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].
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?
It's because miniscule is such a prevalent mis-spelling that it has become border-line accepted and may have been programmed into some spell-checkers.
It's always funny to watch people complain about threads they have the ability to skip by. Do you habitually punish yourself? It takes a certain lack of self awareness.
Provide some meaningful content of your own...bonus points if it is actually chess related.
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
Yes, much sadder, because you're objecting to how people choose their entertainment. Your entertainment is objecting to others'.
@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.
Your puzzle is incorrect. I played 2. ....Ra5 and it was given as wrong.
Oh it is wrong, sorry. Missed a4. I don't like chess.com puzzles. They won't allow you to think for yourself so I treat them as trivial. I've done two and got them both right, though.
@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
<<++ Each position with white to move has an up / down mirror position with black to move.>>
Wouldn't ++ "Each position with white to move has an identical position with black to move" be simpler and clearer? Does it lack any information?
By the way, the initial position hasn't! 
@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.
@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.
You can compare FENs 10^9 times a second and restart SF with a different move without breaking step. Impressive!
But it sort of ignores the fact that the number of FENs is not divided by 4 either.
"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.
That seems to account for all cases. Interesting! Youve just proved that no positions can ever occur in a chess 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.
You don't say what purpose, but if it's anything to do with playing chess you need to take into account more than just diagrams. Otherwise fights would break out when both players are trying to move at the same time.
It'll be solved because AI will calculate everything.
@4945
"You can compare FENs 10^9 times a second"
++ No, not at all. FEN is only compared every 17 s. A comparison is a simple operation.
"That seems to account for all cases."
++ No, the mirror positions cannot transpose into each other.
"You don't say what purpose" ++ For the purpose as a starting point to estimate the number of relevant positions in weakly solving chess.
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.
Well, some infinite numbers (let's presume that means "cardinals" in this context) are large compared with a lot of other infinite numbers. So they can be considered large in the same way as a googol is often viewed as a large integer.
A major example would be a (strongly or weakly) inaccessible cardinal). Any inaccessible cardinal is bigger than any cardinal whose existence is provable in ZFC!
ZFC itself does not imply the existence of an inaccessible cardinal. The existence of one implies the consistency of ZFC, which itself implies that it cannot be proven that the existence of a large cardinal is consistent with ZFC (most mathematicians believe it is)).
That the linked article includes the phrase " Therefore, inaccessible cardinals are a type of large cardinal" and there is a page on said large cardinals shows mathematicians are not averse to the idea of large infinite numbers. Worse, it turns out that there is a whole litany of distinct ways in which cardinals can be large!
@4949
10^17 is a huge number, but it is finite. Chess is finite.
@4945
"You can compare FENs 10^9 times a second"
++ No, not at all. FEN is only compared every 17 s. A comparison is a simple operation.
By which time SF will have used positions rather than equivalence classes of positions 17x10^9 times on you figures.
"That seems to account for all cases."
++ No, the mirror positions cannot transpose into each other.
Well not by themselves. Somebody has to move the pieces.
"You don't say what purpose" ++ For the purpose as a strating point to estimate the number of relevant positions in weakly solving chess.
In which case the Tromp figures are not too high for basic rules chess by a factor of 4 if you're planning to use SF they're correct, The Gurion count is not fit for purpose - your purpose that is, not Gurion's.
Tromp's figure is humongously too low if you plan to use SF for solving competition rules chess.
@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.