I couldn't care less. Not anymore. The landscape is barren. All of it. Nothing bad enough can happen to any of you. Good riddance.
Chess will never be solved, here's why
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Feb 5, 2023
0
#6284
Try to surmise how Greatly, this
Differs, from this
Then you might have it.
Feb 5, 2023
0
#6285
Intellectual_26 wrote:
Try to surmise how Greatly, this
Differs, from this
Then you might have it.
Well give us the solution to the first, then we can start surmising.
Ian_Rastall wrote:
I couldn't care less. Not anymore. The landscape is barren. All of it. Nothing bad enough can happen to any of you. Good riddance.
Apparently he took "physician, heal thyself" to heart. Good for him.
?
Feb 5, 2023
0
#6291
Elroch wrote:
Surprising as it may seem, some chess players are a little unbalanced.
The Patzers are the Worst.
They don't even make good 'Savants!"
LMAO!!
This is interesting
Feb 5, 2023
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#6293
Chess will never be solved because it's been two hours since the last post. It will take an eternity at this rate. Please let's not go on about infinities again.
Feb 6, 2023
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#6294
Elroch wrote:
The solution of checkers amounts to two drawing strategies, each with help from a tablebase (and some handy symmetry-based simplifications).
Being able to repeat positions suffices to draw, so the opponent of each strategy needs to avoid this. This allows truncation of all lines that repeat positions in the analysis that generates two drawing strategies (which is mostly about dealing with the large number of opponent options, first by trying the highest evaluation move, then if that fails the next highest, and so on).
At least that's how it seems to me.
When the objective is to find a winning strategy, any repetition can be viewed the same as a loss: these need to be entirely avoided (to have an efficient winning strategy, with no unnecessary waste of time).
It's worth clarifying one of those concepts - when seeking a winning strategy, you may as well strengthen the objective and seek an efficient winning strategy (one that never repeats a basic chess position against any opposition). It seems impossible for this to not be more economical in computing time. In fact if your strategy provides a single move for each basic chess position, this has to be so (as then a repetition can always be turned into and n-fold repetition and a draw by the opponent).
And another. When seeking a drawing strategy, you can effectively view a single repetition as a draw. The opponent needs to be able to avoid these (by finding an efficient win) to refute your strategy.
And, put like that, it is clear the two are closely related.
I have said many moons ago that the number of positions considered depends on the method of solution.
@tygxc plans to run (unmodified) SF for 17 seconds a large number of times on a cloud engine. The question is how many positions at 10^9 seconds will he be be considering? He cuts down the percentage of the total number of positions in some (cough) ingenious ways, but what total should he be starting off with?
It is possible to avoid repeated positions as you point out, but SF doesn't. This is an example of Stockfish 15 play.
Count the repetitions.
@8594
"the number of positions considered depends on the method of solution"
++ No, it does not.
Strongly solving Chess needs all 10^44 legal positions.
All weak solutions are subsets of the strong solution.
The strong solution needs all legal positions: draws, wins, and losses.
The weak solutions only contain drawn positions.
They hop from the initial drawn position to other drawn positions and finally to a 7-men endgame table base draw, or a prior 3-fold repetition, or another clear draw.
The estimate of 10^17 positions for a weak solution does not depend on the method.
The vast majority of the 10^44 legal positions cannot result from optimal play by both sides because of multiple underpromotions to rooks or bishops by both sides.
A better estimate is thus Gourion's 10^37 positions without promotions to pieces not previously captured. That is a bit too strict: positions with 3 or 4 queens happen in ICCF WC draws that are > 99% certain to be perfect games with optimal play from both sides. Thus multiply by 10 to include 3 or 4 queens, that gives 10^37 * 10 = 10^38.
Inspection of a random sample of 10,000 positions as counted by Gourion reveals none can result from optimal play by both sides.
That leaves 10^38 / 10,000 = 10^34 positions.
Weakly solving needs only 1 black response to each white move, not all responses.
That leaves Sqrt (10^34) = 10^17 positions relevant to weakly solving Chess.
Nowhere in this calculation has the precise method to weakly solve Chess been invoked.
@8595
"Do the math"
++ I have done the math:
Sqrt (10^37 * 10 / 10,000) = Sqrt (10^34) = 10^17
Feb 6, 2023
0
#6297
The square root idea is a very rough one, entirely inappropriate for quantitative analysis. It is based on the NUMBER OF POSSIBLE GAMES for some hypothetical game where there are no transpositions.
Empirically, the solution of checkers achieved about a 2/3 power reduction in complexity compared to a strong solution. Good, but not 1/2.
Of course all this refers to a correct solution as understood in the peer-reviewed literature, not a misunderstanding/corruption of this by @tygxc.
Hi
@8599
Checkers is more crowded: 24 men on 32 squares than Chess 32 men on 64 squares. Checkers has more edge effects: 16 edge squares of 32 squares than Chess: 28 edge squares of 64 squares.
Those are 2 reasons why 1/2 is closer than 2/3.
Beneath the clang of this unstoppable sluice I detect a note. A very noticeable note, that, by commenting upon, I mean to suffuse with a harmonious alliterative splendor that may, God willing, quell with buffing most gentle its jagged and incessant piques.
This notable noticeable note, then, noteworthiness notwithstanding, instantly evokes the vexatious, appetite-ruining keening that one sometimes hears from one's beartraps, when, instead of plump and succulent Ursus, their springs have sprung upon tough and unsatiating Canis, and, lacking the courage to gnaw off its own leg, the miserable creature decides instead to subject Mother Nature's immense and dignified quietude to the ceaseless wail of its final wretched hours.
Perhaps the buffing was more vigorous than I had originally anticipated.