Re: Some crunching of simple contest probabilities

From: Tim Ellis <tim_at_...>
Date: Sat, 01 Nov 2003 13:54:06 -0000

wrote:
>
>Obviously part of what happens with a mastery gap is that you "trade
>in" some portion of your absolute chance of winning for increased
>odds of "winning big" and possibly as important, much reduced odds
>of "losing big." With a mastery gap, for the same spread of skills,
>there are more minor, major, and complete, victories for the
>superior skill, and less marginal ones. Certainly there are times
>where a marginal victory won't do, so you are better off trying to
>adjust thing to hit a mastery gap, willing to accept a marginal
>defeat being more likely to increase your odds of a big win.
>

According to the spreadsheet I wrote when HW first came out**, the odds are as follows (for the higher of the 2 skills):

Contest 15 vs 5
Any victory 61.5%, Minor victory or better 58.25%, Major Victory or better 7.25%, Complete Victory 0.25%, Any Defeat 36.5%, Minor defeat or worse 13.5%, Major defeat or worse 2.5%, Complete Defeat* 0.5% (* includes the "Both Compleat Defeat special case)

Augmenting both sides equally to give a mastery advantage Contest 1W vs 11
Any Victory 56.75%, Minor Victory + 45.5%, Major Victory + 6.75%, Complete Victory 0.25%, Any Defeat 40.5%, Minor defeat - 7.25, Major defeat - 0.25%, Complete Defeat 0%

Having an extra mastery, but a low ability means you will usually be getting a "success", but are vulnerable to being beaten by a low rolling success by your opponent.

Augmenting both sides by 10
Contest 5W vs 15
Any Victory 52.75, minor victory+ 41.5%, Major victory+ 9.75, Complete Victory 1.25%, any defeat 43.5%, Minor defeat- 7.25%, major defeat- 0.25%, Complete Defeat 0

This shows what Bryan described - Your overall chance of winning a round might have gone down, but when you do win it will be a "bigger win", and when you lose it will be "smaller loss".

To continue with the "boundry" examples though Augment both sides to the maximum to maintain the net mastery gain Contest 10W vs 20
Any Victory 58.75%, Minor Victory+ 49.75%, Major Victory+ 2.5%, Complete Victory 0, any defeat 36.25%, minor defeat- 7%, major defeat-  25%, complete defeat 0%
(This is the special case where neither side can fumble)

• I'm trying to write another one to highlight the difference between a minor victory Success vs Fail and a minor victory Crit vs Success, since the latter is more desirable in an extended contest, since you get the benefit of more transfers...