Something Hikaru Said

[rabbits23]

Ronald : This debate on perfect moves in chess is a fairly complicated one. I
don't think the game you gave as an example of a perfect one is accurate though as Black played 2...g5 or even 1... f6 which led to its demise.Yes for White it is a perfect game because it took advantage of Black's mistakes.But it is not a perfect game. Still it doesn't really matter to me. I agree perfect moves are made all the time but in complicated positions they are harder to discover and as you say we don't have the computational resources to verify their perfection.So why worry is my question? Just enjoy the game. And if people want to give handicaps fair enough, but I'm certainly not in that league .
Cheers Allan

[Laskos]

If you take programs from 1970, you would get a completely different perspective vis a vis "doubling". But we are not in 1970.

We are in 1993. I managed to test thoroughly Mephisto Gideon Professional (1993), a FIDE 2300 ELO engine of that time on a 1993 hardware ~200 times slower than 1 core i7. After failing to test properly at fixed time (too many time losses, too long time controls accepted by Gideon), I tested at fixed depth N+1 versus depth N, the gain from one additional ply:


The last measured test point is the gain on 9th ply and is equivalent to tournament time control on an 1993 PC. It corresponds to measured FIDE level of 2300 ELO of Gideon. One can observe a pattern of ELO gain per ply: odd plies behave differently from even ones. I don't know if that is valid for some other engines. The fit is a bit harder to do in this case, so I tested with more points.

The fit: the fitting curve chosen is relevant as I show. It is a/(1+b*(number of plies)^c). {a,b,c} are parameters to fit, and {c} is the relevant exponent here. If {c} is between 0 and 1, then we do have diminishing returns, but the total ELO is unbounded for higher and higher number of plies, therefore the rating of perfect engine is undetermined and high. If c>1, then the perfect engine has a definite limited rating which can be derived.
It turns out that the best fit is c=2.11, which is significantly larger than 1, and the ELO of the perfect engine can be computed and is not very high.
Having the fit, I can compute the ELO of the perfect engine by summing up all gains from depth starting from FIDE ELO 2300 (9th ply). It is ~2500 ELO points above. Therefore, Gideon (1993) shows a FIDE ELO of the perfect engines at about 2300+1500 = 4800 ELO points. Pretty close to 4550 I got with Komodo. So, this value seems to be more or less a universal quantity independent of time frame at least on a span of 23 years, while search techniques and the heuristics changed (no Null Move, no LMR, etc.).

[duncan]

If you take programs from 1970, you would get a completely different perspective vis a vis "doubling". But we are not in 1970.

We are in 1993. I managed to test thoroughly Mephisto Gideon Professional (1993), a FIDE 2300 ELO engine of that time on a 1993 hardware ~200 times slower than 1 core i7. After failing to test properly at fixed time (too many time losses, too long time controls accepted by Gideon), I tested at fixed depth N+1 versus depth N, the gain from one additional ply:


The last measured test point is the gain on 9th ply and is equivalent to tournament time control on an 1993 PC. It corresponds to measured FIDE level of 2300 ELO of Gideon. One can observe a pattern of ELO gain per ply: odd plies behave differently from even ones. I don't know if that is valid for some other engines. The fit is a bit harder to do in this case, so I tested with more points.

The fit: the fitting curve chosen is relevant as I show. It is a/(1+b*(number of plies)^c). {a,b,c} are parameters to fit, and {c} is the relevant exponent here. If {c} is between 0 and 1, then we do have diminishing returns, but the total ELO is unbounded for higher and higher number of plies, therefore the rating of perfect engine is undetermined and high. If c>1, then the perfect engine has a definite limited rating which can be derived.
It turns out that the best fit is c=2.11, which is significantly larger than 1, and the ELO of the perfect engine can be computed and is not very high.
Having the fit, I can compute the ELO of the perfect engine by summing up all gains from depth starting from FIDE ELO 2300 (9th ply). It is ~2500 ELO points above. Therefore, Gideon (1993) shows a FIDE ELO of the perfect engines at about 2300+1500 = 4800 ELO points. Pretty close to 4550 I got with Komodo. So, this value seems to be more or less a universal quantity independent of time frame at least on a span of 23 years, while search techniques and the heuristics changed (no Null Move, no LMR, etc.).

what is the ply level for gideon at 4800 ELO.?
also how many years/centuries per move does it need to play at that level?

