View Single Post
Old 03-23-2011, 10:16 PM   #14
Dragondog
Never Been Pretty
 
Join Date: Jan 2005
Default Re: Chess Skill Levels

Quote:
Originally Posted by Rev. Pee Kitty View Post
If you're using Regular Contests, then the only real question is about differences of skill. Because in GURPS, by the time you get to where the "masters" are playing (e.g., skill-20 vs. skill-16), you'll need to use the rules for adjusting Regular Contests to bring them back down to reasonable levels (in this example, skill-14 vs skill-10). So at high levels, everything will come down to "skill-X vs. skill-10, where X is 10+".

So just to do some quick, back-of-the-envelope math here, a Regular Contest will have one of three results for each roll: A wins (i.e., A succeeds and B fails), B wins (i.e., A fails and B succeeds), or the Contest continues. So all we really have to do is look at the probability of the first two cases and compare them.

Now, the odds work out to be exactly what's shown on p. B171 -- that is, a difference of +1 means that the better player wins 62.5% of the time, +2 means 74.1%, and so on. If you want proof, read the following paragraph. If not, skip it. :)

As explained in paragraph 1, above, it's fairly safe to assume that B will always be 10 (0.50). So the odds of A winning on a given roll are (A * 0.5), while the odds of B winning are ((1-A) * 0.5). Once you know both odds, you sum them to determine the total range of useful possibilities. So (A*0.5) + ((1-A)*0.5) = 0.5*(A + (1-A)) = 0.5*1 = 0.5. This means that the actual odds of A winning, expressed in a way that avoids the chance of infinite ties in the Contest, are (A * 0.5)/0.5, or A. And the odds of B winning are ((1-A) * 0.5)/0.5, or (1-A).

So for the purpose of a Regular Contest, a match between two people with a +2 difference in skill levels makes it 0.741 likely that the better player will succeed. So it sounds to me like every +1 skill is +100 difference in ELO or FIDE or what have you, judging by what I've read here in this thread. (I don't really speak chess rankings, and I tend to avoid playing with people who do -- no offense intended to anyone! Just some people take certain boardgames way too seriously.)
As a simplification for skills higher than 13 this is fine. I've used the same math, but without the simplification, and I've included skills lower than 14 too.

Though I enjoy playing chess, everything I know about the chess rating system I've read online in preparation for posts made in this thread, so none taken.
Dragondog is offline   Reply With Quote