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 03-23-2011, 10:39 PM #11 PK     Join Date: Aug 2004 Location: Dobbstown Sane Asylum 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.) __________________ Reverend Pee Kitty of the Order Malkavian-Dobbsian (Twitter) (LJ) MyGURPS: My house rules and GURPS resources. #SJGamesLive: I answered questions about GURPS After the End and more! {Watch Video} - {Read Transcript}
 03-23-2011, 10:46 PM #12 Purple Haze   Join Date: Jul 2006 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.
03-23-2011, 11:12 PM   #13
Not another shrubbery

Join Date: Aug 2004
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

03-23-2011, 11:16 PM   #14
Dragondog
Never Been Pretty

Join Date: Jan 2005
Re: Chess Skill Levels

Quote:
 Originally Posted by Rev. Pee Kitty 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.

03-23-2011, 11:24 PM   #15
benz72

Join Date: Oct 2006
Location: Chagrin Falls
Re: Chess Skill Levels

Quote:
 Originally Posted by Rev. Pee Kitty 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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03-23-2011, 11:32 PM   #16
Dragondog
Never Been Pretty

Join Date: Jan 2005
Re: Chess Skill Levels

Quote:
 Originally Posted by benz72 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.

03-23-2011, 11:32 PM   #17
lexington

Join Date: Jan 2010
Re: Chess Skill Levels

Quote:
 Originally Posted by Purple Haze 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

03-23-2011, 11:49 PM   #18
Dragondog
Never Been Pretty

Join Date: Jan 2005
Re: Chess Skill Levels

Quote:
 Originally Posted by Not another shrubbery 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.

 03-23-2011, 11:52 PM #19 Purple Haze   Join Date: Jul 2006 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.
 03-24-2011, 12:00 AM #20 Dragondog Never Been Pretty   Join Date: Jan 2005 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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