Wednesday, April 15, 2009

Statistics!

Here's some good gouge I don't want to lose track of.

VARIANCE for XdN: X*(N^2-1)/12
ST DEV = SQ RT of VARIANCE

67%/95% rule (when CLT applies)...
That is, 67% of results fall within a Z-score of 1. 95% of results fall within a Z-score of 2.

4d6 DROP THE LOWEST:
Max 18
Min 3
Mean 12.2446
Std Dev 2.8468

But what does it mean? Simply put, if you roll 4d6 drop lowest, you are most likely to roll a 12. Additionally, there is a ? 68% chance that you’ll roll within one standard deviation of the mean, or [9,15]. The chances that you’ll get any given roll are in the table below:
Roll Probability Frequency ? Odds
3 0.000772 1 1 in 1,295
4 0.003086 4 1 in 324
5 0.007716 10 1 in 130
6 0.016204 21 1 in 62
7 0.029321 38 1 in 34
8 0.047840 62 1 in 21
9 0.070216 91 1 in 14
10 0.094136 122 1 in 11
11 0.114198 148 1 in 9
12 0.128858 167 1 in 8
13 0.132716 172 1 in 8
14 0.123457 160 1 in 8
15 0.101080 131 1 in 10
16 0.072531 94 1 in 14
17 0.041667 54 1 in 24
18 0.016204 21 1 in 62

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