I don't agree with your definition for the side with the disadvantage beck. Sometimes the computer will play moves, especially in an endgame, where they are playing to increase the number of moves to checkmate, but other moves are harder to work out a win against.

That is merely a human weakness. Example, Lasker was said to choose 2nd best moves in tricky positions to pressure his opponent psychologically. A flawed move might work against 99.99% of your opposition, but that doesn't make it a perfect move. A perfect move, is perfect. For instance, endgame tablebases are perfect, or so I am lead to believe.

Ok...not sure what time those marathon runners can actually clock, but I had a friend which had previously competed in the olympics. He was competitive but not the best. He would run a mile in about 4 minutes, rest 30 seconds then do it again. He would do this repeatedly. And yeah, his legs had muscles on muscles. I live in Albuquerque, NM. Some of the marathon runners come here to train because it is 5,000 ft + in the city and of course there are mountains nearby. Funny thing about that kid beating a grandmaster. Was that a simul or a one on one? My guess is if it was a one on one the GM found himself playing the player and not the board. Regardless, the kid was not a 1300!

There is a technical point that most readers surely kind of feel, but is not very often put into words, so I'll try and make that effort for the benefit of all.

How do you feel when you have to confront somebody, say, 100 points above your own level? Say you're an 1672, and the guy's suddenly coming up, full of a towering 1772 points and you've got to play him?

Sure, you keep telling yourself, he's within my range, I should be able to beat him, sure sure, he's not much better, etc. etc. - but deep down you know you're kind of tricking yourself as he's really stronger, knows more, sees more, understands more, is quicker on some stuff, knows some other stuff more deeply... you know that don't you :-)

Then later, suppose you got your training session with him, and now you're (for example) 1670. Next you meet someone who's 1570... you think - oh God he's easy... or - maybe I shouldn't be playing a weak player now, or - well ok, let's relax a little... you know that you beat the guy - well, not every game, but like, it's comfortable playing somebody like that as you know he's edible... not so?

Come to think about it, being 100 points higher than somebody means you're close to twice as good - yeah, that's right, two times better.

How do I know it? Because according to the elo formulas you're supposed to get 64% out of him, and he - 36% out of you.

Maybe this doesn't sound like very much of a difference, but hey, pay attention here - suppose you were to actually play the guy for a 10-game series - then you're supposed to score (and often will score something in the order of) 6.5:3.5, not so?

So - it's almost double, close to twice as good...

if you play to ten, the most likely result is something in the order of 10.5:5.5 - or 10:5, or 10:6... almost twice as good, man, and I mean real close!!

Funny how the formula keeps extending that way, roughly... - 200 points of difference spells three times better (75% - 25%), then 300 points - close to seven times (!!!) better - (85% - 15%).

With 400 points we get to a skill differential of eleven and a half times better (92% - 8%), then it's

500 points - 24 times better (96% - 4%)

(with these large numbers, the approximations are less and less exact of course, especially as I keep rounding it to the closest percent point...)

600 points - 49 times better (98% - 2%), and finally, the last numerical value provided by the formula -

700 points - 99 times better (99% - 1%).

The elo scale is a logarithmic scale! It advances roughly by powers of almost-two.

Each 100 points in the scale, while still beatable, while still accessible, represents a real gap in knowledge, understanding and 'seeing'.

Due to elements of luck and drawing zone, this differential doesn't ever translate to 'always wins', but the 100 point differential is real and BIG.

Amazing that a game can have so many clear and distinct levels in it...

So - can a 1300 beat a 2700? Suppose he didn't learn and improve? Suppose no extreme medical condition occurs?

They are perfect by definition of perfect play (neglecting 50-moves rule). Definition of perfect play is what beck15 explained few posts ago. Here is nothing to agree or disagree about that.

That definition only works if one side has a winning position. It doesn't work for equal positions where neither side is winning by force.

They are perfect by definition of perfect play (neglecting 50-moves rule). Definition of perfect play is what beck15 explained few posts ago. Here is nothing to agree or disagree about that.

That definition only works if one side has a winning position. It doesn't work for equal positions where neither side is winning by force.

It does, because in an equal position, they are both attacking (for shortest victory), as well as defending (for longest resistance). An inaccurate move from either side can spell their downfall. And by definition, an inaccurate move is not perfect.

There is a technical point that most readers surely kind of feel, but is not very often put into words, so I'll try and make that effort for the benefit of all.

How do you feel when you have to confront somebody, say, 100 points above your own level? Say you're an 1672, and the guy's suddenly coming up, full of a towering 1772 points and you've got to play him?

Sure, you keep telling yourself, he's within my range, I should be able to beat him, sure sure, he's not much better, etc. etc. - but deep down you know you're kind of tricking yourself as he's really stronger, knows more, sees more, understands more, is quicker on some stuff, knows some other stuff more deeply... you know that don't you :-)

Then later, suppose you got your training session with him, and now you're (for example) 1670. Next you meet someone who's 1570... you think - oh God he's easy... or - maybe I shouldn't be playing a weak player now, or - well ok, let's relax a little... you know that you beat the guy - well, not every game, but like, it's comfortable playing somebody like that as you know he's edible... not so?

