The number of possible games is irrelevant to an intelligent conversation regarding "solving chess" but so is the total number of possible positions. The only relevancy is the number of relevant positions, which looks a bit circular ..... but a position that is relevant to a solution is one that is reached by a series of moves which doesn't contain any obvious blunders. And, of course, that cuts out an enormous majority of positions from consideration. What's more, another large majority can be removed by cutting out all those which are reached by a series of moves which don't make any "chess sense".
So let's say white opens 1. a3 and then 2. b3 and 3. c3. If black were to reply by any similarly meaningless series of moves, all the positions reachable from such a series, except by transposition, are irrelevant, because one side isn't attempting to profit from the other side's weak moves. The idea that a6, b6 and c6 is black's best way to respond to a3, b3 and c3 isn't reasonable and can be discounted.
In reality, before chess can be properly "solved", it's necessary to analyse it algorithmically to mathematically express (depict) positions that are meaningful in a chess sense rather than in merely a random/legal sense. This is in itself a big job but it would provide a filter that is necessary if meaningful (relevant) positions are to be automatically identified.
This may be a bit difficult to follow, I don't know. But it's how things are.
will chess ever die out once its fully solved?
#964
That is why human assistants should guide the computer search. We can use heuristics. It is not necessary to analyse 1 e4 e5 2 Ba6 to checkmate. It is no priority to look at 1 a3, 1 b3, or 1 c3. If it can be proven that black can draw after 1 e4 and 1 d4, then the other 18 possible first moves become trivial.
With 2 cloud engines during 5 years it is possible to solve 36 carefully selected ECO codes.
#964
That is why human assistants should guide the computer search. We can use heuristics. It is not necessary to analyse 1 e4 e5 2 Ba6 to checkmate. It is no priority to look at 1 a3, 1 b3, or 1 c3. If it can be proven that black can draw after 1 e4 and 1 d4, then the other 18 possible first moves become trivial.
With 2 cloud engines during 5 years it is possible to solve 36 carefully selected ECO codes.
Quite right for the first part. Probable for the second part but starting now, there would be a lot of preparatory work and it still might not lead to a meaningful solution without machine-intelligent methods being developed and starting now, I doubt they could be completed in ten years, even if NASA prioritised them!
#979
It is no NASA priority: they want to put humans on Mars...
The Lomonosov University, or Google, or IBM might make it a priority.
The smart way would be to start with 1 ECO code, e.g. C67.
I don't think we've got the tech to do it, either, except a sort of do-or-die thing in the spirit of the 1969 moon landing that's completely unnecessary in this context. Except of course, putting out signals that it's ok to completely destroy the Earth because WE'VE got people on Mars, as if they'd last 100 years there. Maybe it makes the USA our enemy! ![]()
Humans on Mars cost billions, solving chess costs millions.
https://cloud.google.com/compute/all-pricing
#962
Without excess promotions. There can be promotions, but not to more pieces than in 1 box of chess men and not to 2 same color bishops. That makes sense. The vast majority of the previous number 10^44 are with multiple queens, rooks, knights, and same color bishops. Look at the sample of the 10^44.
The new number 4*10^37 is not even an estimate: it is an upper bound.
Calling the game actually solved (strong-form solved, all legal positions) will require even the silly positions like King and seven knights vs King (or whatever example you like, if that one happens to not be legal). This is simply because it requires all legal positions.
So, I do think 10^44 is the number to focus on, since I wouldn't consider less to be an actual solution (in other words, checkers is only weakly solved, last I checked, because they don't have all positions, but they do have a path from the initial position).
But this part of the discussion doesn't change whether the thing is possible. It is possible, for a sufficiently advanced civilization, that can devote star-level resources to it. It is not possible for us, at least not any time soon.
<<<Calling the game actually solved (strong-form solved, all legal positions) will require even the silly positions like King and seven knights vs King (or whatever example you like, if that one happens to not be legal). This is simply because it requires all legal positions.>>>
Why?