[Laskos]

what is the ply level for gideon at 4800 ELO.?
also how many years/centuries per move does it need to play at that level?

Infinite to both questions. At least as counted here. One can set a limit, say 120 plies to play perfectly and the time would be, knowing the effective branching factor of ~4, 4^110 seconds, or something like 10^70 seconds.

[syzygy]

Ronald : This debate on perfect moves in chess is a fairly complicated one. I
don't think the game you gave as an example of a perfect one is accurate though as Black played 2...g5 or even 1... f6 which led to its demise.

If the opening position is a win for white, then black's 1...f6 and 2...g5 are as perfect as any other move that he could have played. In a lost position, all moves lose so they are all equally perfect.

[APassionForCriminalJustic]

Robert; Just thinking about it whilst struggling to get to sleep on a very hot
night here in Sydney I realized of course that there are many examples of perfect moves. Mate in ...fit the bill perfectly. No doubt there are other examples.
Regards Allan

Perfect moves are played all the time, but for most moves we lack the computational resources to verify their perfection.

I'm reasonably sure that many perfect GM-GM games exist. But we lack the computational resources to figure out which games are perfect and which aren't.

If the opening position is a win for white (unlikely, but not inconceivable), then 1.e4 f6 2.d4 g5 3.Qh5# is probably a perfect game. Otherwise, 1.d4 f6 2.e4 g5 3.Qh5# seems a good candidate (if the opening position wins but 1.e4 draws, then the winning opening move is probably 1.d4). Or simply: 1. e4 1-0 {black resigns}

If the opening position is a draw, then the most boring GM-GM game you can find might be a perfect game. Or simply: 1.e4 1/2-1/2 {drawn by agreement}

In a knight odds game, it will still be difficult for us humans (and engines) to know which moves or whole games are "perfect", but the moves that a good GM will come up with should normally be perfect and as long as the GM manages to play perfect moves, he will win that game. Now and then he might mess up, that is human.

The word "perfect" doesn't belong in the same sentence as "human".

[rabbits23]

Ronald; How do you determine the opening move is a win for White? By the moves that Black plays right? And this is why I think it gets silly and pointless.
There are so many moves Black can play and there is no way of knowing which of its moves are "imperfect' because that is decided by White's moves. And so on and so forth. You could go on forever. I don't want to.For me there are more satisfying topics to think about in chess.
Regards Allan

[syzygy]

Ronald; How do you determine the opening move is a win for White?

For starters, we don't know that the opening position is a win for white. Most likely, it is a draw. If the opening position is a draw, then white has no winning move in that position.

That is why I wrote the following (boldface added):

If the opening position is a win for white (unlikely, but not inconceivable), then 1.e4 f6 2.d4 g5 3.Qh5# is probably a perfect game. Otherwise, 1.d4 f6 2.e4 g5 3.Qh5# seems a good candidate (if the opening position wins but 1.e4 draws, then the winning opening move is probably 1.d4). Or simply: 1. e4 1-0 {black resigns}

If the opening position is a draw, then the most boring GM-GM game you can find might be a perfect game. Or simply: 1.e4 1/2-1/2 {drawn by agreement}

By the moves that Black plays right? And this is why I think it gets silly and pointless.
There are so many moves Black can play and there is no way of knowing which of its moves are "imperfect' because that is decided by White's moves. And so on and so forth.

This is about a theoretical argument. I realise that abstract thoughts are not to everybody's liking, but that will not stop me from entertaining them.

You could go on forever. I don't want to.For me there are more satisfying topics to think about in chess.

Nobody is forcing you to take part in this thread.

[rabbits23]

Ronald My fault. Sorry I said anything.
Allan

[Jesse Gersenson]

Infinite to both questions. At least as counted here. One can set a limit, say 120 plies to play perfectly and the time would be, knowing the effective branching factor of ~4, 4^110 seconds, or something like 10^70 seconds.

Which is 323,623,024,483,699,917,314,317,244,414,671,126,191,944,052,051,527,257,958,294,700 years.