Come to think about it, being 100 points higher than somebody means you're close to twice as good - yeah, that's right, two times better.

How do I know it? Because according to the elo formulas you're supposed to get 64% out of him, and he - 36% out of you.

Maybe this doesn't sound like very much of a difference, but hey, pay attention here - suppose you were to actually play the guy for a 10-game series - then you're supposed to score (and often will score something in the order of) 6.5:3.5, not so?

So - it's almost double, close to twice as good...

if you play to ten, the most likely result is something in the order of 10.5:5.5 - or 10:5, or 10:6... almost twice as good, man, and I mean real close!!

Funny how the formula keeps extending that way, roughly... - 200 points of difference spells three times better (75% - 25%), then 300 points - close to seven times (!!!) better - (85% - 15%).

With 400 points we get to a skill differential of eleven and a half times better (92% - 8%), then it's

500 points - 24 times better (96% - 4%)

(with these large numbers, the approximations are less and less exact of course, especially as I keep rounding it to the closest percent point...)

600 points - 49 times better (98% - 2%), and finally, the last numerical value provided by the formula -

700 points - 99 times better (99% - 1%).

The elo scale is a logarithmic scale! It advances roughly by powers of almost-two.

Each 100 points in the scale, while still beatable, while still accessible, represents a real gap in knowledge, understanding and 'seeing'.

Due to elements of luck and drawing zone, this differential doesn't ever translate to 'always wins', but the 100 point differential is real and BIG.

Amazing that a game can have so many clear and distinct levels in it...

So - can a 1300 beat a 2700? Suppose he didn't learn and improve? Suppose no extreme medical condition occurs?

Hell no!

But maybe yes?

Well said.

So, in a thousand games, an 1300 might draw one game with a 2700 under standard tournament conditions. It is even possible, however remote, that the 1300 might draw the first game.

If we were to simplify and calculate by powers of two, then the chance of the 1300 to 'beat' the 2700 would be one in 2 to the 14th - i.e. one in 16,384 games.

You do notice that I put 'beat' in parenthesis, because if we pay close attention, the formula promises nothing about 'beating' anyone where you have 50% against them or less - it just says 'percentage'. It way well be that the 1300 will NEVER NEVER NEVER NEVER NEVER beat a 2700, no contradiction with any formula (except for the rule that absolutes are unobtainable in this universe... and allowing for people to let their guard down, fall asleep, be bored, want to encourage the 1300 player by letting them win, not trying so hard, relying on habits and missing a detail etc. etc. etc. )

But let's say, like the 'tough liners' that the 1300 can NEVER beat the 2700 in 16,384 games.

What about a couple draws then? By the formula (rounded to 'twice better' for 100 points - actually 'twice better' is probably around 115 or 125 points, but let's just keep it at 100 for the sake of discussion), that's fine too.

Imagine the poor 2700, having to play the 1300 and needing to win ALWAYS ALWAYS ALWAYS. If he's not careful, this can be used against him! He should be allowed the refuge of a draw once every 8,192 games, not so? Or twice every 16,384, just to relax and come back to force, otherwise it's really too monotonous.

- - - - - - - - - - - - - - -

Actually I wanted to write another post here and to develop further the idea of 'logarithmic elo'.

The elo scale as we know it is very counterintuitive. Why?

We know that an 1800 is much much much better than a 1300. An 1800 will explain him the game, teach him, show him stuff, take back his moves because he didn't see this, didn't see that, and still crush them very predictably (although the 1300 will have an insight here and there which will surprise the 1800!). But the numbers aren't THAT far, right?

Put it in a different way, 2600 is only double 1300... only double... but so many different levels, tournament games, experiences and understandings lie in between that it's really impossible to start talking about them.

But the number's only double.

This would never be actually implemented, but how about a more intuitive elo system, reflecting the true relations of power between players?

I think that an absolutely clueless beginner, but who does know how the pieces move (though en passant is too complicated for him and he's not sure where exactly the pieces go in castling and what you can get for a pawn where it promotes, and who will sometimes move a pawn backwards, yes, even to the first rank), is rated about 200. Let's suppose this is the case.

So Let's give him a rating of 1.

Because I'm Solskytz, and in order to not confuse the two rating systems, let's call him an S1, meaning Solskytz rating 1.

He improves and gets to 300? Now he's twice as strong and will beat any beginner 2 to 1, give him S2 (Solskytz rating 2). When he's still between 200 and 300, he should be rated S1.19, or S1.64 etc. Of course he may actually be weaker than 200, and then he'd have S0.78, or S0.2, or maybe even S0.09, one never knows...

So, the 400 who sees a hanging piece from time to time, or who thinks seven minutes and then gets a checkmate (except that his checkmating piece was pinned, of course), is S4. the 500 is S8 (I double the rating every 100 'conventional points), 600 is S16, 700 is S32, 800 is S64, 900 is S128, and 1000, the reasonable social player, is S256.

