#3180
Here is an explanation of the 50 imposed openings in TCEC.
https://www.chessdom.com/tcec-s22-superfinal-starts-today/
"opening lines are risky and have a (very) high bias.
This is necessary to avoid an excessive number of uninteresting draws."
"Statistics of the previous superfinals show that a Leela book exit below +0.30 is an almost 100% certain draw."
#793
The Gourion number is an overestimate.
The positions as randomly sampled by Tromp make no sense at all
7 white rooks
3 black rooks
2 black dark square bishops
5 black knights
I gave a proof game above.
If a cloud engine at 10^9 nodes / second during 60 hours per move is considered a "toddler", then the beings that reach the Tromp samples are not even embryos, maybe amoebes.
That is not odd, It is just stupid.
Besides for weakly solving chess not the full 10^37 positions need visiting, only a small fraction of these.
"I think it's almost definite that the game is a draw theoretically" Fischer
"We do not know for a fact that the starting position is a draw, but it does seem like a safe assumption - Rowson 2005.
Hi, I don't think that's "reasonable doubt". Both are saying they think it's drawn. It seems as though they're just coveing themselves; not wishing to be outspoken. It isn't evidence that they really think it may be a win.
Hi. Possible, but I think they at least think that the evidence is not enough for a scientific proof: would they be so cautious, otherwise?
Apart from that, as I said earlier the modern view on science is that the only real proof is a mathematical proof.
Disagree. But who am I to disagree with anyone? Just that mathematics is used as a depiction of observed results and there can be inaccuracies in the observations and also in methodology shortcuts. Normally, things are described as accurate within limits or an error margin.
Agree, but that's another reason to say that, apart from mathematics, strictly speaking science cannot prove things.
But let's assume that we can consider something "scientifically proven" the old way, i.e. a theory is proven, if experiments consistently confirm it. Can we say that it is scientifically proven that the game-theoretic value of chess is a draw? Imo no, because the game-theoretic value is the best outcome that a player can force. If we don't know for sure that the value is forced, the experiments that we can run (games between more or less strong players) cannot confirm nor contradict the statement. The increasing draw rate in games between engines of the same strength, and in particular in autoplay, can be explained with the increasing stability of the evaluation functions, both because of the introduction of neural networks, and because the evaluations become (on average) more stable with depth.
I think you're just describing normal, experimental error. There's no reason to assume that a way is going to be found to eliminate it and when we describe something as "proven" it really can be via the pragmatic method.
There is a difference, though. We can scientifically prove which is the accuracy of the devices used to measure physical quantities, and we have a variety of statistical tools to analyze samples. So, roughly speaking, when we measure a phenomenon we can assume that the mean of the sampled data is the "real" value of the physical quantity we are measuring, within a confidence interval. In our case, I don't think we can say that the outcome we more often observe, is the best that actually can be forced.
For this reasons it becomes more and more difficult to overcome an opponent of the same strength, but that does not mean that the game value is a draw. I think that if the increasing drawing rate depended on the game-theoretic value, we should not see the playing strength and ratings of the top engines increase at the current rate.
I don't follow that so it must be a piece of inductive thinking. It doesn't seem safe or relevant.
Of course, it's not safe (in fact I said "I think")! I wrote that, because @tygxc claims his explanations for the observed data are the only possible ones. I just think that other explanations are more plausible, but equally not sufficient for a proof.
yes
simple!
"I think it's almost definite that the game is a draw theoretically" Fischer
"We do not know for a fact that the starting position is a draw, but it does seem like a safe assumption - Rowson 2005.
Hi, I don't think that's "reasonable doubt". Both are saying they think it's drawn. It seems as though they're just coveing themselves; not wishing to be outspoken. It isn't evidence that they really think it may be a win.
Hi. Possible, but I think they at least think that the evidence is not enough for a scientific proof: would they be so cautious, otherwise?
Apart from that, as I said earlier the modern view on science is that the only real proof is a mathematical proof.
