Something Hikaru Said

[Laskos]

I should know better than to jump into this... but I'm curious.

Doesn't an ELO difference of X indicate a particular chance of loss or draw regardless of the actual numbers? And if so, where is the breakdown of just comparing ELO for this handicap?

a) perhaps my understanding is off
b) perhaps ELO doesn't apply to handicap games, just regular chess
c) perhaps we lack ELO alignment between computers and humans

A couple are making the assumption that suddenly Elo is meaningless when talking about odds games, that somehow a player with a rating of 2700 in normal chess has an infinite rating when a knight ahead. I don't see any justification for such an assumption, however.

The question is how much improvement can we get with knight odd thanks to better hardware.


What is the difference in rating between Komodo 24 cores without a knight and Komodo 1 core without a knight(when both play against chess engines).

I do not have komodo and do not have 24 core machine but I guess that we are going to see less than 50 elo difference against engines if we use 10 minutes/40 moves or slower time control when the difference between 1 core and 24 cores is more than 200 elo in normal chess.

You are thinking way too small. Crafty, today, hits 100M nodes per second on my 20 core box. We are talking what about something that is 10,000,000 times faster, or even more. NOT what is possible today. The original question was what about 32 piece endgame tables. Could a computer beat a gm with knight odds or better given either 32 piece eg tables, or such incredible search depth that it plays such positions perfectly anyway. The hypothesis has been offered that once a GM is a knight ahead, he can play _perfectly_ and no machine will ever be able to beat him. I don't see any evidence to support that. For my 7 orders of magnitude improvement in speed, that is close to 24 doublings. That's not going to be 50 or 100 Elo improvement. And that is just the beginning.

I think both computers and chess programs have a long way to go before things flatten out. I'm not sure a knight will be impossible. I don't know, but I certainly know there is no evidence to suggest any sort of limit like that exists. Yes a queen and two rooks is enough and then some. But a knight. Knight and pawn? Rook? impossible to guess.

Well, let's see what happens for 4 doublings at ultra-fast controls with thousands of games. Keep in mind that the following effect is magnified at long time controls.

Knight handicap is worth 538 ELO points at 10,000 nodes per move with Stockfish. It is worth 984 ELO points at 160,000 nodes per move (4 doublings). It means the Knight handicap ELO value increases by 446 ELO points.

The ELO difference in normal chess between 160,000 and 10,000 nodes is 674 ELO points.

Therefore, the ELO difference in Knight-odds chess is 674 - 446 = 228 ELO points.

So, even at ultra-fast controls, an ELO increase in normal chess by 674 ELO points brings only 228 ELO points to Knight-odds chess. 228 ELO points increase in Knight-odds performance is about half a pawn additional allowed handicap at regular time control.

This effect will be magnified at LTC, and we will see improvements of hundreds ELO points in normal chess with only dozens ELO in Knight-odds chess. One simply has to assume that perfect chess ELO is some reasonable finite value to see that handicap increase will be limited to a small fraction of this ELO limiting value.

[syzygy]

You are thinking way too small. Crafty, today, hits 100M nodes per second on my 20 core box. We are talking what about something that is 10,000,000 times faster, or even more.

And all those zillion nodes per second will be of no help whatsoever unless the opponent blunders away the win. And if the opponent does that, in the majority of cases current SF and Komodo will already be strong enough to take advantage of the mistake.

The hypothesis has been offered that once a GM is a knight ahead, he can play _perfectly_ and no machine will ever be able to beat him.

I don't think anybody said that. Humans will obviously make blunders now and then. The question is only if the human can play out the majority of games perfectly, i.e. make only moves that transition a winning position in another winning position. To do that the GM will have to play carefully, not take risks, and be sure to make use of the extra knight he has to control the game.

Hikaru believes that piece odds will now and forever favor the GM.

"favor" the GM does not require the GM to score 100%.

