Chess will never be solved, here's why

Sorry for the missunderstanding. I totally agree. We are talking about the same thing. Schematic moves does write out all moves and counter moves. In the same way that in math N*2 writes out every possible even number.

Read the 500+ pages of the thread. You'll see that beside Tygxc, the undisputed king of repetition, Optimissed is a worthy queen. There hasn't been a new idea out of him on this topic for years. Not surprising, since he doesn't understand it from either the math end or the computer science end.

What he does do:

- Complain about the established nomenclature, then make up his own definitions.

- Posit algorithmic solutions when he cannot begin to codify them...functionally no different than a call to magic.

- Claims he knows chess is a draw by virtue of his own experience/playing skill when super GMs will only say "chess is probably a draw with best play".

The situation has not changed. Solving chess is out of reach:

- The number of unique positions to traverse for a real proof is 10^44. There are some theories that this number can be dropped to 10^43 by further pruning. There are no viable theories about pruning 10^44 to 10^17. That's pure fantasy. To do so would effectively mean that only 1 in 1.000,000,000,000,000,000,000,000,000 chess positions would be considered "valid" positions to be checked. Does that sound right to you?

- If you spent the entire wealth of the planet to build a server farm just to process evaluations and left humanity to starve and rot it would still take millions of years to calculate with current technology. If you mined the entire asteroid belt of the solar system to make a storage array, it could not hold the evaluation results. Etc.

- Quantum computing is not able to even touch this problem as things sit; it is not in the sweet spot of things that quantum computing is good for (like cryptography), and there's a currently insurmountable destructive read problem in the way as well even if the quantum computer's instruction set could do the job.

- There's no progress, zero, nada, zilch in terms of building an algorithmic solution that "proves" best play as it goes along. You can prove who will will a pawn race, sure. You cannot begin to prove "best play" in a middlegame. Letting the best engines sit on a position for 5 days (or 50 days, or 500 days) does not prove best play in terms of solving chess.

Your assertion doesn't come from that figure; there's no accurate way of recognising errors from the starting position. The figure doesn't say that, it comes from your big red telephone.

Try going through the games I posted with the Nalimov and Syzygy tables.

@10685

"Schematic moves does write out all moves and counter moves."
++ For weakly solving chess, we only need 1 black move to counter all reasonable white moves.

Yes.

Wow! Tell us what it is!

How excactly do you know 1 a4 is not the solution? Do you take it for garanted that white either win or its a draw? What if white is doomed to loose because moving first is a zugzwang where black just follows a ginormus matrix that leads to the second mover always winning?

@10690

"Tell us what it is."
++ From the ICCF World Championship Finals:
On 1 e4 either 1...e5, or 1...c5, or even 1...e6.
On 1 d4 either 1...Nf6 or 1...d5.
On 1 Nf3 either 1...d5 or 1...Nf6.

That's three. You said you only need one.

@10691

"How excactly do you know 1 a4 is not the solution?" ++ By logic. 1 e4 opens diagonals for Bf1 and Qd1, occupies a central square e4 and controls 2 central squares e5, d5. 1 a4 contributes nothing.

"Do you take it for garanted that white either win or its a draw?" ++ From the ICCF World Championship Finals: 106 draws out of 106 games. White has the advantage of the initiative, +1 tempo = + 1/3 pawn, not enough to win and gets diluted by every further move.

"What if white is doomed to loose because moving first is a zugzwang"
++ It goes contrary to the knowledge that the initiative is an advantage, albeit unsuficient to win. Moreover, any consistent tentative black win can be disproven by strategy stealing.
If 1 e4 c5 were a black win, then 1 c3 e5 2 c4 would win for white. If 1 d4 Nf6 2 c4 g6 3 Nc3 d5 were a black win, then 1 Nf3 d5 2 g3 c5 3 d3 Nc6 4 d4 would win for white.

@10693

"You said you only need one"
++ For each N white moves 1 black move.
So instead of N * N = N² moves N * 1 = N = Sqrt(N²) moves.
That explains why 10^17 = Sqrt (10^34) positions are needed to weakly solve Chess.

What do you mean by "weakly solving"? Is that in any way relatable to the chatolic church "weakly solving" the universe by placing the earth in the center and letting the sun revolve around it?

It's OK I was just responding in the jocular spirit it was offered.

I take it 10^34 is the number of times you can avoid understanding any of the refutations of what you laughingly call your proofs.

He is of course wrong in one crucial respect.

We need one black move to counter EACH LEGAL white move. You can't legitimately ignore opponent moves based on a zero ply analysis. Such as those moves that give up material or which involve moving a knight backwards or which double pawns. Because such moves are sometimes the best moves. The notion of ignoring virtually every legal set of opponent choices from each position (the amount of ignoring goes up exponentially with depth!) is even more obviously misguided.

@10696

"What do you mean by weakly solving?"
++ There are 3 kinds of solving a game.
'Ultra-weakly solved means that the game-theoretic value of the initial position has been determined,
weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition,
and strongly solved is being used for a game for which such a strategy has been determined for all legal positions.'
Games solved: Now and in the future

The game of Hex has been ultra-weakly solved: the first player wins, but we do not know how.
The game of Checkers has been weakly solved: it is a draw and we know how, but we do not know the outcome of all legal positions.
Chess has been strongly solved for 7 men or less. Strongly solving Chess to a 32-men table base with all 10^44 legal positions is beyond present technology.

@10698

"We need one black move to counter ALL LEGAL white moves."
++ That is purism. It is not imperative to shut down the brain when solving a game.
On the contrary given the huge size of the task all use of game knowledge is beneficial.
1 e4 e5 2 Ba6? needs no investigation.
1 a4 needs no investigation.
A known drawn opposite colored bishop ending as the ICCF example given needs no further investigation.
A known drawn rook ending as in the ICCF example given needs no further investigation.
Use of a computer does not prohibit thinking.

@10697

"10^34 is the number of times"
++ 10^34 is the number of reasonable positions, derived from 10^37 positions without promotions to pieces not previously captured, multiplied by 10 to include positions with 3 or 4 queens, divided by 10,000 on the basis of a sample of 10,000 positions.
Thus 10^37 * 10 / 10,000 = 10^34
Then to weakly solve requires Sqrt (10^34) = 10^17 positions.

No it hasn't. Do you not read the posts?

@10703

"typical 40 legal choices"
++ That is an illusion. There are average at most 3 legal choices that do not transpose.
Proof is by the pigeonhole principle.
There are no more legal chess positions than there are legal chess positions.
I go with the number 10^38 positions without underpromotions to pieces not previously taken, but you can take the whole number of 10^44 legal positions if you want.
10^38 = 3^76 = 3^(2*38)
That means 3 non transposing choices per move reach all legal positions in 38 moves.
Coincidently an average ICCF World Championship Finals game lasts 38 moves.
So 3 is the number and 40 is not.