@7116
"which ended in an agreed draw with 13 men on the board"
++ The transition to a 7-men endgame table base draw is forced.
"This is the same game continued using Arena/Stockfish." ++ Very well, this shows the need for human assistants to cut short such needless calculations and call it a draw.
"All the other perfect games reach the 7-men endgame table base draw or a prior 3-fold repetition sooner. Big red telephone again?"
++ No, statistics. Between 13 and 119 moves, 42 moves average, with standard deviation 16.
"If you calculate all reasonable white moves, then 1 tentative black response, then all reasonable white moves, then 1 tentative black response and so on then the 7-men endgame table base draw or a prior 3-fold repetition is reached in at most 119 moves, i.e. 238 ply.
You don't have a reasonable definition of reasonable".
++ That is just the best first heuristic as used in solving Checkers and Losing Chess.
If the 4 best moves cannot win for white, then the worst moves cannot win either.
"But perfect games need only perfect moves"
++ Statistics applied to the ICCF WC Finals games show they are > 99% sure to be perfect games i.e. they contain optimal moves from both sides.
"Tromp's estimate of the number of basic rules positions is 4.82 x 10^44"
Yes, but the factor 4.82 is irrelevant and should be 1.205 because of up / down symmetry and left / right symmetry after loss of castling rights.
"2^148 < 4.82 x 10^44 <2^149" ++ Yes
"By digital decisions I assume you mean choices of moves"
++ Yes, less than 149 choices between 2 moves, or less than 74 choices between 4 moves.
"You make no mention of whether the moves are perfect or not"
++ That is only legal choice, if they need to be perfect there is even less choice.
"I can't find anywhere in that game the position after 1.e4 e5 2.Ba6. Can you?"
++ It is clear that 2 Ba6? is not optimal play by white.
"Wouldn't that be included in Chess?" ++ Yes, 1 e4 e5 2 Ba6? belongs to the 10^44 legal positions, but not to the 10^17 relevant positions.
"Neither can I find any of the positions with the same diagram and ply count 13 under the 50 move rule" ++ The 50-moves rule plays no role. Games with optimal play from both sides end in draws long before the 50-moves rule would trigger.
"How are you going to make it generate only moves tygxc thinks are reasonable?"
++ Stockfish ranks the legal moves. Then it is the best first heuristic.
If the best white moves cannot win, then the worse white moves cannot win either.
"If a 7-men endgame table base draw or a prior 3-fold repetition is reached,
then that validates all black responses as fit to draw."
++ People here still fail to understand this, though it is simple.
If all reasonable white moves fail to win against a black response, then that black response is optimal. It does not matter how that black response was obtained. It does not matter if other black responses draw as well or not.
If white cannot win against those black responses, then Chess is weakly solved.
If the black responses lead to a table base draw or a prior 3-fold repetition,
then they are optimal in retrospect.
@7107
"What on Earth are you talking about?" ++ This is the longest perfect game with optimal play from both sides to reach the 7-men endgame table base draw.
https://www.iccf.com/game?id=1164280
No it's not.
It's Jon Edwards v Sergey Adolfovich Osipov from the ICCF WC 32, which ended in an agreed draw with 13 men on the board.
This is the same game continued using Arena/Stockfish. It ended with a claim under the 50 move rule on move 236.
It took 119 moves to the 7-men endgame table base draw i.e. 238 ply.
You may as well leave out the endless translations from moves to ply; I think we can all manage it. Especially since you appear to have insurmountable problems counting up to 7.
All the other perfect games reach the 7-men endgame table base draw or a prior 3-fold repetition sooner.
Big red telephone again, right?
"But how does that relate to your proposed method of solution?"
++ If you calculate all reasonable white moves, then 1 tentative black response, then all reasonable white moves, then 1 tentative black response and so on then the 7-men endgame table base draw or a prior 3-fold repetition is reached in at most 119 moves, i.e. 238 ply.
You don't have a reasonable definition of "reasonable".
You claim that all perfect games that are not Jon Edwards v Sergey Adolfovich Osipov from the ICCF WC 32 reach the 7-men endgame table base draw or a prior 3-fold repetition sooner than Jon Edwards v Sergey Adolfovich Osipov from the ICCF WC 32. That's true of perfect games that reach one or other, but only because Jon Edwards v Sergey Adolfovich Osipov from the ICCF WC 32 never reached either.
But perfect games need only perfect moves, they don't have to include moves that tygxc thinks are reasonable. You make no connection between perfect moves and moves that tygxc thinks are reasonable.
Indeed, earlier in the thread you accused the Syzygy tablebase of trolling in this game.
Is it your contention that Syzygy is trolling and all it's moves are reasonable?
Another explanation: chess has 10^44 legal positions. 10^44 = 2^146.
Here you're a victim of your own misinformation.
Tromp's estimate of the number of basic rules positions is 4.82 x 10^44. NOT 10^44.
2^148 < 4.82 x 10^44 <2^149.
So after 146 digital decisions you get the whole of Chess.
By "digital decisions" I assume you mean choices of moves. (Or are you still struggling to count up to 7 on your fingers?)
You make no mention of whether or not the moves are perfect so the continuation of Jon Edwards v Sergey Adolfovich Osipov would be a case in point.
I can't find anywhere in that game the position after 1.e4 e5 2.Ba6. Can you? Wouldn't that be included in Chess?
Neither can I find any of the large number of positions with the same diagram and ply count, say, 13 under the 50 move rule. Would they not also be included in Chess (though of course not in Tromp's number)?
Checkmates that exceed 146 moves exist, but they must contain a string of forced moves.
So far as I can understand your logic (not very far), that seems to rest on on the obviously invalid assumption that the number of basic rules positions associated with the competition rules positions occurring in all continuations is the product of the number of choices of moves in each such competition rules position or something of the sort. Choice of perfect moves maybe?
That would need Tromp's upper bound rather than his estimate for a valid proof (as well as a different argument). Also you would need to say exactly what you mean by "forced" and how many moves constitute a "string". (Do you include strings of one?.)
Here is a provably perfect (just in case it needs to be) checkmate in 148. Can you indicate some strings of forced moves?
Mainly, I can't see your point even if what you say is true. It is to be expected that with most definitions of "forced move" such strings will occur in a long sequence of moves whether as part of a win or draw. Are you trying to make a relevant point or are you just away wi' the fairies?
Edit: sentence reinserted for context ->But how does that relate to your proposed method of solution? "Stockfish doesn't do perfect play."
++ Agreed, but that does not matter. Stockfish only needs to generate the reasonable white moves.
In the vanishingly unlikely event that you ever got a sponsor it might matter to him.
How are you going to make it generate only moves tygxc thinks are reasonable?
Stockfish then selects the 1 black response without worry if perfect or not.
If a 7-men endgame table base draw or a prior 3-fold repetition is reached, then that validates all black responses as fit to draw.
Obviously not.
"99.9 % of my games are perfect" ++ No, they are not.
Are so !
"same way you got your ICCF stats." ++ No.
++Yes. So there !