#704
The relevant software exists: any chess engine e.g. Stockfish. Likewise checkers was solved using the checkers program Chinook.
Present cloud chess engines have reached 10^9 nodes / s. No need for new hardware.
It is not necessary to trace every possible line of chess. Necessary is to prove that 1 black move exists for all reasonable white moves to hold the draw.
#705
Of course chess is much more complex than checkers (= 8*8 draughts), but the same 3-pronged method can be applied:
1) humanly preparing tabiya for further analysis (26 men for chess)
2) calculating from the tabiya to the table base with a chess engine (Stockfish for chess)
3) looking up in the table base (7 men for chess)
#708
What I propose is to calculate with Stockfish from the tabiya at a pace of say 60 h / move until it hits the table base and then look up that it is a draw. That is not yet proof, that is begin of proof.
Then retract the last white move and verify it is a draw as well. Then retract the second-last move and verify it is still a draw. Then peel further back like that to arrive at the full proof.
#709
The output would be one large pgn file per tabiya with the core perfect game and its variations, all leading to table base draws.
#676
I cite a scientific paper, it describes in detail how they arrive at the 3*10^37. You ask for algebra. The algebra is in the paper. I do not have to copy/paste the algebra of the paper here. You either accept the outcome of the scientific paper, or you at least read their algebra.
You do cite the paper and indeed it does arrive at a figure of 3*10^37 as an upper bound on the number of legal chess diagrams without promotion under basic rules.
You use it in your calculation as an upper bound on the total number of legal positions under competition rules.
If you had taken my advice and read and understood #581 you wouldn't still be making that mistake.
Tromp's latest estimate (not upper bound) for the total number of legal positions under basic rules is (2.6+-2.9)x10^44 and so far as I know no more accurate estimate has so far been produced by Tromp or anybody else.
The figure you should have used in your calculation (legal positions under competition rules) is therefore (2.6+-2.9)x10^46 the index being increased by 2 to account for the 50 move rule.
I don't think it's the algebra in the paper that @playerafar is complaining about.
#712
On average there are only like 3 reasonable candidate moves. Carlsen said in an interview he looks at 3 candidate moves. Sometimes like check or recapture there is only 1 forced move. We only need to look at alternative moves for white, as long as the first choice for black has lead to a table base draw. We already start the tabiya around move 10. So for a 60 moves game that leaves 3^50 = 7e23. 60 moves may be a stretch, usually the game will be down to 7 men before move 60.
#713
Please stop with your smoke curtains and red herrings.
I have pointed out several times that almost all positions counted by Tromp are insensible and will never be reached in a reasonable game because they contain multiple excess underpromotions. That is why the Tromp count is way too high for the purpose of assessing the feasibility of solving chess.
Please stop with your rambings about competition rules. I have pointed out several times that we can consider the 50-moves rule as unwritten for the purpose of solving chess. It is a practical rule to ascertain that games and tournaments end in time and to prevent physical exhaustion of the players.
#715
Step by step:
1.08e37+6.14e36+3.19e36+5.66e35=2.07e37 legal, sensible positions from 26-men tabya
To account for positions rendered irrelevant by each pawn move and each capture, in analogy to the checkers proof: square root (2.07e37) = 4.55e18
Assuming a cloud engine at 1e9 nodes / second: 4.55e18 / 1e9 = 4.55e9 s = 1263812 h = 52658 days = 144 years for the whole of chess i.e. all 500 ECO codes A00 to E99.
Thus 144/500 = 0.28 year for 1 ECO code = 3.4 months.
As said 19 ECO codes suffice to prove a draw against 1 e4, hence 19*0.28 = 5.4 years to prove the draw against 1 e4 on1 cloud engine.
Likewise a 2nd cloud engine for 1 d4 and a 3rd cloud engine for other first white moves not transposing.
@tygxc #716
"Please stop with your smoke curtains and red herrings.
I have pointed out several times that almost all positions counted by Tromp are insensible and will never be reached in a reasonable game because they contain multiple excess underpromotions. That is why the Tromp count is way too high for the purpose of assessing the feasibility of solving chess.
Please stop with your rambings about competition rules. I have pointed out several times that we can consider the 50-moves rule as unwritten for the purpose of solving chess. It is a practical rule to ascertain that games and tournaments end in time and to prevent physical exhaustion of the players."
And I have pointed out in #581 (have you read it yet?) - whether or not the positions are 'sensible' has no relevance to your calculations.
I've also shown you that the Syzygy 7 man solution can easily produce excess (under)promotions.
You adopt the Bellman's approach, "What I tell you three times is true". But what you tell me three times is patently false.
It's no use telling me you've pointed something out, when I've already shown the flaw in what you've pointed out, unless you have given a valid rebuttal of my objection. Which you haven't.
My "smoke curtains", "red herrings" and "ramblings" do, in fact, completely destroy your thesis.
All this squabbling over a couple of insignificant powers of ten is a smokescreen. ...
It's rather more than a couple.
And it would extend the estimated time required for a solution, on @tyxgc's own basis (which needs further discussion), from 5 years to around a quarter of a million years. It was not intended as a smokescreen.
@Optimissed
"It is all unfocussed stuff ..."
I think what you meant to say is that the particular reader is unfocussed.
#665
The algebra is in the paper for you to read.