[bob]

I don't know that the machine will be able to win, but there is absolutely ZERO evidence to support that it will always lose. Absolutely ZERO. To make such a claim, there must be something to support it.

what is the reason that this statement of larry would not be evidence that the machine will lose to knight handicap ?

is it because he has not proven that K/C ratio cannot be 64%, or something else. ?

http://www.talkchess.com/forum/viewtopi ... 49&t=58846

Let's say that there is some handicap that would produce an even score in a serious match between Komodo and Magnus Carlsen. I would estimate that this handicap would be in the 1 to 1.5 pawn range based on Komodo's eval after a long think. Let's say 1.25. Now both Komodo and Carlsen make errors of some average magnitude. We'll call Carlsen's error rate C, and Komodo's K. I think it's pretty obvious that K is much less than C, let's say K = .4xC. If a future engine drops the error rate to zero, then C - K increaases to 5/3 of it's former value, so the proper handicap should also increase in that ratio. That would put it at 208, a bit over two pawns but way below the roughly 3.5 value of knight odds. Of course there is a lot of uncertainty in the above, but I don't think the estimate would be way off. In order for the estimate to reach knight odds, the K/C ratio would have to be about 64%, which does not seem plausible to me

How can you prove anything with no way to verify? He said something like the thought Komodo was within 1 pawn of playing perfectly. Not from the games I have seen. It is very strong, but it is FAR short of playing perfectly, based on analysis of output I have seen... And that is just today, of course. What happens in the future, or even beyond the future with the hypothetical access to 31 piece endgame tables?

If you backed up in time, say 20 years, would anyone be claiming that a computer could give a GM anything and still win? Not in any discussion I ever took part in, even at ACM/ICGA/ICCA chess events. So the bar has moved higher in 20 years. Is there empirical evidence that suggests that we are "at the max point of computer chess strength" already?

10-20 years ago we had lots of claims that computers were GMs when they were not. Now we seem to be at the point where some think the computer plays almost perfect chess, which it can't. And then some also assume that a human can play a knight odds game perfectly. He can't play a non-odds game perfectly so what suggests that taking away one of the opponent's pieces suddenly increases his skill level so dramatically?

I don't know what the max odds will be, and don't really care either. But to claim there is some asymptote that can't be crossed seems just a tae premature when there is no evidence to support this.

[bob]

I should know better than to jump into this... but I'm curious.

Doesn't an ELO difference of X indicate a particular chance of loss or draw regardless of the actual numbers? And if so, where is the breakdown of just comparing ELO for this handicap?

a) perhaps my understanding is off
b) perhaps ELO doesn't apply to handicap games, just regular chess
c) perhaps we lack ELO alignment between computers and humans

A couple are making the assumption that suddenly Elo is meaningless when talking about odds games, that somehow a player with a rating of 2700 in normal chess has an infinite rating when a knight ahead. I don't see any justification for such an assumption, however.

The question is how much improvement can we get with knight odd thanks to better hardware.


What is the difference in rating between Komodo 24 cores without a knight and Komodo 1 core without a knight(when both play against chess engines).

I do not have komodo and do not have 24 core machine but I guess that we are going to see less than 50 elo difference against engines if we use 10 minutes/40 moves or slower time control when the difference between 1 core and 24 cores is more than 200 elo in normal chess.

You are thinking way too small. Crafty, today, hits 100M nodes per second on my 20 core box. We are talking what about something that is 10,000,000 times faster, or even more. NOT what is possible today. The original question was what about 32 piece endgame tables. Could a computer beat a gm with knight odds or better given either 32 piece eg tables, or such incredible search depth that it plays such positions perfectly anyway. The hypothesis has been offered that once a GM is a knight ahead, he can play _perfectly_ and no machine will ever be able to beat him. I don't see any evidence to support that. For my 7 orders of magnitude improvement in speed, that is close to 24 doublings. That's not going to be 50 or 100 Elo improvement. And that is just the beginning.

