Uri Blass wrote: bob wrote: Uri Blass wrote: bob wrote: Terry McCracken wrote: bob wrote:
that 2060 stuff shows such an incredible lack of comprehension that it really doesn't deserve a comment at all. It is a ridiculous statement. Only down-side is that I doubt I will live long enough for the idiocy of that statement to be proven. I'm almost 60 now. I'd need to live past 120 to see that fallacy put to rest...
chess won't be solved by 2060. Or even 2160.
Robert..Never say Never! I think throwing out a number like that was irresponsibly stupid as well, but we don't know when or exactly how chess will be solved. However, I do believe it's possible with the right technology and methods.
Simply not possible with any conceivable approach. More chess positions than atoms in the universe, by a _large_ margin. Even using quantum states to store multiple bits per atom would not be possible as there are not enough states.
This is something that simply is not going to happen. Even a density of one billion times one billion times greater than today's chips won't even come close...
This is not correct that there are more chess positions than atoms in the universe.
number of atoms in the universe is clearly more than 10^50 when number of chess positions is clearly less than 10^50
Number of chess positions also prove nothing about the possibility of solving chess because it may be possible to solve chess without analyzing all positions.
It takes 2^160 bits to encode a chess position. And that ignores the 50 move rule and repetitions. To prove the game won, lost or drawn is _far_ more than just enumerating all the possible positions. Pathways have to be included and that turns this into a _huge_ problem. And "huge" doesn't really do it justice.
1)In case that the result is draw even without considering the 50 move rule no path needs to be included.
How do you prove the result without considering those cases? There are obviously _many_ games that will go beyond 50 moves.
drawn 6 position by tablebases are drawn.
Won chess position by tablebases may be not won because of the 50 move rule but if you say that 6 piece position is drawn I consider it as solving the position and solving the initial position of chess is considered by me as solving chess.
Such claims would be wrong however. You could follow the computer's suggestions perfectly and a forced win would turn into a draw because in real games, _all_ rules have to be followed...
So you either have to store the endgame tables that are large enough such that you reach 'em from the starting position, or you have to be able to search deeply enough to reach positions you can evaluate with 100% accuracy. Either task is way beyond daunting. Not enough storage to store those endgame tables. 5 pieces take 7 gigs. 6's take way over 1 TB (a factor of at least 100x larger). Just the 10 piece endings would blow the capacity of every disk drive ever made added together.
If you build 32 piece tablebases then it is clear that drawn positions are draw and if we find by these tablebases that the opening position is drawn position then chess is solved to be a draw.
There we agree. But building such databases is, and always will be, completely impossible, until you can find a way to store billions of petabytes in a single atom.
Solving a game does not mean solving every possible chess position but only determining the value of the opening position.
2)Note that even if you consider the 50 move rule then you can still solve every possible chess position in case that you have enough memory and 10^50 bits are clearly enough.
What good is that? we don't have any way to store 10^50 bits, which I don't believe is enough. If you don't index intelligently, which would require more like 2^160 entries, then the cost of searching for a position match would be just as daunting as trying to store the thing in the first place...
You simply divide the position to classes based on material and pawn structure and do a loop on all chess positions in a class.
first step:is determining the result of mate position.
second step is determining the result of positions when the side to move can mate in 1 move or play winning capture or pawn move in one move as win in 1(I assume that you already built the class of positions with less position or with more advanced pawn structure earlier).
You can continue in this way 100 times and say that the rest of the positions in a class are drawn by the 50 move rule.
That won't work, and is the same flaw as in the current endgame tables. Things drawn by 50 moves are not absolute draws if you can take time out to reset the 50-move counter by making an unimportant trade or pawn push to delay the 50-move rule kicking in. You can't just say "this is drawn because no pawn has been pushed nor piece captures in the last 50 moves." So you end up having to have _all_ the complete N-x piece endgame tables before you can do the Nth. If you think this can be done in 50 years, more power to you. Based on the last 50 years of development, the next 500 years won't produce enough advances to touch this problem. Nor the next 5000. By the time our sun starts to dim, in a few hundred million years, we _might_ have made a dent in the problem, but not solved it.
Considering repetition is also no problem because you can mark position that were repeated twice in the game earlier as a draw(position that happened in the past of the game only one time are not relevant because the shortest way to win does not include repeating them twice so the number of legal chess positions is more than 10^1000 if you include paths but you have an algorithm to solve every possible chess position in O(10^50) steps(assuming that you enough memory).
No assumptions allowed here. You _must_ have it. And that is a problem. 10^50 is a number way beyond doing...