We keep advancing and find the 1100 rated S512, and when he becomes a 1200, a social player to be quite feared, a guy who quite regularly beats his friends and boasts knowledge of some interesting points of endgame and opening, the guy who sometimes sees a 3-move capturing sequence without mistake, but the guy who is the total cannonfodder at any club, should he try to visit one, is already up there at the thousand range, with around S1000 (for simplicity I calculate 2 to the 10th power equals 1000).

the Solskytz thousands are the amateur range. Below that we have the beginner range and the social range. Now our heroic dragonslayer 1300 from this thread becomes an S2000 player. Impressive and towering above everybody hereto, and shows the road he's come - but in his club he'll meet and be regularly mocked for his shortcoming by the 1400, or the S4000, and the 1500, who is S8000.

8000 rating points show clearly that really nobody outside the club stands a chance against this guy (they will all have around a thousand, probably much much much less). It's an overwhelmingly high rating.

Who's better than him at the club? The S16K (1600), S32K (1700) and S64K (1800). These players boast a 5-digit rating, clearly showing their status as medium to advanced club players, and on top of them all stands the 1900, with 128,000 Solskytz rating points. This player is very advanced, and everybody at the club (remember the S8000 from last paragraph) should be awed by this enormous number.

Strong as he may be, with the 2000, rated a quarter of a million solskytz, as he's already the expert, we enter the millionaire club.

Although this guy, an absolute killer for amateurs as we all know, whose teeth are sharp and stained with the chess-blood of many, has very little to show at that prestigious club, holding merely a quarter of a single million points...

indeed, requirements change as you move up the rating ladder, as a wise guy here already observe - we, 2000 players, totally suck at chess!! But of course, only when compared to the rest of the millionaire 'caste', not to mention the billionaire computer programs, today rated 3000 and up.

His situation improves if and when he makes 2100, as he reaches half a million.

The 2200, or the candidate master, finally stands upon a full million solskytz rating points. An 2300 FIDE master will have 2M (so if I'm 2050 today, how much do I miss in order to become a master? Probably I should improve something like 5.5 times... I should be 5.5 times better than my current level - maybe know, understand, see 5.5 times more than I currently do, or have my game become 5.5 times subtler).

2400 IM will be rated S4,000,000, 2500 GM is S8,000,000.

What is nice about this rating system, is that you can see right away that when a S128,000 (the 1900) plays a S64,000 (the 1800), he should score double - it's immediately clear.

In the elo system, elo scores are added to or subtracted from as a player wins, loses and draws.

In solskytz rating, they will be multiplied by a certain factor (+10 elo change will correspond, at a guess, to about X1.06 solskytz rating change - 1.06 estimated by myself (I'm not checking) to be close to the tenth root of 2, just as 10 (for elo points) is one tenth of the 100 elo point differential, which I translate into "twice better").

So - two 128,000s play, and one beats the other - he now becomes around 134,000, the loser going down to around 122,000. Very similar to elo, but you multiply and divide rather than add and subtract.

Just to end our list, the 2600 super-GM will be rated 16 million solskytz rating points, and the 2700 superstar GM will now have as many as 32,000,000 points to reflect his actual strength, or playing skill.

The S2,000 player (1300) looked quite impressive when compared to his friends who played at the beach or at home, but what chance does he have against someone who is rated 32 million? right, one in 16,384, and now the numbers finally show it. I would bet on two draws.

Upsets do happen! A 900 should get one point in a thousand against an 1900.

Let's imagine an enormous playing hall, with 300 chess tables. Everyone who's ever been in a chess tournament will appreciate how big this hall should be, to house 600 competitors on 300 tables.

Let's get a couple more halls like this, and then, for good measure, add a smaller hall with a further 100 tables on it. That's a thousand tables in total.

Let's put a thousand 900 players on one side of each of the thousand tables. Give white to half of them and black to the others (imagine the noise!)

Let's bring an equally warmongering 1,900 elo squad, a thousand strong, to patiently face these guys on each and every table.

Four big, bustling rooms, full of people, clocks, pieces, boards, referees, orange juice and refreshment...

and you want to tell me that nowhere in these four rooms will a measly couple of draws be found?

Or that in no place the unbelievable will occur, and the 900 will actually upset the 1900?

(substitute 1300 and 2300 for 900 and 1900 for all I care... it really matters very little).

elo ratings, as you know well, are some estimates of a player's ability, form, knowledge, understanding, sharpness, you name it... general - how well does the guy play in PT (in Present Time, that is to say).

How good a guy is? If he's 2800 I'll give him 64,000,000 solskytz points - I guess that he knows about a thousand times more than an 1800 (64,000),or a million times more than a 800-rated (S64) novice.

If his name is Magnus Carlsen, he'd get something in the order of (I guess) 85 million solskytz points.

Now suppose he makes one of these draws with the elite, which typically cost him one elo point? One being one hundredth of a hundred, it means that the new estimate of his strength is that he's the hundredth root of two times weaker than thought before, if I'm telling by the elo formula. He has that many units of knowledge and understanding, or chesspower less. How much is the hundredth root of two? I suppose (again without checking) that it should be division by 1.007, more or less... right? (check me pls). So his new rating should be, instead of 85,000,000, something like 84,400,000 solskytz points.