I think both computers and chess programs have a long way to go before things flatten out. I'm not sure a knight will be impossible. I don't know, but I certainly know there is no evidence to suggest any sort of limit like that exists. Yes a queen and two rooks is enough and then some. But a knight. Knight and pawn? Rook? impossible to guess.

Well, let's see what happens for 4 doublings at ultra-fast controls with thousands of games. Keep in mind that the following effect is magnified at long time controls.

Knight handicap is worth 538 ELO points at 10,000 nodes per move with Stockfish. It is worth 984 ELO points at 160,000 nodes per move (4 doublings). It means the Knight handicap ELO value increases by 446 ELO points.

The ELO difference in normal chess between 160,000 and 10,000 nodes is 674 ELO points.

Therefore, the ELO difference in Knight-odds chess is 674 - 446 = 228 ELO points.

So, even at ultra-fast controls, an ELO increase in normal chess by 674 ELO points brings only 228 ELO points to Knight-odds chess. 228 ELO points increase in Knight-odds performance is about half a pawn additional allowed handicap at regular time control.

This effect will be magnified at LTC, and we will see improvements of hundreds ELO points in normal chess with only dozens ELO in Knight-odds chess. One simply has to assume that perfect chess ELO is some reasonable finite value to see that handicap increase will be limited to a small fraction of this ELO limiting value.

The only thing I don't buy is the "some max elo". If a chess program just crushes the best GMs on the planet, it will take forever to reach +800 elo. But then along comes a stronger chess program on future hardware and crushes that program. +800. And then along comes another. +800. I don't see anything to support some max upper bound, because this same topic came up 20-30 years ago with humans and 2800. Yet it was passed. All blowing one of these ceilings up requires is just one new program or hardware platform.

You can argue diminishing returns, but it is hard to specify a formula that is "the final word" so that one can take the limit of that function to get the max possible rating. Diminishing returns has been a fact, but it has never been a stable function. Along comes something new and the new max is raised, and the slope of the diminishing returns function now predicts a higher rating. We are not only talking about just raw hardware speed increases here, there will be software improvements as yet not even dreamed of. Sort of silly to try to predict future possibilities looking only at todays facts.

[Laskos]

The only thing I don't buy is the "some max elo".

Max ELO can be broadly theoretically derived.
If a typical game of chess is 100 moves, and the typical branching factor is 30, then the random mover will play perfectly at least ONE in 30^100 games, or one in ~ 10^150. So the random mover will score at least half a point point out of 10^150 games against perfect engine. The ELO difference between random mover and perfect engine is then no larger than 150*400 = 60,000 ELO points. Therefore Max ELO is lower than FIDE or CCRL rating of ELO 60,000.

[syzygy]

The only thing I don't buy is the "some max elo".

Max ELO can be broadly theoretically derived.

Chess is finite. Q.E.D.

From a mathematical point of view there is no difference between chess and tic-tac-toe.

(I realise now that Kai attempts to derive an upper bound on max Elo. That is of course more work than a simple proof of existence.)

[bob]

You are thinking way too small. Crafty, today, hits 100M nodes per second on my 20 core box. We are talking what about something that is 10,000,000 times faster, or even more.

And all those zillion nodes per second will be of no help whatsoever unless the opponent blunders away the win. And if the opponent does that, in the majority of cases current SF and Komodo will already be strong enough to take advantage of the mistake.

The hypothesis has been offered that once a GM is a knight ahead, he can play _perfectly_ and no machine will ever be able to beat him.

I don't think anybody said that. Humans will obviously make blunders now and then. The question is only if the human can play out the majority of games perfectly, i.e. make only moves that transition a winning position in another winning position. To do that the GM will have to play carefully, not take risks, and be sure to make use of the extra knight he has to control the game.

Hikaru believes that piece odds will now and forever favor the GM.

"favor" the GM does not require the GM to score 100%.

If you look back through this thread, the claim has been made that "GMs play perfectly with a knight advantage." If that were true, then they would, in fact, score 100%. Since 100% would be the definition of perfect play.

