Re: Some crunching of simple contest probabilities

From: Bryan <bethexton_at_...>
Date: Fri, 31 Oct 2003 14:58:51 -0000

• In HeroQuest-rules_at_yahoogroups.com, Henk Langeveld <hlangeveld_at_m...> wrote:
  >
  > How would you factor in the effects of 'bumping', and the whole
  scale
  > of success levels (marginal, minor, major). The 9W<->11 "loss" may
  > have the same narrative effect as the 19<->2 "win".
  >
  Sorry, perhaps I wasn't clear about wins and losses. I was calling any level of victory a win, and any level of failure a loss, and the cases with a mastery included the effect of the bump. In other words, in a 5W versus 17, if the superior ability rolls 19 and the inferior ability rolls 18, the superior ability's roll is bumped from a failure to a success, which makes it success versus a failure, for a minor victory, which I call a win for the superior ability.

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.

I was a little surprised to see the odds of winning between two skills with the same gap vary depending on the offset. After all, one of the cool things about the system is that is slides scales well. This is still broadly true, 15W4 versus 5W4 has the same odds of success as 15 versus 5. It is just interesting how different the odds are for 5W versus 15, given the same 10 point gap. Although the effect is not so large that you will notice it often, it is probably enough to keep in mind as a narrator—you can use a scary big skill gap without quite such an imbalance if you keep the score split evenly spread over the mastery step—or as a more tactician oriented player. Well, OK, something to keep in mind if you are freakishly obsessed with numbers the way I am :)

Obviously people who have had a chance to play the system a lot will have simply internalized much of this. But those who don't get to do, analyze.

--Bryan