He fell 600,000 points! That's the entire elo score of someone who's around 2130... just the differential in the estimate of his chesspower following the loss of one measly elo point, translates to the entire repertoire and knowledge of an 2130 being dropped out of the estimate of how strong Magnus Carlsen is - gives you an insight into the true difference between the levels...

Magnus Carlsen went to play a game with an orange juice that is a couple of days old, he plays 5 elo points beneath his usual form - and who would notice it?

But it looks like he forgot the full 'database' of knowledge of a FIDE master... which is of course just a tiny fraction of his own knowledge and ability. that's how strong the guy is.

And please, don't get me started about computer programs...

That's some interesting math. To be sure, I have to come back and read it all again, but, going back to your original statement, yes. It's GOOD that you didn't put it as an absolute.

The 2700 player got drunk after the tournament and stumbled up on a fellow at the bar with a chessboard, and although the fellow was only a 1200 rated player, he won.

The 2700 player just lost his family, and the 1200 rated player wins.

The biggest problem with ratings like online is the quick attachment of the number to the player.

Having won my first game at another place (and in 11 moves) I was assigned a 2149 rating. Some deep water sharks would sniff that number and wander in and challenge me. A quick perusal at my games, however, and they would lose interest. I would actually have to go out and drag them back to the board...only... then they would stuff me into a shoebox and throw me out of the plane without a parachute. Or with even ONE chute. But the rating?

I'm a 1500...maybe a 1600 if I would concentrate more on games.

Nowhere near 2149.

Well, unless I could keep my opponents drunk. Which STILL wouldn't work with some of the older masters who lived drunk.

(small note...the 2700 player's family didn't die, by the way. He just lost them. Probably at the mall. Dang! Have you SEEN those places, lately?)

The only way I can think of is if the 1300 player was a high rated player(strong in his/her game) before playing on the chess.com website and played the 2700 player. there are many strong players in the world that do not play in Official tournaments, like taking their show on the road so to speak, or such circles. that is why an "Unrated" new player can be a dangerous opponent. but I say if you have nothing to lose and everything to gain by trying... by all means TRY !!!

They are perfect by definition of perfect play (neglecting 50-moves rule). Definition of perfect play is what beck15 explained few posts ago. Here is nothing to agree or disagree about that.

That definition only works if one side has a winning position. It doesn't work for equal positions where neither side is winning by force.

It does, because in an equal position, they are both attacking (for shortest victory), as well as defending (for longest resistance). An inaccurate move from either side can spell their downfall. And by definition, an inaccurate move is not perfect.

If neither side has a won position, you've got the task of working out which of the selection of non-losing moves is preferable. This isn't so easy. "The shortest victory" only makes sense if the player can force victory, i.e. has a won position already.

Every move that keep position drawn is perfect. That s quite arbitrary, but it still works.

If you're happy with that as a definition of perfect, then fair enough. But I was trying to do better than that - to find a way of distinguishing between them. If we settle for your definition, then 1. a3 is a perfect move on the grounds that it doesn't lose by force, and nothing else wins by force.

How often does a grand master even bother to play a 1300?

I'd say that depends on the number of students they have and if his little nephew wants to play during a visit.

I'd think that if the GM thinks the kid rated at 1300 feels like making a little kid feel good, he might go easy on the kid and even purposely lose the game. I'd bet there are other examples of professionals losing to kids because they only give it 10% to boister the kid's self esteem, for photo shoots, etc.

Others would argue there aren't any records of such games...

I know Kasparov played against some celebreties, and they were probably around that range, like Kasparov vs. Letterman. I don't know Letterman's rating, and it's hard to tell from this game since any amateur will look like an idiot against someone like Kasparov.

@pellik: There is evidence I use to convince myself of my opinion, but of course, we all probably have disagreements as to what counts as evidence.

For me, just the fact that I have seen lots of grandmaster blunders, whether in tournament games or in bullet, suggests to me that we can expect extremely basic errors to happen once in a blue moon, though extremely rarely. It is probably due to the sort of temporary blindness we all get, like when we mispronounce a word, even though we know very well the correct way to pronounce it. It just happens, for some people more than others.

Although it's true that you can argue that perhaps blunders are more likely to come when you are under pressure, or feel tension (which might more often happen against a strong player; for instance, when GM Stripunsky hung his bishop and rook against GM Onishcuk, maybe it was because he was nervous playing Onischuk), it's one assumption against another -- it's just as easy to claim that it might actually be more likely for a grandmaster to make such a basic mistake against an amateur (but again, it is still ridiculously unlikely), simply because if he feels overconfident in his position then he might not be quite as careful as he would be if he had a harder game.

The above paragraph is the only counter argument I can find against the paragraph above that. I can not repeat enough that no matter what the psychological circumstances are, it will always be extremely unlikely for this kind of thing to happen; but again, I am not arguing for likely; I am arguing for possible.

solskytz, beautiful post. Romantic and logical, although a bit flawed IMO (MC dropping 1 elo = knowledge base of a whole FM? Really?). Reminded me of dbz.

I rarely read walls of text, however I read it and liked it.

I don't agree with your definition for the side with the disadvantage beck. Sometimes the computer will play moves, especially in an endgame, where they are playing to increase the number of moves to checkmate, but other moves are harder to work out a win against.