I don't believe humans can play perfectly even in endings like KQ vs KR. I believe most good players can win KQ vs KR after studying it a bit, but always playing the move that leads to the shortest mate? Not going to happen.

[syzygy]

If you look back through this thread, the claim has been made that "GMs play perfectly with a knight advantage." If that were true, then they would, in fact, score 100%. Since 100% would be the definition of perfect play.

I looked at the very first post and there is no claim that the GM would score 100%.

Some posts may have simplified the argument to "GMs play perfectly with a knight advantage". But the point of this thread is not to deny that GMs are human.

The claim is that top GMs in good health on normal days and at reasonable time controls should be able to outscore current and future top engines when given a knight advantage. The argument to support this claim is that in order to win a particular game it is sufficient for the GM to play that particular game perfectly. If the GM can do that in a particular game, no amount of processing power will help the engine. Zillions of nps in a lost position only help the engine to see more quickly that it is dead lost.

The definition of perfect play is not "scoring 100%" at all. For starters, 100% against a fallible opponent does not imply perfect play.

The definition of perfect play is very simple: play winning moves in a theoretically won position, play drawing moves in a theoretically drawn position.

Finding a "perfect" move can be difficult in a position that is still undecided from a human point of view. It is considerably easier in a position where one side has a clear winning advantage.

Given the lack of hard evidence, the question whether knight odds is already sufficient may still be largely a matter of opinion. But it seems rather reasonable that a top GM will be able to use the extra knight to control the game to such a degree that he can avoid taking risks and calmly but steadily increase his advantage.

[Laskos]

I should know better than to jump into this... but I'm curious.

Doesn't an ELO difference of X indicate a particular chance of loss or draw regardless of the actual numbers? And if so, where is the breakdown of just comparing ELO for this handicap?

a) perhaps my understanding is off
b) perhaps ELO doesn't apply to handicap games, just regular chess
c) perhaps we lack ELO alignment between computers and humans

A couple are making the assumption that suddenly Elo is meaningless when talking about odds games, that somehow a player with a rating of 2700 in normal chess has an infinite rating when a knight ahead. I don't see any justification for such an assumption, however.

The question is how much improvement can we get with knight odd thanks to better hardware.


What is the difference in rating between Komodo 24 cores without a knight and Komodo 1 core without a knight(when both play against chess engines).

I do not have komodo and do not have 24 core machine but I guess that we are going to see less than 50 elo difference against engines if we use 10 minutes/40 moves or slower time control when the difference between 1 core and 24 cores is more than 200 elo in normal chess.

This was a good estimate. As I wrote earlier I had an ultra-fast controls result that going from 10,000 nodes per move to 160,000 nodes per move (4 doublings) Stockfish increases the strength in normal chess by 674 ELO points, in Knight-odds chess by 228 ELO points. Therefore a fraction of 34%.

Now I tested for the fifth doubling: going from 160,000 nodes per move to 320,000 nodes per move increases the strength in normal chess by 158 ELO points, in Knight-odds chess by 43 ELO points. A fraction of 27%.

The fraction decreased from 34% to 27% to fifth doubling. Going to LTC on many cores means at least 10 more doublings and arguably below 20% fraction. So, from 1 to 24 cores there are ~200 ELO points gain in normal chess, and below 40 ELO points increase in Knight-odds chess. Your estimate was almost spot on.

[bob]

The only thing I don't buy is the "some max elo".

Max ELO can be broadly theoretically derived.
If a typical game of chess is 100 moves, and the typical branching factor is 30, then the random mover will play perfectly at least ONE in 30^100 games, or one in ~ 10^150. So the random mover will score at least half a point point out of 10^150 games against perfect engine. The ELO difference between random mover and perfect engine is then no larger than 150*400 = 60,000 ELO points. Therefore Max ELO is lower than FIDE or CCRL rating of ELO 60,000.

For discussions here, 60,000 is equivalent to infinite, when many postulate 3600 or whatever as the max. That was my point. A 60,000 Elo computer might easily win knight odds.