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Old 03-23-2011, 10:39 PM   #11
PK
 
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Default Re: Chess Skill Levels

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.)
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Old 03-23-2011, 10:46 PM   #12
Purple Haze
 
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Default Re: Chess Skill Levels

Okay. Assuming you normalize so that the weaker player has a skill of 10, then a skill of 12 wins about 74% of regular contests.

Code:
Elo          Skill
 800         6
1000         8
1200         10
1400         12
1600         14
1800         16
2000         18
2200         20
2400         22
2600         24
2800         26
3000         28
Means Magnus Carlsson has 68 points in chess, 13,600 hours, that's probably close.
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Old 03-23-2011, 11:12 PM   #13
Not another shrubbery
 
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Default Re: Chess Skill Levels

Quote:
Originally Posted by Dragondog
I'm using the probabilities given by the ranking system to determine a skill level. The only way to change things would be to change what skill level corresponds with grandmaster (2500) as everything else depends on that.
For me, I would rather peg the top skill level in the 20-25 range, assume the default level rating is something close to Purple's proposal of 800, equate that to a SL of 6, then distribute the FIDE rating range {typical beginner; Kasparov} evenly around the GURPS skill level range {6;20-25}. For the purpose of allowing even higher ratings open to our theoretical maximum of 25, we can assign Kasparov's peak rating something less... say, 24. 18 GURPS SLs would be representing 2000 FIDE rating points, so each SL would be ~111 points. This gives us some benchmarks:
  • The average USCF tournament player's converted FIDE rating would be about 1200, corresponding to ~SL 10.
  • A USCF Class A player would be about SL 15
  • A USCF Expert would be about SL 17
  • An FIDE Master, ~ SL 19
  • An IM, ~ SL 21
  • A GM, ~SL 22
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Old 03-23-2011, 11:16 PM   #14
Dragondog
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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.
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Old 03-23-2011, 11:24 PM   #15
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Default Re: Chess Skill Levels

Quote:
Originally Posted by Rev. Pee Kitty View Post
snip...
I tend to avoid playing with people who do -- no offense intended to anyone! Just some people take certain boardgames way too seriously.)
I don't know why I found this to be so funny, but it just seems... strange, like Star-Wars fans laughing at those silly Trekkies or something.


Anyway, OT, I'd be more concerned with the contest results than the ratings numbers. Those are just flavor. If you are going to peg rating ranges to skill levels though you may want to make sure they are continuous but not overlapping.
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Old 03-23-2011, 11:32 PM   #16
Dragondog
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Default Re: Chess Skill Levels

Quote:
Originally Posted by benz72 View Post
I don't know why I found this to be so funny, but it just seems... strange, like Star-Wars fans laughing at those silly Trekkies or something.


Anyway, OT, I'd be more concerned with the contest results than the ratings numbers. Those are just flavor. If you are going to peg rating ranges to skill levels though you may want to make sure they are continuous but not overlapping.
The range I listed in my first post for some skill levels, where not the range for the skill level, but rather a range for the breaking point for that skill level. Or in other words (using the numbers in my first post), the lowest rating for skill 12 would somewhere in the 2157-2197 range. The lowest for skill 13 would be in the 2260-2300 range. And everything in between would be skill 12. But I could have made that clearer.
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Old 03-23-2011, 11:32 PM   #17
lexington
 
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Default Re: Chess Skill Levels

Quote:
Originally Posted by Purple Haze View Post
Means Magnus Carlsson has 68 points in chess, 13,600 hours, that's probably close.
Kromm just had a post that went into detail about how you can't go backward from points in a skill to hours of practice/study.

http://forums.sjgames.com/showpost.p...9&postcount=20
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Old 03-23-2011, 11:49 PM   #18
Dragondog
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Default Re: Chess Skill Levels

Quote:
Originally Posted by Not another shrubbery View Post
For me, I would rather peg the top skill level in the 20-25 range, assume the default level rating is something close to Purple's proposal of 800, equate that to a SL of 6, then distribute the FIDE rating range {typical beginner; Kasparov} evenly around the GURPS skill level range {6;20-25}. For the purpose of allowing even higher ratings open to our theoretical maximum of 25, we can assign Kasparov's peak rating something less... say, 24. 18 GURPS SLs would be representing 2000 FIDE rating points, so each SL would be ~111 points. This gives us some benchmarks:
  • The average USCF tournament player's converted FIDE rating would be about 1200, corresponding to ~SL 10.
  • A USCF Class A player would be about SL 15
  • A USCF Expert would be about SL 17
  • An FIDE Master, ~ SL 19
  • An IM, ~ SL 21
  • A GM, ~SL 22
What I want to do is keep the internal probabilities given by the rating system. By doing that, I cannot arbitrarily assign how many points each skill level represents. From SL 14 and up, each skill level is about 90 points, but as RPK points out it can be rounded to 100 points to simplify things. But if we compare SL 13 with SL 15, that’s a difference of 240 rating points.

Setting 2800-2899 as skill 24, for Kasparov, 21 would be 2500 for GM. And using some simplifications, we have:

19: FIDE 2300
17: FIDE 2100
15: FIDE 1900
14: FIDE 1775
13: FIDE 1650
11: FIDE 1450
9: FIDE 1250
7: FIDE 1050
5: FIDE 800

But setting all living grandmasters, over a thousand of them, as Top Master Alive, seems too much to me.
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Old 03-23-2011, 11:52 PM   #19
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Default Re: Chess Skill Levels

Except that in Magnus's case it is most likely true, he seems an otherwise unremarkable 18 year old, and he has spent his entire life studying chess.
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Old 03-24-2011, 12:00 AM   #20
Dragondog
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Default Re: Chess Skill Levels

Setting SL 6 as FIDE 800 gives GM skill 22+, and Kasparov a skill of 26. Which is too high.

6: FIDE 800
8: FIDE 1000
10: FIDE 1200
12: FIDE 1400
13: FIDE 1500
15: FIDE 1750
17: FIDE 1950
19: FIDE 2150
21: FIDE 2350
23: FIDE 2550
25: FIDE 2750
26: FIDE 2850
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