#667
I repeatedly said to forget the 50-moves rule. It is a red herring. It is a practical rule to make games and tournaments end in time and to prevent physical exhaustion of players. For the purpose of solving chess it can be considered non existent.
You have repeatedly said many dubious things.
Of course 1 e4 e5 hence white to move. Do not tell me 1 e3 e5 2 e4 black to move. White has no reason to lose a tempo, unless chess were a win for black. Even in that case black would not play 1 e3 e5. The position is symmetrical hence it does not matter.
Even an asymmetrical position is the same. 1 e4 c5 is white to move. Do not say 1 e3 c5 2 e4 black to move. White has no reason to lose a tempo. Even if white does, the position after 1 e3 c5 2 e4 is the same as 1 c4 e5 with colors reversed and already accounted for.
There is no reason to count positions twice.
I'm not counting positions twice, I'm counting diagrams twice, once for each side to move. There is every reason to do that.
Let us take the symmetrical diagram I posted and I'll break it down into words of one syllable. (Still one too many for @Optimissed, I fear.)
Consider that you're proposing to produce a weak solution under competition rules, for which the Wikipaedia definition is adequate.
"Weak: Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. That is, produce at least one complete ideal game (all moves start to end) with proof that each move is optimal for the player making it."
There are many ways to reach the diagram. (It would be א₀ under basic rules, but far fewer under competition rules. In the latter case it would depend on the ply count, but finite at any rate.)
I won't consider all possible ways of reaching the diagram, but look only at the ways you suggest.
The diagram is symmetrical, so it's either a draw with either side to move, a win for the player having the move or a win for the opponent of the player having the move. This is true under both basic and competition rules, but which applies is not necessarily the same under both.
Let us assume that it is a draw under competition rules with either side to move. (Unknown, but conceivable.)
If a solution is obtained for White, then arbitrary Black moves must be taken into account if the solution is to satisfy Wikipaedia's criterion. So if 1.e3 occurs in the solution then 1...e5 must also.
On the further assumption that the position after 1.e3 is also drawn under competition rules (again unknown, but conceivable) the diagram would occur in some weak solution from the starting position. If 1.e3 e5 occurs in a solution then so also would 2.e4.
This is not necessarily in the solution you would arrive at, but you don't know that until you finish your computation.
Similar considerations pertain on the assumption that the solution is for Black or that the position is a win for the first player under competition rules or that the position is a win for the second player under competition rules (again all unknown, but conceivable).
In general you're interested in the positions that may be needed in your computation, not the ones that appear in your eventual solution, so the positions that you must keep are not restricted to those that might occur in any weak solution anyway.
So you have no case for ruling out the positions with either side to move in the above diagram.
Tromp's estimate of the number of legal positions under basic rules already includes separate positions depending on the side to move and excludes positions where the side not to move is in check. It is that figure (2.6+-2.9)x10^44, adjusted for competition rules, that you should be using.
I'll try to get the post number right this time; please try reading and understanding #584.
At least you appear to have read it, even if it's apparent from the comments you inserted that you haven't understood it.
Possibly only makes the difference between chess being a win or a draw, but still, I think, not entirely irrelevant.
I'd agree you shouldn't rely on Wiki.
As for the rest, stop embarrassing yourself.
To be fair, I don't make a habit of telling people I'm cleverer than they are but unfortunately, it's slipped out in the past and I'm never allowed to forget it. I used to find it frustrating that people couldn't follow my arguments, or didn't want to. I tend to accept it nowadays. It's just a phenomenomoenomenon which sometimes repeats itself and, if it isn't important, which is most of the time, I let it go.
You can readily dispense with the "phenomenon" aspect of this by simply rewriting the paragraph much more simply, like so:
"Lots of people don't agree with or understand the reasoning I put forth...I routinely ignore them."
Once de-obfuscated, the underlying sentiment makes it quite easy to understand why this unfathomable phenomenon repeats itself.
*Edit: Wow. I wrote the above when I first read the above post snippet while catching up, then I read the rest of the posts I have missed the past day or two. So I guess I will not reopen any cans of worms by responding directly to any more posts, but I will finish out by saying that posters that assume that anyone that disagrees with them all belong to some secret cabal, or worse, are all personas of one single poster...well, it's just a bad coping mechanism that can't really do any good for anybody involved.
Although the details of how to go about producing a universally accepted proof is interesting, and the personal attacks are sometimes amusing and sometimes exasperating, the inclusion of the word "never" in the original question means that we are all making completely unreasonable assumptions concerning the limits of human ingenuity. To assert that our present capabilities are the measure of the future, that computing techniques and speeds cannot increase to the point of making a seemingly-impossible task doable, or that no genius will appear with a revolutionary rethinking of methodology, seems entirely too pessimistic. Although I must admit the ever-increasing possibility that extreme climate change could disrupt our present civilization severely enough to result in its collapse may put quits to my optimism.
#700
I am talking about checkers (= 8*8 draughts) as there we have a proof it is a draw and I propose to solve chess using the same strategy.
As said in chess each capture and each pawn move renders huge numbers of positions irrelevant: never again reachable henceforth.
How many positions are that? We do not know until chess is solved.
It is plausible to assume that in analogy to the checkers proof it is the square root as well. Maybe more, maybe less. Right now taking the square root as well is the best we can do.