Disagree. But who am I to disagree with anyone? Just that mathematics is used as a depiction of observed results and there can be inaccuracies in the observations and also in methodology shortcuts. Normally, things are described as accurate within limits or an error margin.
Agree, but that's another reason to say that, apart from mathematics, strictly speaking science cannot prove things.
But let's assume that we can consider something "scientifically proven" the old way, i.e. a theory is proven, if experiments consistently confirm it. Can we say that it is scientifically proven that the game-theoretic value of chess is a draw? Imo no, because the game-theoretic value is the best outcome that a player can force. If we don't know for sure that the value is forced, the experiments that we can run (games between more or less strong players) cannot confirm nor contradict the statement. The increasing draw rate in games between engines of the same strength, and in particular in autoplay, can be explained with the increasing stability of the evaluation functions, both because of the introduction of neural networks, and because the evaluations become (on average) more stable with depth.
I think you're just describing normal, experimental error. There's no reason to assume that a way is going to be found to eliminate it and when we describe something as "proven" it really can be via the pragmatic method.
There is a difference, though. We can scientifically prove which is the accuracy of the devices used to measure physical quantities, and we have a variety of statistical tools to analyze samples. So, roughly speaking, when we measure a phenomenon we can assume that the mean of the sampled data is the "real" value of the physical quantity we are measuring, within a confidence interval. In our case, I don't think we can say that the outcome we more often observe, is the best that actually can be forced.
For this reasons it becomes more and more difficult to overcome an opponent of the same strength, but that does not mean that the game value is a draw. I think that if the increasing drawing rate depended on the game-theoretic value, we should not see the playing strength and ratings of the top engines increase at the current rate.
I don't follow that so it must be a piece of inductive thinking. It doesn't seem safe or relevant.
Of course, it's not safe (in fact I said "I think")! I wrote that, because @tygxc claims his explanations for the observed data are the only possible ones. I just think that other explanations are more plausible, but equally not sufficient for a proof.
yes
simple!
i say "yes"!
'Somebody' wants the 'small fraction' to be a trillionth of a trillionth of the number of positions in the task.
The number of possible positions in chess versus the number of possible games ... well they're both enormous numbers.
But the second ...
try an analogy.
The number of possible chess positions could be something like the number of atoms within the planet Jupiter. The largest planet.
Close to it? Not the point.
The point is its a very very big number - but its finite.
But the number of possible games ?
That could be more like the number of atoms in the universe - whether finite or infinite universe.
Result: the number of possible positions is easier to work with.
And in the endgame tablebases - its even Known for small numbers of pieces !!
Issue: But for 'solving' positions - you can't completely get away from both 'games' and 'elements of games'.
In other words sequences of moves.
Can't be avoided.
That's the central issue.
Getting around the daunting 'game variations' - but in a way that's both mathematically and scientifically valid.
'Scientifically valid' for the computers. Practical.
And for now - there's no way to do that.
And no money from smart people thrown away on such a thing.
But there are related projects though.
Lots of them. One of them ... 'Stockfish'
"By publishing a monograph on the 5...e5 system in 1988, I practically exhausted this variation."
- Sveshnikov
If Sveshnikov did that on his own in 1988 without engines or table bases,
then it is plausible to weakly solve chess in 5 years with modern computers and good assistants.
Two HUGE errors. Sorry, three.
On the plus side, you said "plausible", which means you realise you could be wrong, which is entirely reasonable.
#3205
He said:
"Since that time only some details have been developed, without introducing anything particularly new: the evaluations of the main lines have hardly changed." - Sveshnikov
In the Anand - Gelfand match white got nothing with the main line 7 Bg5.
https://www.chessgames.com/perl/chessgame?gid=1666526
In the Caruana - Carlsen match white first avoided the Sveshnikov B33 with 3 Bb5, got nothing and then played the 7 Nd5 line and got nothing either.
https://www.chessgames.com/perl/chessgame?gid=1937913
So it seems that the teams of grandmasters and engines just agreed with Sveshnikov.
