Chess will never be solved, here's why

What?

@8739

"1. Quantum computers cannot be used to solve chess as they currently exist, or even as they are predicted to evolve in the foreseeable future." ++ Quantum computers are commercially available and they can run Stockfish if translated from C++ to Python. Quantum computers may be much faster in generating 8- or 9- men endgame table bases in the foreseeable future.

"2. If you spent the entire world's collected wealth (estimated at ~80 trillion dollars) on the fastest supercomputers (over a quarter million of them), the combined petaFLOPS still take millions of years to solve the 10^44 unique positions." ++ Solving Chess does not need a single Floating Point Operation, so petaFLOPS are irrelevant. Indeed strongly solving Chess to a 32-men table base with all 10^44 legal positions is beyond existing technology.

"3. There's no basis for 10^17." ++ There is solid basis for that. Per Tromp there are 10^44 legal positions, but as the 3 displayed randomly sampled positions show, the vast majority has > 3 rooks and / or bishops per side, so they never can result from optimal play from both sides.
Therefore Gourion's 10^37 is a better estimate. It is a bit too restrictive: positions with 3 or 4 queens do occur in perfect games with optimal play from both sides. So multiply by 10 to incorporate these. That is where the * 10 comes from.
However, a random sample of 10,000 positions as counted by Gourion show none can result from optimal play by both sides. That is where the / 10,000 comes from.
Weakly solving only needs 1 strategy to draw for black, not all black moves.
So instead of w^(2d) positions only w^d = Sqrt (w^(2d)) positions
That is where the square root comes from.
So

• 10^37 from Gourion
• * 10 to accomodate positions with 3 or 4 queens
• / 10,000 to remove positions that cannot result from reasonable play
• Square root as the difference between strongly and weakly solving

Yields: Sqrt (10^37 * 10 / 10,000) = 10^17 positions relevant to weakly solving Chess.

Never is too long. 

(and assumes things stay stagnant/progress at whatever current rates are thought possible in terms of computing...)

What a game chess is... It's almost frightening

Tygxc you do realize that a node isn’t a correctly evaluated position right?

your entire calculation is based on that a node correctly looks at a position

i eat glue

@8740

"Here's some numbers I posted in 2015"
++ You keep repeating the same mistakes.
Weakly solving is not the same as strongly solving.
Weakly solving requires far less positions than strongly solving.
The strong solution includes all weak solutions.
A weak solution shows one way for black to draw against all white opposition, not all ways.
The weak solutions only show how to draw, not how to win if either white or black play an error.

"100 PetaFLOPS" FLOPS = ++ Floating Point Operations Per Second. Solving Chess reaquires zero Floating Point Operations. Count the nodes/s.
Cloud engines reach 10^9 nodes / s, a typical desktop 10^6 nodes/s.

@8746

"a node isn’t a correctly evaluated position"
++ A diagram is the location of the men on the board.
A position is a diagram + side to move + castling rights + en passant flag
A node is a position + evaluation + history

"your entire calculation is based on that a node correctly looks at a position"
++ No, the entire calculation is based on jumping from node to node until reaching a 7-men endgame table base draw or a prior 3-fold repetition.
Any engine can weakly solve Chess, only a bad engine takes more time as it will run astray more.
The only real evaluation is that from the 7-men endgame table base.
That is also how Schaeffer weakly solved Checkers: calculation from 19 of the 300 openings to his 10-men endgame table base.
That is also what GM Sveshnikov said: calculate from the opening to technical endgames with modern engines piloted by good assistants.

Everything after Tromp's number is just conjecture and assumptions.  Gourian = not proven or peer reviewed.  Dividing by a further 10,000 is just a number you had to use to reach your 10^17 goal, and has no basis.  Taking the square root is a *possibility*, but not proven to work for Chess.  So, the only real number we're working with here is 10^44.  All the rest of your stages of implausible reductions depend on assumptions you cannot prove.

So, your premise that is we assume all of this unproven steps reducing from 10^44 to 10^17 are perfect, that your prediction of error rates from engine evaluations holds up, *and* that 3 human beings can correct for errors that slip through without making mistakes themselves in 5 years.  That is laughably weak.

“Weakly solving only needs 1 strategy to draw for black, not all black moves.
So instead of w^(2d) positions only w^d = Sqrt (w^(2d)) positions
That is where the square root comes from.”

assumes pre existing knowledge of which positions to evaluate

Tygxc you do realize that Sveshnikov was exaggerating right.  Like that should be obvious to you

@8750

"Everything after Tromp's number"
++ Tromp's number 10^44 is relevant for strongly solving Chess to a 32-men table base.
For weakly solving Chess Sqrt (10^37 * 10 / 10^4) = 10^17 positions are relevant.

.

Incorrect.  10^44 is the only relevant and reliable number for both solutions currently, until you can prove differently, and you cannot, and have not in several years of posting the same thing over and over.   There's not a single valid number in your red equation above.

@8751

"assumes pre existing knowledge of which positions to evaluate"
++ No, it does not assume any knowledge of which positions to evaluate.
It is just like Schaeffer did for Checkers. Each pawn move and each capture along the seeded line shrink the relevant search space and the stored boundary.

@8752

"Sveshnikov was exaggerating"
++ Sveshnikov was right.

He was right to exaggerate.  It was a great quote, reflecting how computers were transforming chess.  But it wasn’t literal.  Otherwise he wouldn’t have said that

Then how come schaeffer didn’t evaluate the square root of positions?

That’s argument from repetition.  

You literally contradict yourself here.  10^17 isn’t the search space of a weak solution, it’s the total positions that make up the weak solution.  10^34 / 44 is the search space.  

How do you determine which move by white to do?