That is merely a human weakness. Example, Lasker was said to choose 2nd best moves in tricky positions to pressure his opponent psychologically. A flawed move might work against 99.99% of your opposition, but that doesn't make it a perfect move. A perfect move, is perfect. For instance, endgame tablebases are perfect, or so I am lead to believe.

Ok...not sure what time those marathon runners can actually clock, but I had a friend which had previously competed in the olympics. He was competitive but not the best. He would run a mile in about 4 minutes, rest 30 seconds then do it again. He would do this repeatedly. And yeah, his legs had muscles on muscles. I live in Albuquerque, NM. Some of the marathon runners come here to train because it is 5,000 ft + in the city and of course there are mountains nearby. Funny thing about that kid beating a grandmaster. Was that a simul or a one on one? My guess is if it was a one on one the GM found himself playing the player and not the board. Regardless, the kid was not a 1300!

Hey you live in Albuquerque? Seen any of that blue crystal knocking about?

There is a technical point that most readers surely kind of feel, but is not very often put into words, so I'll try and make that effort for the benefit of all.

How do you feel when you have to confront somebody, say, 100 points above your own level? Say you're an 1672, and the guy's suddenly coming up, full of a towering 1772 points and you've got to play him?

Sure, you keep telling yourself, he's within my range, I should be able to beat him, sure sure, he's not much better, etc. etc. - but deep down you know you're kind of tricking yourself as he's really stronger, knows more, sees more, understands more, is quicker on some stuff, knows some other stuff more deeply... you know that don't you :-)

Then later, suppose you got your training session with him, and now you're (for example) 1670. Next you meet someone who's 1570... you think - oh God he's easy... or - maybe I shouldn't be playing a weak player now, or - well ok, let's relax a little... you know that you beat the guy - well, not every game, but like, it's comfortable playing somebody like that as you know he's edible... not so?

Come to think about it, being 100 points higher than somebody means you're close to twice as good - yeah, that's right, two times better.

How do I know it? Because according to the elo formulas you're supposed to get 64% out of him, and he - 36% out of you.

Maybe this doesn't sound like very much of a difference, but hey, pay attention here - suppose you were to actually play the guy for a 10-game series - then you're supposed to score (and often will score something in the order of) 6.5:3.5, not so?

So - it's almost double, close to twice as good...

if you play to ten, the most likely result is something in the order of 10.5:5.5 - or 10:5, or 10:6... almost twice as good, man, and I mean real close!!

Funny how the formula keeps extending that way, roughly... - 200 points of difference spells three times better (75% - 25%), then 300 points - close to seven times (!!!) better - (85% - 15%).

With 400 points we get to a skill differential of eleven and a half times better (92% - 8%), then it's

500 points - 24 times better (96% - 4%)

(with these large numbers, the approximations are less and less exact of course, especially as I keep rounding it to the closest percent point...)

600 points - 49 times better (98% - 2%), and finally, the last numerical value provided by the formula -

700 points - 99 times better (99% - 1%).

The elo scale is a logarithmic scale! It advances roughly by powers of almost-two.

Each 100 points in the scale, while still beatable, while still accessible, represents a real gap in knowledge, understanding and 'seeing'.

Due to elements of luck and drawing zone, this differential doesn't ever translate to 'always wins', but the 100 point differential is real and BIG.

Amazing that a game can have so many clear and distinct levels in it...

So - can a 1300 beat a 2700? Suppose he didn't learn and improve? Suppose no extreme medical condition occurs?

Hell no!

But maybe yes?

They are perfect by definition of perfect play (neglecting 50-moves rule). Definition of perfect play is what beck15 explained few posts ago. Here is nothing to agree or disagree about that.

That definition only works if one side has a winning position. It doesn't work for equal positions where neither side is winning by force.

They are perfect by definition of perfect play (neglecting 50-moves rule). Definition of perfect play is what beck15 explained few posts ago. Here is nothing to agree or disagree about that.

That definition only works if one side has a winning position. It doesn't work for equal positions where neither side is winning by force.

It does, because in an equal position, they are both attacking (for shortest victory), as well as defending (for longest resistance). An inaccurate move from either side can spell their downfall. And by definition, an inaccurate move is not perfect.

There is a technical point that most readers surely kind of feel, but is not very often put into words, so I'll try and make that effort for the benefit of all.

How do you feel when you have to confront somebody, say, 100 points above your own level? Say you're an 1672, and the guy's suddenly coming up, full of a towering 1772 points and you've got to play him?

Sure, you keep telling yourself, he's within my range, I should be able to beat him, sure sure, he's not much better, etc. etc. - but deep down you know you're kind of tricking yourself as he's really stronger, knows more, sees more, understands more, is quicker on some stuff, knows some other stuff more deeply... you know that don't you :-)

Then later, suppose you got your training session with him, and now you're (for example) 1670. Next you meet someone who's 1570... you think - oh God he's easy... or - maybe I shouldn't be playing a weak player now, or - well ok, let's relax a little... you know that you beat the guy - well, not every game, but like, it's comfortable playing somebody like that as you know he's edible... not so?

