 28.0% 79.0%
9 8 8.0% 36.0% 72.0%
10 9 9.0% 45.0% 64.0%
11 10 10.0% 55.0% 55.0%
12 9 9.0% 64.0% 45.0%
13 8 8.0% 72.0% 36.0%
14 7 7.0% 79.0% 28.0%
15 6 6.0% 85.0% 21.0%
16 5 5.0% 90.0% 15.0%
17 4 4.0% 94.0% 10.0%
18 3 3.0% 97.0% 6.0%
19 2 2.0% 99.0% 3.0%
20 1 1.0% 100.0% 1.0%
25+




With ~ Range Bands for 2d20

Range Band P(iin Range)
9-13  for an easy action 44.0%
14-18 for a doable action 25.0%
19-20 for a hard action 3.0%
25+ for a nearly impossible action

Probabilities for 2d12

N on 2d12 Freq(N) P( N) P(≤N) P(≥N)
2 1 0.7% 0.7% 100.0%
3 2 1.4% 2.1% 99.3%
4 3 2.1% 4.2% 97.9%
5 4 2.8% 6.9% 95.8%
6 5 3.5% 10.4% 93.1%
7 6 4.2% 14.6% 89.6%
8 7 4.9% 19.4% 85.4%
9 8 5.6% 25.0% 80.6%
10 9 6.3% 31.3% 75.0%
11 10 6.9% 38.2% 68.8%
12 11 7.6% 45.8% 61.8%
13 12 8.3% 54.2% 54.2%
14 11 7.6% 61.8% 45.8%
15 10 6.9% 68.8% 38.2%
16 9 6.3% 75.0% 31.3%
17 8 5.6% 80.6% 25.0%
18 7 4.9% 85.4% 19.4%
19 6 4.2% 89.6% 14.6%
20 5 3.5% 93.1% 10.4%
21 4 2.8% 95.8% 6.9%
22 3 2.1% 97.9% 4.2%
23 2 1.4% 99.3% 2.1%
24 1 0.7% 100.0% 0.7%
28 or 30+ 0 0.0% 100.0%

With ~Range Bands for 2d12 
Range BandP(iin Range)
11-16  for an easy action43.8%
17-22 for a doable action22.9%
23-27 for a hard action2.1%
28+ for a nearly impossible action

And here's the picture












4 comments:

  1. You are welcome. I didn't explain much so I hope the meaning was clear.

    If you are familiar with Excel it is easy to create tables like this and calculate the probabilities.

    ReplyDelete
  2. Nice! As someone who is terrible with probabilities, this is very helpful! Thanks for posting it.

    ReplyDelete
  3. I'm glad it was helpful to both of you. :-)

    ReplyDelete