#1747
Definitions are clear:
"weakly solved means that for the initial position a strategy has been determined to achieve the game theoretic value against any opposition"
https://web.archive.org/web/20170912011410/https://pdfs.semanticscholar.org/8296/bc0ab855841088b31190c9f2923951853d7b.pdf
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Actually, definitions in the links you have so far provided are not clear.
The first link you provided here was Wikipaedia
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.
This gives two incompatible definitions in its two sentences.
If the game is basic rules chess but with arts. 2.2 and 2.3 replaced to give this as the starting position
then the algorithm for White
Play 1.Qe7
secures a draw for White against any possible moves by Black, so counts as a weak solution according to the first sentence. But it doesn't lead to a complete ideal game with proof that each move is optimal for the player making it, so doesn't count as a weak solution according to the second sentence.
If instead the rules are adjusted to make this the starting position
and an extra art. is added to the effect that if a king steps onto a corner square the board is replaced by a large block of chocolate with a poisoned corner square and the game continues (with the opponent to move) according to the rules of Chomp, then the game
1.Nc3+ Kc1
2.Ne2#
is a complete game where it's possible to prove that each move is optimal for the player making it, but it doesn't lead to 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, so it's a weak solution according to the second sentence, but not the first.
If the starting position is amended to
then the moves
2n+1. Kh8
2n. Kg8
n∈ℕ
together with any choice of legal responses for black provide a complete game in which it can be proved that each move is optimal for the player making it, so it is a weak solution according to the second sentence and it also provides an algorithm that secures a draw for White against any possible moves by Black, so counts as a weak solution according to the first sentence too.
But it's not what anyone else would recognise as a weak solution, and neither are the previous.
The second link you provided here to this paper
defines "weakly solved", as you say, by
for the initial position a strategy has been determined to achieve the game theoretic value against any opposition
If the starting position is taken to be
then the strategy for White
Play 1.Qa7+
achieves the game theoretic value against any opposition. But again it's not what anyone would recognise as a weak solution.
Edit: added black pawn c7 to correct last diagram.
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#14
Chess even stays a draw if stalemate = win.
The paper shows that the draw rate increases with more time.
Compare figure 2 (a) and (b).
[snip]
If Haworth's law (http://centaur.reading.ac.uk/36276/3/HaworthLaw.pdf) continues to hold up to 32 men there would be winning positions where the forced mates need at least tens of trillions of moves against accurate defence. The performance of anything that plays chess in much simpler positions such as the one above hardly inspires confidence in their assessments.
what
What what?
If you're querying the tens of trillions I have to admit to some unreliability on the back of my envelope. I've run it through Javascript and it should have read 3 trillion.
What about that surprising result that the longest mate discovered with 8 pieces was shorter than the longest one in the (complete) 7 piece tablebase. Is that still true?
See https://www.chess.com/blog/Rocky64/eight-piece-tablebases-a-progress-update-and-some-results