Chess will never be solved, here's why

You are right that my comparison with the 5 piece tablebase was a little glib.

But for practical purposes, the number of files is pretty much irrelevant.The number of positions is what matters to the calculation. The size on disk is not important, because the Syzergy tablebase has to be used online anyway.

Of course, the tablebase files are all very much smaller than 7 piece ones because two pieces are in one of 2 configurations rather than ~4032 (actually symmetry adjusts that, but still a big ratio.

I see now the number is different to the 5 piece tablebase but only because one essential piece - a king - is accounted for. There is no such effect on other rooks.The extra freedom is to have one of 10 types of piece in place of the king already accounted for, But the ratio is reduced by an increased chance for repeated other pieces (eg a position with two queens has just under about half the positions of one with queen and king. And one with 3 pawns has about 3 times fewer positions than one with king and 2 pawns. (And the pieces have somewhat fewer square to go on due to the king and rook. Illegal checks have a less clear effect).

Overall, this is not going to make it more than 10 times bigger than the 5 piece tablebase, IMO, but bigger it will be. But still more than 1000 times smaller than Syzygy (which is 16,000 times more positions than a 5 piece tablebase).

Still a lot of work, but if you feel up to it ...

tygxc when you realize how wrong you are, are you going to delete your posts?

He's posted to many the only way to delete them is to permanently mute himself unless he wants to take the 24+ hours worth of deleting notes

he could also just delete the posts he made at the top of forums, or edit the main ones to admit his mistakes.

I have this 'scientific theory' that tygxc won't do that.

@12579

"do we have the 1st 20-ply completely described yet ?"

The proof tree starts:
1 e4
1...e5
1...c5
1...e6
1 d4
1...Nf6
1...d5
1 Nf3
1...Nf6
1...d5

We have more than 20 ply:
1 e4 (also tried 1 d4: 54 draws, 1 Nf3: 18 draws)
1...c5 (backup 1...e5: 21 draws, 1...e6: 2 draws)
2 Nf3 (also tried 2 Nc3: 6 draws + 1 transposition)
2...d6
3 d4 (also tried 3 Bb5+: 2 draws)
3...cxd4
4 Nxd4
4...Nf6
5 Nc3
5...a6
6 Be3 (also tried 6 f3: transposing, 6 Bg5: 1 draw, 6 Nb3: 1 draw)
6...e5
7 Nb3
7...Be6
8 f3 (also tried 8 h3: 2 draws)
8...h5
9 Nd5 (also tried Be2: 1 draw, Qd2: 1 draw)
9...Bxd5
10 exd5
10...Nbd7: 3 draws

note that tygxc is missing the billions upon billions of moves that need to be verified along this tree. a couple lines is not proof, and tygxc fundamentally doesnt understand this. a weak solution to chess will have the entire tree mapped (either literally or algorithmically), tygxc does neither because he doesnt understand basic game theory or mathematical proof.

nerds 😂

No.

A proof tree has to meet the standards of a proof tree in mathematical logic. It is an example of such. That means that if a proposition is logically equivalent to 20 other propositions, you need to prove all those 20 other propositions, not 3 or 4 of them plus a logically inadequate excuse why you are failing to prove the others.

To learn what you have to do, try to get a less flawed understanding of the weak solution of other games. If you find anything that would lead you to think the logical requirements can be ignored, you are misunderstanding it, because they never can in the mathematical sciences.

I think it's less an issue of understanding of game theory and moreso a fundamental lack of grasping of what a mathematical proof even is. because we could explain to him the game theory if he knew what a mathematical proof was, and would likely gather how stupid he sounds right now if he did know.

it is still absolutely goofy that tygxc claims to present a proof "tree" when in reality is giving a single branch

If we could convert @Optimissed's ego and @tygxc's obstinacy into computational power, we could get it done by Friday.

@12956

"if a proposition is logically equivalent to 20 other propositions,
you need to prove all those 20 other propositions"

'Chess is a very logical game' - Capablanca

'From the outset two moves, 1.e4 or 1.d4, open up lines for the Queen and a Bishop.
Therefore, theoretically one of these two moves must be the best,
as no other first move accomplishes so much' - Capablanca

If black can draw against the 2 best moves 1 e4 and 1 d4, then it is trivial that black can at least draw against the 18 inferior moves too. To be sure we could include 1 Nf3 and 1 c4.

If that makes you happier, then partition the weak solution of Chess in two parts.
Part 1: how black draws against 1 e4 and 1 d4.
Part 2: how black draws (or even wins) against the other 18 legal first moves.

My interest is in part 1. If you have an interest in part 2, then by all means go for it.

It may be slightly enlightening that a proof tree for a drawing strategy is better thought of as a proof that the opponent does _not_ have a way to win against the strategy. This explains why a return to a position already in the tree (a repetition) is as good as a stalemate for the proof. And it is of course, also the reason you need to analyse all the opponent moves. Guessing one does not win is not good enough for a mathematical proof!

You don't know what logic is, @tygxc.

That is a literal, serious point. Logic is solely about deduction using explicit logical rules. You fail to meet the latter absolute requirement every single time you use the word.

Capablanca was using the word imprecisely too, as a chess player, not a mathematician. If his "logic" was correct 1. c4 would be a bad first move - it only helps to develop the queen, not any other piece! 1. Nf3 would be a blunder. There is no empirical evidence to support inferiority of these moves.

Chess is almost all about playing moves in positions which are NOT amenable to rigorous calculation, not about proving the correctness of mate in N problems. The latter IS logic, the former is not.

Question for @tygxc: when proving a mate in 2 problem (surely stupendously easier than solving chess) is correct, how many of the opponents legal responses to the first move can you ignore?

You misunderstood what he meant by his first quote. It referred to my observation that proving a first move for white (at least) draws is equivalent to proving none of the 20 black replies wins for black. That is a logical equivalence, one of the two basic steps in the construction of a proof tree. Just another 10^30 or so to do.

With @tygxc's cavalier disregard for logic, it is puzzling why he wastes time with the ICCF data. Surely he can "prove" chess is a draw by proclaiming it is obvious that none of the 20 replies to 1. d4 wins for black? It would surely be "inconceivable" that any of them did win! [See above video].

oh my b. That is a logical equivalence, of course the total amount of replies proven would need to be the total in order to be true equivalence (if vs iff)