i wonder how good the world would be if elroch and optimissed didnt waste their time and energy arguing over pointless topics
I half agree!
Infinitesimal impact on the world but infinity impact on this Forum. 
Throughout this thread, some have mistakenly considered extremely large finite numbers to be the equivalent of infinity....."for all practical purposes". This is a mistake. No matter how large a finite number is, it is not the equivalent of infinity....or even close.... period. And any logic or conclusions that follow that assumption are false.
You don't get any large finite numbers, they're all completely miniscule compared with practically all the rest. Come to that you don't get any large infinite numbers either.
You don't get any large finite numbers, they're all completely miniscule compared with practically all the rest. Come to that you don't get any large infinite numbers either.
"Minuscule" is one of the most commonly misspelled words in our language. How did spell check not catch that?
im just pointing out the almost funny sadness of it all... taking 5 seconds to do so is not equivalent to you guys writing essays also that was pretty funny elroch i cant lie
I am worried about all these schools nowadays where 2-3 paragraphs are given credit as an "essay" .
Wow
@4908
"It's just a theorem, not a proven fact."
++ It is the first mathematical theorem proven by a combination of humans and computers.
https://en.wikipedia.org/wiki/Four_color_theorem
Weakly solving chess should be done by a similar tandem
of good assistants with the latest computers during 5 years.
@4921
"At this stage all the unevaluated positions must be draws."
++ Think again. 1 g4 e5 2 f4 is no draw.
@4919
"What does this have to do with the solvability of chess? Different rules, fewer possible moves."
++ It proves that the number of relevant positions 10^17 to weakly solve Chess
can be much lower than the number of legal positions 10^44.
@4928
"2-3 paragraphs are given credit as an "essay""
++ A short post is not understood, a long post is not read.
@4928
"2-3 paragraphs are given credit as an "essay""
++ A short post is not understood, a long post is not read.
Short and long are subjective. These are not absolutes any more than 10^17 is an absolute .
Chess is better not solved
[Link removed]
get 20% off the courses with my link
Spam is better not posted. This also applies to the emoji posts above.
Edit: Yay, some moderation, the emoji spam is gone.
@4935
"These are not absolutes any more than 10^17 is an absolute"
++ If anybody has an argument why it should be 10^18 or 10^16 I am all ear.
You don't get any large finite numbers, they're all completely miniscule compared with practically all the rest. Come to that you don't get any large infinite numbers either.
"Minuscule" is one of the most commonly misspelled words in our language. How did spell check not catch that?
Indeed. Red face.
I always ignore the spell check because it works in Americanese.
i wonder how good the world would be if elroch and optimissed didnt waste their time and energy arguing over pointless topics
I half agree!
Infinitesimal impact on the world but infinity impact on this Forum.
The main problem is the circularity and repetition of disagreements. I'm quite optimistic but not holding my breath.
This is true and should be repeated ad nauseum.
[ok, a tad of irony there].
@4935
"These are not absolutes any more than 10^17 is an absolute"
++ If anybody has an argument why it should be 10^18 or 10^16 I am all ear.
You could easily argue for 10^18 or 10^19 yourself just by not systematically dropping the mantissa in each of your reductions, e.g. not rendering Tromp's estimate of 4.85304e+44 +- 3.9004e+42 basic rules positions as 10^44. You don't need someone else to do it (and in any case you've comprehensively proved you're all deaf ear.)
Wouldn't say anything about reality either way.
@4937
"rendering Tromp's estimate of 4.85304e+44 +- 3.9004e+42 as 10^44".
++ Each position with white to move has an up / down mirror position with black to move.
Each position with lost castling rights has a left / right mirror position.
That yields 1.21326e+44 +- 0.00975e+44, so 1e44 is close enough.
Likewise the Gourion estimate of 3 × 10^37 becomes 1.5 × 10^37
https://arxiv.org/abs/2112.09386
@4937
"rendering Tromp's estimate of 4.85304e+44 +- 3.9004e+42 as 10^44".
++ Each position with white to move has an up / down mirror position with black to move.
Each position with lost castling rights has a left / right mirror position.
That yields 1.21326e+44 +- 0.00975e+44, so 1e44 is close enough.
Likewise the Gourion estimate of 3 × 10^37 becomes 1.5 × 10^37
https://arxiv.org/abs/2112.09386
That ignores the fact that you're planning to use SF which has to keep track of triple repetitions. It can't do that if it take symmetries into account, because the equivalence classes under symmetries can occur three times without the game necessarily being drawn.
Gourion talks only about diagrams, not positions under either basic or competition rules.
It can't use basic rules in the first place.
If you check the positions after move 34 in the mainline and variation here you will find the FENs are identical so the basic rules positions are the same. The mainline is a draw at that point while the variation is a mate in 17. Unfortunately it appears that your workhorse is not up to mating with a king and pawn against a lone king.
By the way that's another of your 1 in 10^zillion cases where SF's top four moves lose half a point.
White to move
Black to move
@4942
"That ignores the fact that you're planning to use SF which has to keep track of triple repetitions."
++ No, I do not use Stockfish to track triple repetitions, I just compare FENs.
"equivalence classes under symmetries can occur three times"
++ No they do not.
The up/down and left/right mirror images do not occur and certainly not in the same game.
"Gourion talks only about diagrams, not positions."
++ Tromp calculates diagrams and multiplies by 2 to get positions.
That is why the Tromp count is a factor 4 too high for this purpose
and the Gourion count is only a factor 2 too high for this purpose.
[snip]
chess is a finite game
Can you support this?
If I might interject, I think that perhaps you are thinking that without the 50 move rule, endless repetitions can occur and so chess is therefore infinite and could not be solved...but in terms of solving, an endless repetition is simply a draw, and the calculations move onward.
In the case of tablebases, they are built going backwards from checkmate. So, you cannot ever logically reach an endless repetition in a regression like this. We're at 7 man tablebases right now, so for 7 pieces or less, if the position is *not* forced mate and not in the tablebase, it is therefore a draw. Draws are inferred by exclusion.
When thinking about the logic of generating tablebases I came to the conclusion that at each pass of the algorithm, as you add the evaluation of more positions further from mate, at some point you have a step when no more are added. At this stage all the unevaluated positions must be draws. (The reason being that every mate in N leads to at least one mate in N-1 on the next move, so if there are no mate in N, there can be no mate in more than N). Is this convincing?
I also thought along the lines of btickler for a version of chess with no repetition/50 move rules, that for mathematical purposes alone you can extend to infinite games and say an infinite game is a draw. This could be made finite without changing anything significant about the value of starting positions (I assert) by adding either a very large N-move rule or a repetition rule.