Come to think about it, being 100 points higher than somebody means you're close to twice as good - yeah, that's right, two times better.

How do I know it? Because according to the elo formulas you're supposed to get 64% out of him, and he - 36% out of you.

Maybe this doesn't sound like very much of a difference, but hey, pay attention here - suppose you were to actually play the guy for a 10-game series - then you're supposed to score (and often will score something in the order of) 6.5:3.5, not so?

So - it's almost double, close to twice as good...

if you play to ten, the most likely result is something in the order of 10.5:5.5 - or 10:5, or 10:6... almost twice as good, man, and I mean real close!!

Funny how the formula keeps extending that way, roughly... - 200 points of difference spells three times better (75% - 25%), then 300 points - close to seven times (!!!) better - (85% - 15%).

With 400 points we get to a skill differential of eleven and a half times better (92% - 8%), then it's

500 points - 24 times better (96% - 4%)

(with these large numbers, the approximations are less and less exact of course, especially as I keep rounding it to the closest percent point...)

600 points - 49 times better (98% - 2%), and finally, the last numerical value provided by the formula -

700 points - 99 times better (99% - 1%).

The elo scale is a logarithmic scale! It advances roughly by powers of almost-two.

Each 100 points in the scale, while still beatable, while still accessible, represents a real gap in knowledge, understanding and 'seeing'.

Due to elements of luck and drawing zone, this differential doesn't ever translate to 'always wins', but the 100 point differential is real and BIG.

Amazing that a game can have so many clear and distinct levels in it...

So - can a 1300 beat a 2700? Suppose he didn't learn and improve? Suppose no extreme medical condition occurs?

Hell no!

But maybe yes?

Well said.

So, in a thousand games, an 1300 might draw one game with a 2700 under standard tournament conditions. It is even possible, however remote, that the 1300 might draw the first game.

Most games between 1300s and 2700s are over before move 12.

Some would argue most games between 1300s and 2700s are over before move1 :)

Others would argue there aren't any records of such games...

<Ziryab> I'm happy that you liked my post :-)

If we were to simplify and calculate by powers of two, then the chance of the 1300 to 'beat' the 2700 would be one in 2 to the 14th - i.e. one in 16,384 games.

You do notice that I put 'beat' in parenthesis, because if we pay close attention, the formula promises nothing about 'beating' anyone where you have 50% against them or less - it just says 'percentage'. It way well be that the 1300 will NEVER NEVER NEVER NEVER NEVER beat a 2700, no contradiction with any formula (except for the rule that absolutes are unobtainable in this universe... and allowing for people to let their guard down, fall asleep, be bored, want to encourage the 1300 player by letting them win, not trying so hard, relying on habits and missing a detail etc. etc. etc. )

But let's say, like the 'tough liners' that the 1300 can NEVER beat the 2700 in 16,384 games.

What about a couple draws then? By the formula (rounded to 'twice better' for 100 points - actually 'twice better' is probably around 115 or 125 points, but let's just keep it at 100 for the sake of discussion), that's fine too.

Imagine the poor 2700, having to play the 1300 and needing to win ALWAYS ALWAYS ALWAYS. If he's not careful, this can be used against him! He should be allowed the refuge of a draw once every 8,192 games, not so? Or twice every 16,384, just to relax and come back to force, otherwise it's really too monotonous.

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Actually I wanted to write another post here and to develop further the idea of 'logarithmic elo'.

The elo scale as we know it is very counterintuitive. Why?

We know that an 1800 is much much much better than a 1300. An 1800 will explain him the game, teach him, show him stuff, take back his moves because he didn't see this, didn't see that, and still crush them very predictably (although the 1300 will have an insight here and there which will surprise the 1800!). But the numbers aren't THAT far, right?

Put it in a different way, 2600 is only double 1300... only double... but so many different levels, tournament games, experiences and understandings lie in between that it's really impossible to start talking about them.

But the number's only double.

This would never be actually implemented, but how about a more intuitive elo system, reflecting the true relations of power between players?

I think that an absolutely clueless beginner, but who does know how the pieces move (though en passant is too complicated for him and he's not sure where exactly the pieces go in castling and what you can get for a pawn where it promotes, and who will sometimes move a pawn backwards, yes, even to the first rank), is rated about 200. Let's suppose this is the case.

So Let's give him a rating of 1.

Because I'm Solskytz, and in order to not confuse the two rating systems, let's call him an S1, meaning Solskytz rating 1.

He improves and gets to 300? Now he's twice as strong and will beat any beginner 2 to 1, give him S2 (Solskytz rating 2). When he's still between 200 and 300, he should be rated S1.19, or S1.64 etc. Of course he may actually be weaker than 200, and then he'd have S0.78, or S0.2, or maybe even S0.09, one never knows...

So, the 400 who sees a hanging piece from time to time, or who thinks seven minutes and then gets a checkmate (except that his checkmating piece was pinned, of course), is S4. the 500 is S8 (I double the rating every 100 'conventional points), 600 is S16, 700 is S32, 800 is S64, 900 is S128, and 1000, the reasonable social player, is S256.

