Chess will never be solved, here's why

@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

It obviously may need to analyse a number of black responses to find one, if the most likely response doesn't work. The sq rt cuts out the unnecessary black responses but they AREN'T unnecessary in all cases. You still have to find the one response which works and the most likely response will not work all the time. It may be that, on average, two black responses must be analysed each move.

So for that reason alone, your maths seems wrong.

I think it means that if you analyse 4 white responses on each move and the rest of your maths is right, which I doubt very much, it adds 20% to your time-frame. But it will be just one of many flaws, all of which will be on the reductive side. In any case, I thought your basic time frame of five years is really ten, even assuming your methodology is correct; and of course, your costing is way, way out. So an extra 20% on ten years is twelve. Nearly a third of the productive, working life of each person working full time on the project. You'd have to pay them MUCH better than you're proposing. 

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.

@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.

But 1/2 is wrong in any case. It's wishful thinking taken to the extreme.

Yet one more, multiple of 100. Post I made.

Elroch wrote: 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.>>>


I think that's one reason for the sq rt idea and I thought it was dodgy when it was proposed a few years ago. However, I had the feeling that tygxc's reasoning might be based on the idea that he proposes to explore fully four candidate moves for each ply but he's proposing instead to explore only one black move instead of four, and that gives exactly a square root but it's wrong for a different reason. I always assumed it was regarding the transposition idea, I haven't read tygxc's posts with any concentration for at least half a year, and I suddenly got the idea, since he never explains himself, that he's having a private laugh because it's all about just exploring one black move. In any case, nothing tygxc makes much sense regarding his obsession with the so-called weak solution and he refuses to explain himself or is incapable of it.

You're trying to make the other 99% of the posts look worthwhile by comparison?

This is an interesting empirical phenomenon I have noticed for a long time. It is much the same as in human games. What it amounts to is exploration of the possibilities on the board in a position where thorough calculation is too hard. Having explored a branch and reached a repetition, there are a lot more positions that have a provisional or solid evaluation that can guide further exploration (away from now excluded regions).

Hmm

@8604

"The number of calculations involved was 10^14, which were done over a period of 18 years."
++ Schaeffer spent most of his time on his 10-men endgame table base.
For chess the 7-men endgame table base is already there.
Chess with 10^17 positions relevant to weakly solve it is 1,000 times more complicated than Checkers.

"The process involved from 200 desktop computers at its peak down to around 50."
++ I propose 3 cloud engines, that is the equivalent of 3,000 desktops.
Present day desktops are more powerful than desktops in 2007.

"As of January 2023, the longest forced mating sequence was discovered for the 8-man tablebase (also ignoring the 50-move rule), which was discovered in mid-2022 by developer, computer chess enthusiast, and physicist Marc Bourzutschky. The 8-man tablebase is currently incomplete, though, so it is not guaranteed that this is the absolute limit for the 8-man tablebase."

https://en.wikipedia.org/wiki/Solving_chess#Endgame_tablebases

Oh Lordy/

Mandela effect is real I'm not usually this pretty today

<<<Shannon then went on to estimate that solving chess according to that procedure would require comparing some 10 ^120 possible game variations, or having a "dictionary" denoting an optimal move for each of the approximately 10 ^43 possible board positions>>>

That's just nonsense though. An optimal move means a "good" move. That can be defined as one that doesn't change the game state.

Therefore most positions would have several or many "optimal" moves.

<<Furthermore, Shannon's calculation for the complexity of chess assumes an average game length of 40 moves>>

This, of course, is complete nonsense, leading one to think that Shannon wasn't on top of HIS game at all and that nothing he imagines can be taken seriously.

Obviously, this is because humans tend to play games of about that length. Actually 40 seems too small even for humans. However, he's talking about the entire number of possible games, for which the average game length will be over 100 moves. Maybe 200 to 300 moves in reality, without artificial procrastination, although of course, most longer games wouldn't be significant.

<<Indeed, some expertly played games (grandmaster-level play) have been as short as 16 moves.>>

That isn't possible unless it was an agreed draw.

<<For these reasons, mathematicians and game theorists have been reluctant to categorically state that solving chess is an intractable problem.[5][10]>>

If that is so ("for these reasons, (they) have been reluctant .... ) then they don't really know what they're doing, because those reasons are nonsensical.