Re: Re: odds

From: Gavain Sweetman <gavain.sweetman_at_...>
Date: Fri, 6 Nov 2009 02:04:27 -0800 (PST)


> ----- Original Message ----
> From: Todd Gardiner <todd.gardiner_at_...m>
<snip table>

> Totals
> Ties 14 or 3.5%
> Skill 10 wins 180 or 45.0%
> Skill 15 wins 205 or 51.3%
> Both lose 1 or .3%

> Skill 15 has an 6.3% edge over Skill 10.

This is correct but by breaking it down even further:

Skill 15 vs resistance of 10:

Complete Victory 1 = 0.3%

Major Victory       23 = 5.8%
Minor Victory      139 = 34.8%
Marginal Victory   42 = 10.5%
Tie                      15 = 3.8%  (including the 20 vs 20 roll)
Marginal defeat   107 = 26.8%
Minor Defeat        59 = 14.8%
Major Defeat        13 = 3.3%

Complete Defeat 1 = 0.3%

so yes skill 15 has the better chance of winning but they also have a better chance of winning better.

The number I like to calculate is the ratio of wins to losses which gives the odds of winning. For skill 15 vs 10 that is 1.14. The relationship is non-linear so the rate of increase in the win ratio increases with each extra point:

skill 16 vs 10 = 1.21
skill 17 vs 10 = 1.29
skill 18 vs 10 = 1.40
skill 19 vs 10 = 1.53

The rate of increase falls again going past the mastery point

skill 1w vs 10 = 1.54
skill 2w vs 10 = 1.55
skill 3w vs 10 = 1.57
skill 4w vs 10 = 1.61
skill 5w vs 10 = 1.67
skill 6w vs 10 = 1.75
skill 7w vs 10 = 1.86
skill 8w vs 10 = 1.99
skill 9w vs 10 = 2.17
skill 10w vs 10 = 2.39
skill 11w vs 10 = 2.67
skill 12w vs 10 = 3.00
skill 13w vs 10 = 3.40
skill 14w vs 10 = 3.88
skill 15w vs 10 = 4.48
skill 16w vs 10 = 5.25
skill 17w vs 10 = 6.27
skill 18w vs 10 = 7.70

skill 19w vs 10 = 9.81
skill 20w vs 10 = 9.81

No only that but your quality of wins gets greater and the quality of losses gets less :-))

for skill 10w vs 10 the complete breakdown looks like this:

Complete Victory 19 = 4.8%

Major Victory        99 = 24.8%
Minor Victory      164 = 41.0%
Marginal Victory     0 = 0.0%
Tie                        0 = 0.0%
Marginal defeat    99 = 24.8%
Minor Defeat        18 = 4.5%
Major Defeat          1 = 0.3%

Complete Defeat 0 = 0.0%

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