We keep advancing and find the 1100 rated S512, and when he becomes a 1200, a social player to be quite feared, a guy who quite regularly beats his friends and boasts knowledge of some interesting points of endgame and opening, the guy who sometimes sees a 3-move capturing sequence without mistake, but the guy who is the total cannonfodder at any club, should he try to visit one, is already up there at the thousand range, with around S1000 (for simplicity I calculate 2 to the 10th power equals 1000).

the Solskytz thousands are the amateur range. Below that we have the beginner range and the social range. Now our heroic dragonslayer 1300 from this thread becomes an S2000 player. Impressive and towering above everybody hereto, and shows the road he's come - but in his club he'll meet and be regularly mocked for his shortcoming by the 1400, or the S4000, and the 1500, who is S8000.

8000 rating points show clearly that really nobody outside the club stands a chance against this guy (they will all have around a thousand, probably much much much less). It's an overwhelmingly high rating.

Who's better than him at the club? The S16K (1600), S32K (1700) and S64K (1800). These players boast a 5-digit rating, clearly showing their status as medium to advanced club players, and on top of them all stands the 1900, with 128,000 Solskytz rating points. This player is very advanced, and everybody at the club (remember the S8000 from last paragraph) should be awed by this enormous number.

Strong as he may be, with the 2000, rated a quarter of a million solskytz, as he's already the expert, we enter the millionaire club.

Although this guy, an absolute killer for amateurs as we all know, whose teeth are sharp and stained with the chess-blood of many, has very little to show at that prestigious club, holding merely a quarter of a single million points...

indeed, requirements change as you move up the rating ladder, as a wise guy here already observe - we, 2000 players, totally suck at chess!! But of course, only when compared to the rest of the millionaire 'caste', not to mention the billionaire computer programs, today rated 3000 and up.

His situation improves if and when he makes 2100, as he reaches half a million.

The 2200, or the candidate master, finally stands upon a full million solskytz rating points. An 2300 FIDE master will have 2M (so if I'm 2050 today, how much do I miss in order to become a master? Probably I should improve something like 5.5 times... I should be 5.5 times better than my current level - maybe know, understand, see 5.5 times more than I currently do, or have my game become 5.5 times subtler).

2400 IM will be rated S4,000,000, 2500 GM is S8,000,000.

What is nice about this rating system, is that you can see right away that when a S128,000 (the 1900) plays a S64,000 (the 1800), he should score double - it's immediately clear.

In the elo system, elo scores are added to or subtracted from as a player wins, loses and draws.

In solskytz rating, they will be multiplied by a certain factor (+10 elo change will correspond, at a guess, to about X1.06 solskytz rating change - 1.06 estimated by myself (I'm not checking) to be close to the tenth root of 2, just as 10 (for elo points) is one tenth of the 100 elo point differential, which I translate into "twice better").

So - two 128,000s play, and one beats the other - he now becomes around 134,000, the loser going down to around 122,000. Very similar to elo, but you multiply and divide rather than add and subtract.

Just to end our list, the 2600 super-GM will be rated 16 million solskytz rating points, and the 2700 superstar GM will now have as many as 32,000,000 points to reflect his actual strength, or playing skill.

The S2,000 player (1300) looked quite impressive when compared to his friends who played at the beach or at home, but what chance does he have against someone who is rated 32 million? right, one in 16,384, and now the numbers finally show it. I would bet on two draws.

Upsets do happen! A 900 should get one point in a thousand against an 1900.

Let's imagine an enormous playing hall, with 300 chess tables. Everyone who's ever been in a chess tournament will appreciate how big this hall should be, to house 600 competitors on 300 tables.

Let's get a couple more halls like this, and then, for good measure, add a smaller hall with a further 100 tables on it. That's a thousand tables in total.

Let's put a thousand 900 players on one side of each of the thousand tables. Give white to half of them and black to the others (imagine the noise!)

Let's bring an equally warmongering 1,900 elo squad, a thousand strong, to patiently face these guys on each and every table.

Four big, bustling rooms, full of people, clocks, pieces, boards, referees, orange juice and refreshment...

and you want to tell me that nowhere in these four rooms will a measly couple of draws be found?

Or that in no place the unbelievable will occur, and the 900 will actually upset the 1900?

(substitute 1300 and 2300 for 900 and 1900 for all I care... it really matters very little).

Think about it...

And a little, further thought...

elo ratings, as you know well, are some estimates of a player's ability, form, knowledge, understanding, sharpness, you name it... general - how well does the guy play in PT (in Present Time, that is to say).

How good a guy is? If he's 2800 I'll give him 64,000,000 solskytz points - I guess that he knows about a thousand times more than an 1800 (64,000),or a million times more than a 800-rated (S64) novice.

If his name is Magnus Carlsen, he'd get something in the order of (I guess) 85 million solskytz points.

Now suppose he makes one of these draws with the elite, which typically cost him one elo point? One being one hundredth of a hundred, it means that the new estimate of his strength is that he's the hundredth root of two times weaker than thought before, if I'm telling by the elo formula. He has that many units of knowledge and understanding, or chesspower less. How much is the hundredth root of two? I suppose (again without checking) that it should be division by 1.007, more or less... right? (check me pls). So his new rating should be, instead of 85,000,000, something like 84,400,000 solskytz points.