So the silicon evaluation just confirmed the human evaluation.
#3207
That is how it works
Here is an ICCF game from the last WC.
It is 99% sure to be a perfect game without any error.
If tic tac toe can be solved, then chess can too!
lmao I'm maybe just kidding
#3207
That is how it works
Here is an ICCF game from le tast WC.
It is 99% sure to be a perfect game without any error.
...according to some imperfect engines that are still incrementally improving each release...
People used to think Deeper Blue was pretty accurate. It would lose most games to a current top engine.
"By publishing a monograph on the 5...e5 system in 1988, I practically exhausted this variation."
- Sveshnikov
If Sveshnikov did that on his own in 1988 without engines or table bases,
then it is plausible to weakly solve chess in 5 years with modern computers and good assistants.
We must all agree that. If the antecedent is false then the implication is true.
People used to think Deeper Blue was pretty accurate. It would lose most games to a current top engine.
This is a good point - but even on that - 'current top engine' (one of them) assigns wins to obviously drawn positions.
Stockfish.
Astutely posted by MARattigan.
But these realities are lost on those rejecting such reality.
Its similiar to flat earthism.
#3211
It is 99% sure to be a perfect game.
I calculated before
17 ICCF (grand)masters with engines, round robin, 5 days / move
136 games
126 drawn games with 0 errors: ideal games with optimal moves i.e. perfect play
9 decisive games with 1 error
1 drawn game with 2 errors
That is the only consistent way to explain the observed data.
Bear in mind that the tournament lasts about 2 years and that the 17 ICCF (grand)masters use one or more multicore engines each, so the result of 136 games represents a century of engine calculation guided by human ICCF (grand)masters.
#3193
"I just think that other explanations are more plausible, but equally not sufficient for a proof."
++ No, you cannot explain that.
AlphaZero autoplay data:
1 s/move: 88.2% draw, 7.72% white wins, 4.09% black wins (a data set of 10,000 games)
1 min/move: 97.9% draw, 1.8% white wins, 0.3% black wins (a data set of 1,000 games)
Assume for argument's sake unlimited time and unlimited engines available.
If the time per move keeps increasing, the draw rate keeps increasing too, to near 100%.
However, if the time per move keeps increasing more, it comes at some finite but huge time/move at a point where it exhausts all finite number of chess positions.
Now if chess were a white win, then the draw rate would keep getting closer and closer to 100% with increasing time per move and then suddenly plummet to 0%.
That is absurd.
This proves that chess being a white win is inconsistent with the observed data.
Likewise for the hypothesis chess being a black win.
Remains: chess is a draw.
The last completed ICCF WC had 127 draws, 6 white wins 3 black wins.
I explain these data under the assumption that chess is a draw: 126 perfect games with no errors, 1 draw with 2 errors, 9 decisive games with 1 error. I can even pinpoint the 1 error in the 9 decisive games.
-> Please tell under the assumption that chess were a white win:
How many of the 127 draws have 1 error, 3 errors, 5 errors... ?
How many of the 6 white wins have 0 errors, 2 errors, 4 errors...?
How many of the 3 black wins have 2 errors, 4 errors, 6 errors...?
I have already wrote my objections to your calculations many posts ago, but there is no point in debating them, before the issues highlighted in the previous post are dealt with.
Please tell under the assumption that chess were a white win:
How many of the 127 draws have 1 error, 3 errors, 5 errors... ?
How many of the 6 white wins have 0 errors, 2 errors, 4 errors...?
How many of the 3 black wins have 2 errors, 4 errors, 6 errors...?
It's impossible to tell before a weak solution is determined, either under the assumption that the game is a draw or a win.
Do you consider proven to your satisfaction:
"the number of legal chess positions is approximately (4.82 +- 0.03) * 10^44" ?
I already answered your question, and I ask you if you know of anyone who says that it's proven.