Will computers ever solve chess?

Impenetrable wall?  Vast emptiness?  Ok, I get it...this is a metaphor for your head.

I've been intrigued by the amount of work that is done to discover new prime numbers. There's no end to them, and they have almost no practical value. But the amount of work done to find new ones is immense.

Two of the most recent ones found are:
2,996,863,034,895  × (2)^1,290,000 - 1
and:
2,996,863,034,895  × (2)^1,290,000 + 1

They have more than 300,000 digits but this pair is only two digits apart. I guess that is pretty cool. In contrast, solving chess would be almost as useless (but maybe just as cool).

Really. Twin primes are very rare. 

Trial division (TD) is too slow for finding huge Primes. 

They have to use mathematical theory which reduces the computations, but even so, the reduced number sometimes requires days of calculation.

TD would probably take centuries, if not millions of years for a very large number.

Bigfoot is definitely more the speed of the would-be chess solvers here.

"Any argument that goes "This was hard, but we did it, this is hard, we'll do it" is a bad argument.

Here's a neat exercise for you:
- look up how big the problem approximately is (google is your friend)
- look up how many calculations the best computers can do a sec
- extrapolate ^ that number with Moore's law (you can assume the exponential growth continues, which it won't, but hey you know what? Say it only takes half that time to double )
- see how long it would take before we have a computer that could solve it in a million years

It's all pretty basic math, but the numbers get really intense. I think it'll be a fun experience ."

To a certain extent I agree with you.  On the other hand I don't think it will really matter even if computers DO solve chess.  It will change opening theory a lot, the new theory will replace the old, and then the games will go on just as before.  And proven expertise and successes in the past is not THAT bad of an argument for the expectation of successes in the future!

It is possible that in future some system of using patterns/methods could be used to simplify problem compared to current brute force method, making it solvable.  Or some new way of calculating things.  Or enough brute force...   if you had self replicating computers, possible that number of calculations per minute could be doubled every day or less.

(By new way of calculating things, I mean quantum mechanics, etc where old rules don't apply because more than binary choices)

Prime numbers are not useless. The have a wide applicability in the field of encrypting data. As such, finding big prime numbers is an extremely important aspect of our daily lives.

https://stackoverflow.com/questions/439870/why-are-primes-important-in-cryptography

It would perhaps be better to use bit boards like they do with chess engines.

You would use the UNIT64 (unsigned 64 bit integer) data type to represent game state.

For example, a single integer would be used to store the position of the white king.

If the WK is on A1 it would be 1 bit + 63 zero bits, with the 1 bit at MSB (most significant bit).

If the WK is on H8 it would be 63 zero bits + 1 bit, with the 1 bit at LSB (least significant bit).

Another single integer variable would be used for all white pawns, etc, etc.

For the other game state components a single integer can be used with bits set to represent game state. In the diagram below a rook represents a bit value of 1 and an empty square is a bit value of zero.

Here it is white to move (e4), white can castle both ways, c6 is the en passant capture square, black can only castle king side, when black to move e4 is set to zero and e5 is set to 1 etc etc.

Note that you can use one single integer variable to store 4 different types of data because the bit flags do not overlap: Player to move (rank 4 and 5), White castling rights (rank 1), Black castling rights (Rank 8), En passant capture square (ranks 3 and 6).

In binary this would be, from A1 to H8 reading left to right.

1 0 0 0 0 0 0 1

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1

The rows above each represent a rank, the actual decimal number is 9,295,429,665,254,539,265.

Note that I just included the above number to show it in decimal form, I used an online converter, I did not bother checking if the converter has doing it for unsigned 64 bit or for signed 64 bit (one bit is used to indicate a positive or a negative number).

Note that the actual decimal number means nothing, when working with bit boards you use bit operations to set or clear individual bits.

These bit operations are very fast and you could, for example, in just a few steps calculate if a position had any passed pawns etc etc etc.

You can not use a Zobrist hash key for these bit boards to represent all possible chess positions, you will have collisions, you would need to use a composite bit board primary key, this in turn leads on to the next problem, how big is the database?

There is a way to only have to store or use half the possible positions in chess, any ideas?

Today... Giri vs Caruana 

Stockfish gave +4.5 White is winning. White made the suggested best move by the program and the evaluation went to +1.5 White is better. White won another pawn. Stockfish kept insisting White was close to winning. White B+ 2pawns vs Black's N. 

Draw. No way to win. Programs have a very Loooooooooong way to go.

Don't forget, you don't have to save every line of analysis. It is possible to  determine (for example), 1.Na3 leads to a draw, then move on and erase that analysis.

interesting primes - a prime number can never end with "0" (it would have 10 as a factor) but this twin prime has an exponent that ends with "0000". That's pretty cool.👾

I ignored this thread for many months, and coming back I find the discussion pretty much where I expected it to be if I found it still alive.

Its predictability and permanence are almost a comfort in this chaotic universe, like stable ground underneath one's feet.

A bit like chess then

Especially with the "almost" part, very much like chess indeed!

I asked a question.

I was kinda expecting a quick response.

This website is full of "experts" and "geniuses", should be no problem for them.

Let N be the total number of possible chess positions.

Let M be half the total number of possible chess positions.

M = N / 2

What simple thing do you do to reduce N to M.

What about Fischer Random or my game Final Wars, both have a random starting position.

You almost answered the question but not quite.

Reflection about Y-axis?

Triangulation does not apply to every position.

I mean, for example, in a position it is white to move but white or black can not triangulate due to the position on the board, like pawn structure, space, pieces present, like if knights they can not triangulate but bishops can lose a move on a diagonal.

It is possible that some of those positions could be reached by transposition but that is only an assumption, it is not a concrete fact that can be measured, at least for now

Conclusion: Not every position can be either white to move or black to move.