He fell 600,000 points! That's the entire elo score of someone who's around 2130... just the differential in the estimate of his chesspower following the loss of one measly elo point, translates to the entire repertoire and knowledge of an 2130 being dropped out of the estimate of how strong Magnus Carlsen is - gives you an insight into the true difference between the levels...

Magnus Carlsen went to play a game with an orange juice that is a couple of days old, he plays 5 elo points beneath his usual form - and who would notice it?

But it looks like he forgot the full 'database' of knowledge of a FIDE master... which is of course just a tiny fraction of his own knowledge and ability. that's how strong the guy is.

And please, don't get me started about computer programs...

That's some interesting math. To be sure, I have to come back and read it all again, but, going back to your original statement, yes. It's GOOD that you didn't put it as an absolute.

The 2700 player got drunk after the tournament and stumbled up on a fellow at the bar with a chessboard, and although the fellow was only a 1200 rated player, he won.

The 2700 player just lost his family, and the 1200 rated player wins.

The biggest problem with ratings like online is the quick attachment of the number to the player.

Having won my first game at another place (and in 11 moves) I was assigned a 2149 rating. Some deep water sharks would sniff that number and wander in and challenge me. A quick perusal at my games, however, and they would lose interest. I would actually have to go out and drag them back to the board...only... then they would stuff me into a shoebox and throw me out of the plane without a parachute. Or with even ONE chute. But the rating?

I'm a 1500...maybe a 1600 if I would concentrate more on games.

Nowhere near 2149.

Well, unless I could keep my opponents drunk. Which STILL wouldn't work with some of the older masters who lived drunk.

(small note...the 2700 player's family didn't die, by the way. He just lost them. Probably at the mall. Dang! Have you SEEN those places, lately?)

The only way I can think of is if the 1300 player was a high rated player(strong in his/her game) before playing on the chess.com website and played the 2700 player. there are many strong players in the world that do not play in Official tournaments, like taking their show on the road so to speak, or such circles. that is why an "Unrated" new player can be a dangerous opponent. but I say if you have nothing to lose and everything to gain by trying... by all means TRY !!!

They are perfect by definition of perfect play (neglecting 50-moves rule). Definition of perfect play is what beck15 explained few posts ago. Here is nothing to agree or disagree about that.

That definition only works if one side has a winning position. It doesn't work for equal positions where neither side is winning by force.

It does, because in an equal position, they are both attacking (for shortest victory), as well as defending (for longest resistance). An inaccurate move from either side can spell their downfall. And by definition, an inaccurate move is not perfect.

If neither side has a won position, you've got the task of working out which of the selection of non-losing moves is preferable. This isn't so easy. "The shortest victory" only makes sense if the player can force victory, i.e. has a won position already.

Every move that keep position drawn is perfect. That s quite arbitrary, but it still works.

If you're happy with that as a definition of perfect, then fair enough. But I was trying to do better than that - to find a way of distinguishing between them. If we settle for your definition, then 1. a3 is a perfect move on the grounds that it doesn't lose by force, and nothing else wins by force.

How often does a grand master even bother to play a 1300?

I'd say that depends on the number of students they have and if his little nephew wants to play during a visit.

I'd think that if the GM thinks the kid rated at 1300 feels like making a little kid feel good, he might go easy on the kid and even purposely lose the game. I'd bet there are other examples of professionals losing to kids because they only give it 10% to boister the kid's self esteem, for photo shoots, etc.

Others would argue there aren't any records of such games...

I know Kasparov played against some celebreties, and they were probably around that range, like Kasparov vs. Letterman. I don't know Letterman's rating, and it's hard to tell from this game since any amateur will look like an idiot against someone like Kasparov.

@pellik: There is evidence I use to convince myself of my opinion, but of course, we all probably have disagreements as to what counts as evidence.For me, just the fact that I have seen lots of grandmaster blunders, whether in tournament games or in bullet, suggests to me that we can expect extremely basic errors to happen once in a blue moon, though extremely rarely. It is probably due to the sort of temporary blindness we all get, like when we mispronounce a word, even though we know very well the correct way to pronounce it. It just happens, for some people more than others.

Although it's true that you can argue that perhaps blunders are more likely to come when you are under pressure, or feel tension (which might more often happen against a strong player; for instance, when GM Stripunsky hung his bishop and rook against GM Onishcuk, maybe it was because he was nervous playing Onischuk), it's one assumption against another -- it's just as easy to claim that it might actually be

morelikely for a grandmaster to make such a basic mistake against an amateur (but again, it is still ridiculously unlikely), simply because if he feels overconfident in his position then he might not be quite as careful as he would be if he had a harder game.The above paragraph is the only counter argument I can find against the paragraph above that. I can not repeat enough that no matter what the psychological circumstances are, it will always be extremely unlikely for this kind of thing to happen; but again, I am not arguing for likely; I am arguing for possible.

solskytz, beautiful post. Romantic and logical, although a bit flawed IMO (MC dropping 1 elo = knowledge base of a whole FM? Really?). Reminded me of dbz.

I rarely read walls of text, however I read it and liked it.