Chess will never be solved, here's why

In the computer chess community they use the term "incesttesting" for testing programs against close relatives of themselves. Johan de Koning invented the term.

That's (corrupt)stats not maths even in stats you don't assume anything so it isn't really guessing but stats can be confused as guesswork if done poorly

IDK

So, given that this argument would be the same pre-Alpha Zero, how did you feel after the new engine methodology completely overturned the previous march towards endless draws? How do you feel about people that argued before Alpha Zero came out that engines had exhausted the depths of possible chess play? Why assume that this won't happen again with better machine learning on faster hardware?

Don't spam.

Enjoy your upcoming mute, I guess?

I messaged him some advice on posting etiquette. He ignored it.

Waiting when he gets banned...lucky him he can post more than five comments (I can't )

you arent wrong, although the solution you gave is a 'strong' solution of chess.

tygxc literally just has no idea what he's talking about.

tbf the spam just means that more people wont see tygxc's delusion.

Clearing the board for somebody who cuts and pastes all their arguments at this point doesn't hinder him much .

LOL fair.

To be as fair as possible, @tygxc tries to argue why chess being a draw is very likely and says that is reason enough to be certain and thus constitutes a proof.

The first part has some problems but many people would be inclined to agree, and both of the other two steps are nonsense.

It is enlightening to contrast @tygxc's (frankly) sloppy thinking with the work of those that he refers to (albeit often inaccurately) by John Tromp, Peter Österlund (both European computer scientists) et al. I have been looking in more detail at their work on counting legal chess positions and my respect has grown for how good a job they have done. I will attempt to summarise it as an example of doing approximate calculations right.

The first step is to order the unchecked positions. These have only the most basic of checks done - whether the set of pieces on the board is compatible with the fact that you start with certain pieces and all the changes in the set are captures or promotions from pawns.

Then there is a clever technique which is a very detailed development of a relevant notion I thought of merely the first part of - the grouping of positions together based on the types of transitions that occur between positions. My idea was to group positions into equivalence classes by the partial order of existence of paths of moves between them (i.e. two positions are in the same class if there are paths in BOTH directions between them). The idea being that in a game you enter a class, stay there a while, then move to another class by an irreversible move. But they make rather larger classes, grouping them by the material on the board and the order of the pawns on each file. The idea being that moving between classes now always involves a change in the material on the board, by promotion or capture.

The mapping from positions to classes of positions is why they call this a "proof kernel", similar to a notion familiar to mathematicians where you kind of merge elements together and get a simpler object (quotients of algebraic objects in particular).

For the purpose of legality checking they are interested in the existence of moves between classes. A move between a class and another class is given by a move between some position in one class and some position in another. (Mathematicians: think about the idea of mapping something in the original object into something in the quotient object, where you have factored out the kernel).

For a position to be legal it is necessary (but not quite sufficient) for there to be a sequence of such kernel moves between the class of the initial position and the class of the position itself. If the position is legal, what happens is that a sequence of moves that get to the positions gets turned into a (generally shorter) series of moves between classes (because a lot of moves stay within a class so are ignored.

ok. Now what they do is to generate a set of random integers. Each random integer maps to a candidate position. This position has some class and they try to find out whether there is a sequence of moves between kernel classes that gets to the class of the position. If they can prove not (lots of details skipped over by me here), the position is illegal. If there is, the position MAY be legal. If I recall they then try to find a proof game for the position (I.e. to check explicitly if the position is legal).

It turns out there is rarely a position that is not legal but that there the sufficient condition is true. (there is a "proof game" of moves between kernel classes). And in the rare cases where it is misleading, there are additional checks that can be added to catch even more illegal positions.

Anyhow here is the solid statistical part. By having a decent size perfectly random sample of candidate positions it is possible to check that you can verify the legality of a large fraction of them by the simplified method. Having done that, you can take a larger sample, do the approximate check and have a statistically reliable estimate of how many of those positions are legal with a quantified uncertainty (based on the statistics for the smaller sample, where you checked in detailed how good the approximation was).

So that's how Tromp et al got to estimates of the number of legal positions. Very clever simplification, approximation, and solid statistical inference.

Apologies to the experts for anywhere I have been misleading.

One interesting fact I picked up along the way is that most of the legal chess positions have 27 or 28 pieces on the board. This is because of the way the size of the tablebases rises rapidly at first, then reaches a peak and falls again - the latter two phenomena being mainly because the biggest tablebases are much more restricted in the set of pieces that can be on the board.

To put it another way, the majority of chess positions are those where there have been exactly 4 or 5 captures. In terms of promotion these positions can't have as many promoted pieces as some of the smaller tablebases - you need captures of pawns or by pawns to make promotion even possible, and each capture can't enable more than two promotions (this happens when a pawn captures an adjacent pawn or captures a piece behind an adjacent pawn, also clearing its own file for the opposite colored pawn) so these positions have between 0 and 10 promotions. Of course the 29 piece positions have 6 or fewer promotions and so on.

Yes, Tromp's work is solid.

Those of a mathematical or computational bent may enjoy the original source of what I have clumsily summarised. I found it a genuinely enjoyable read on the train today!

This is a more generally accessible source for the bottom line of the reasoning that led to the legal position number estimates, emphasising the process of random sampling, determining legality and extrapolation with quantified uncertainty.

Isn't it:

(total number of promotions) <= 2 * (number of captures by a pawn)

rather than "on average"?

Pawn captures can also enable zero or one possible promotions.

reminder to all that tygxc's claims have been rebutted by literal mathematicians and he continues to ignore them.

And by people who have barely taken half a stats class lmao like all you have to do is learn the basics and go "oh wait this doesn't follow the guidelines " of errors and not assuming anything

chess will never be solved beacuse for example, we strong players think its a blunder but what about in a million moves?

I assume it drew itself then and future ones will draw themselves any engine has drawn itself in opening position since forever and once you do reach the table base its got lots of wiggle room with equal material for draws and even more so with the 50 move rule. So its not brute force solved without a full table base but it seems obvious. There is not a single line that doesn't currently go to 0.00 on modern engines and the stronger they get the faster they seem to get to 0.00. So I think its a draw and we probs wont get hit by comet and by 30XX if we still exist our tech will have a way to solve this in a more efficient way than any of us can imagine today. I cannot imagine a forced win line and the ideas would need to be pretty damn deep because tons of people with engines tablebases databases haven't found a forced winning idea it always goes to 0.00. So not solved yet but would be shocked if there was some forced mate in 500 from the opening esp given the 50 move rule lol.