checkers was loosely solved. why not chess ...
Because chess requires ~10^27 more positions to be calculated.
That's 100,000,000,000,000,000,000,000,000 times more positions than checkers. Get to work.
checkers was loosely solved. why not chess ...
Because chess requires ~10^27 more positions to be calculated.
That's 100,000,000,000,000,000,000,000,000 times more positions than checkers. Get to work.
#3606
"Because chess requires ~10^27 more positions to be calculated."
++ Get at least your facts straight.
Checkers has 500,995,484,682,338,672,639 legal positions.
Chess has 4.82 * 10^44 legal positions.
The ratio is 10^24 not 10^27.
Not all of these positions are to be calculated.
For checkers only 10^14 needed calculation for the proof.
For chess an estimated 10^17 are legal, sensible, reachable, and relevant.
"For chess an estimated 10^17 are legal, sensible, reachable, and relevant."
No. That's wrong. The only part of the post I read.
That's simply a syllogism/mantra/pitch/slogan repeated over and over.
As silly as trying to insist that only four move options at a time could be relevant.
Its reasonable to say you don't know.
And without assuming.
The nature of not knowing something. Accepting not knowing.
"white wins more-doesn't mean he has a forced win"
Yes it does.
It means that you suspect there may be a forced win.
In reality, the slight excess of white wins over black ones can be adequately explained by other means and therefore there's no need to believe that white has a forced win.
I agree. And there is also no need to believe that chess is a forced draw.
But, at the highest level, which humans will never achieve, it's one or the other. It's either a forced win for one side, or, a forced draw. So I choose forced win for white. Because of the reasons already mentioned.
What do you mean you choose forced win for white? You mean thats your guess? Why do you wanna make a guess based on very unconvincing or nonexistent reasoning, isn't it just reasonable to say we don't know until chess is solved. This convo is confusing me.
Yes. It's reasonable to say you don't know. It's reasonable to say it's a forced draw. And it's reasonable to say it's a forced win for white. They are all perfectly reasonable. But since at a level we as humans will never achieve it's one or the other, I choose forced win for white.
That's all true, so long as it's reasonable to assume it's a draw.
It's still all true, so long as it's reasonable to assume it's a win for white.
It's also still true, so long as it's reasonable to assume we don't know.
I agree with those who have said it doesn't matter. Humans will never reach the level of play where it will matter. So, lets assume chess is a forced win for white. All good openings lead to the same result, bad openings lead to the same result even sooner. And lets say it takes 10,450 moves (or less if its a really bad opening). I just don't see how it will matter. Humans playing against other humans will still win with black. Even at the highest level.
The ratio is 10^24
That's ok then.
If solving checkers costs a cent (underestimate, in case you haven't noticed), solving chess will cost $10,000,000,000,000,000,000,000.
Start saving.
The ratio is 10^24
That's ok then.
If solving checkers costs a cent (underestimate, in case you haven't noticed), solving chess will cost $10,000,000,000,000,000,000,000.
Start saving.
That's starting to seem very doable. With the current boneheads in charge it wont take long before one of your numbers equals the other.
Yeah. Print the money. Institute 10,000 dollar bills.
For a 10,000 billions of year 'project' regarding motions of chess pieces.
But still nobody seems to have noticed that the time and space could be reduced by a huge factor if "chess" (whatever version) is a win in a modest number of moves (though not with @tygxc's approaches).
Also checkers has 500,995,484,682,338,672,639 positions under basic rules if you equate positions with nodes in the state space, but vastly more than that under tournament rules (assuming resignations, agreed draws, time controls and forfeit rules are ignored; like chess the game is insoluble with checkers tournament rules as stated in the link). The increase is because the tournament rules include 40 move and triple repetition rules.
Similarly the number of nodes in the state space for competition rules chess is vastly more than 4.82 * 10^44, but the salient point is the ratio between the number of nodes in the state space for competition rules chess and that for tournament checkers is also vastly more than 10^24 (or 10^27 for that matter - three orders of magnitude wouldn't be significant in the context).
The solution for checkers hugely restricted the search space (as opposed the state space) by incorporating the Kishimoto-Müller algorithm into the Chinook program, but this doesn't appear to have been implemented in any Stockfish version so far as I can see.
#3621 Given that we don't play perfectly, a computer does not need to play perfectly to beat us. If a computer solved chess it wouldn't give an advantage of about half a pawn from the starting position, but instead would either give an advantage of 0.0 or of mate in some number of moves.
#3617
"Start saving"
++ The number of legal positions only matters to strongly solve chess, i.e. a 32-men table base.
Schaeffer has weakly solved checkers considering 10^14 positions.
Chess has 10^17 legal, sensible, reachable, and relevant positions, that is a factor 1000.
Computer power costs less now than in 1989 - 2007.
3 cloud engines and 3 (ICCF) (grand)masters during 5 years would cost 3 million $.
That is still the impeding factor and the only reason why chess has not yet been solved
and may not be solved soon.
Chess has 10^17 legal, sensible, reachable, and relevant positions
If there were merely 4 table-base correct moves leading to novel positions this number of positions would be reached in 30 half moves. So either 15 moves for both sides or no more than 30 moves if one side uses a deterministic strategy.
I am not sure if you've heard but it is not the exception for chess games to last a lot longer than this.
#3625
"this number of positions would be reached in 15 moves"
++ That is not true because chess has so many transpositions:
different move orders that lead to the same position. E.g.
1 e4 e5 2 Nf3 Nc6 3 Bc4 Bc5 4 d3 Nf6
1 e4 e5 2 Nf3 Nc6 3 Bc4 Nf6 4 d3 Bc5
1 e4 e5 2 Bc4 Nf6 3 d3 Nc6 4 Nf3 Bc5
etc. etc.
Those don't lead to the same game states under competition rules. They lead to the same positions under basic rules only.
The term "position" is used in different senses, but "game state" would seem to be the only sensible meaning if it's to relate to a proposed solutions based on a forward search by some version of Stockfish.
#3627
That does not matter. The same position per Laws of Chess 9.2.2 has the same evaluation.
Besides often there are not even 2 viable moves. If I take your queen, then often the only reasonable move is to recapture my queen.
In the Candidates' Madrid 2022 the average game length past a predecessor was 34 moves.
For weakly solving it is only necessary to look at all reasonable alternatives for 1 side.
#3625
"this number of positions would be reached in 15 moves"
++ That is not true because chess has so many transpositions [ . . . ]
So if you prune all but 4 candidates for White and one for Black (so you said) and search only 10¹⁷ different positions, what are the average branching factor and depth of the tree? We have already asked you several times to translate in pseudocode, with the same level of details, the algorithm you described in your obscurantistic language, but you never did. With the very strict constraints you give, you cannot simply get away with a convenient: "we will know only when the search will be concluded", or with a guess out of nowhere, as you did before.
#3627
That does not matter. The same position per Laws of Chess 9.2.2 has the same evaluation.
No it doesn't. I keep trying to tell you that.
Besides often there are not even 2 viable moves. If I take your queen, then often the only reasonable move is to recapture my queen.
In the Candidates' Madrid 2022 the average game length past a predecessor was 34 moves.
Is the preceding meant to be relevant to the size of the state space in some way? It's not at all obvious how.
For weakly solving it is only necessary to look at all reasonable alternatives for 1 side.
What you think is reasonable has no connection with the size of the state space or solving chess. Indeed your meaning of "reasonable" is ill defined as @Elroch pointed out a few posts ago.
checkers was loosely solved. why not chess ...