Humans on Mars cost billions, solving chess costs millions.
https://cloud.google.com/compute/all-pricing
For whatever reason, I don't believe that. If solving chess only cost millions, it would have been done by now. There is always some eccentric billionaire that loves to spend millions on something nobody cares about, just to say he did it.
If chess is solved and white always wins a perfectly played game, it wont matter. Because to answer the question of this topic, yes, chess will have died out once it's "fully" solved, because people will have died out before it's solved. So it will only matter to the computers who are left roaming the earth in our place. And it seems unlikely competing computers would play a solved game when they could instead be trying to figure out how to bring people back and/or invade Zurkon.
Anyway, why are you both talking about this irrelevant rubbish, which is as bad as Coolout's? It's all about semantics in a way. In calculating the number of relevant lines you use the most efficient way of reaching a position and all the rest is redundant.
If it's irrelevant rubbish, then don't even bother to mention about it. Also, "the rest" is not redundant at all. It's actually necessary to calculate.
Our minds are computers ourselves. Do you feel its necessary to calculate giving all your pieces away even though its possible? How long do you sit there contemplating that during a match? When you calculate all the different scenarios you are playing out, do you play out those moves that should not even be considered viable?
I do. That's part of the reason I'm such a terrible chess player. I'm always looking for ways to give all my pieces away. My best so far is a 3 piece sacrifice mate.
<<<Calling the game actually solved (strong-form solved, all legal positions) will require even the silly positions like King and seven knights vs King (or whatever example you like, if that one happens to not be legal). This is simply because it requires all legal positions.>>>
Why?
It''s by definition. "Solved" is defined a couple ways by the folks working on this. Strong form definition includes all legal positions. Weak form definition has an aspect of what's reasonable, and mainly is only interested in the shortest path from the opening position.
I prefer the strong one because, well, it's not like this is actually useful anyway, it is? I mean, anytime I visit a tablebase site, after looking at whatever I really was looking for, I always wind up looking at silly things like four knights vs queen, or whatever. Because, I guess, "why not?"
<<<Calling the game actually solved (strong-form solved, all legal positions) will require even the silly positions like King and seven knights vs King (or whatever example you like, if that one happens to not be legal). This is simply because it requires all legal positions.>>>
Why?
It''s by definition. "Solved" is defined a couple ways by the folks working on this. Strong form definition includes all legal positions. Weak form definition has an aspect of what's reasonable, and mainly is only interested in the shortest path from the opening position.
I prefer the strong one because, well, it's not like this is actually useful anyway, it is? I mean, anytime I visit a tablebase site, after looking at whatever I really was looking for, I always wind up looking at silly things like four knights vs queen, or whatever. Because, I guess, "why not?"
Then I disagree with the "strong" and "weak" terminology they've employed to reinforce their weak case. It's equally (and some might say "better") argued by calling their strong version the weak one.
Anyhow, if you did that, it would make you feel better about yourself if 4 knights vs. Q was considered the weak variation.
The technique used to solve chess, the length of time it might take to do so, and whether humans will be playing chess on Mars in the not-too-distant future are irrelevant to the original question. I think nearly everyone agrees that chess is too interesting to too many people to die out just because future supercomputers might be able to play every game perfectly to a draw or win.
Anyhow, if you did that, it would make you feel better about yourself if 4 knights vs. Q was considered the weak variation.
Not sure what you mean by "the weak variation." I don't think "weak" modifies "variation" in the same way it modifies "solution."
But it would amuse me to look at that solution. And I may do it. It already exists, since it's within the already completed seven man tablebases (and they are complete, strong form, solutions).
#968
Starting from 26 men i.e. after 3 trades: 2.07*10^37 positions.
Of these the square root relevant like in the checkers' proof: 4.54*10^18 relevant positions.
On a cloud engine of 10^9 nodes / second: 144 years to solve all 500 ECO codes.
0.28 year on 1 cloud engine for 1 ECO code.