Chess will never be solved, here's why

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XOXOXOexpert

Solved 32 piece chess game needs approximately 3 x 10^60 Bytes of data storage.

tygxc

@5761
I verified and the engine always plays a table base correct move as its top 1 move. Not always the fastest, but never a mistake.

 

Now please a KRPP vs. KRP that draws.

[Variant "From Position"]
[FEN "2r5/8/8/2pP3K/2P5/3R2k1/8/8 b - - 0 1"]

1... Kf4 2. Kg6 Ke5 3. Kf7 Rc7+ 4. Ke8 Kd6 5. Rg3 Rc8+ 6. Kf7 Rc7+ 7. Kf6 Ra7 8. Kf5 Ra4 9. Rg6+ Ke7 10. Rg4 Kd6 11. Re4 Kd7 12. Kf4 Ra3 13. Re3 Ra4 14. Rc3 Ra1 15. Kf3 Kc7 16. Re3 Ra4 17. Re4 Kb7 18. Kf4 Kc7 19. Ke5 Ra3 20. Ke6 Rh3 21. Ke7 Rh7+ 22. Ke8 Rh8+ 23. Kf7 Kd8 24. Ke6 Re8+ 25. Kf5 Rf8+ 26. Kg4 Rg8+ 27. Kf3 Rh8 28. Ke2 Rh3 29. Re3 Rh4 30. Kd3 Rh6 31. Rf3 Kc7 32. Rf7+ Kd6 33. Rf8 Rh3+ 34. Kc2 Ke5 35. Re8+ Kd4 36. d6 Rh7 37. Re7 Rh2+ 38. Kb3 Rh3+ 39. Ka4 Kxc4 40. Re4+ Kd3 41. d7 Kxe4 42. d8=Q Rh5 43. Qg8 Rf5 44. Qe6+ Re5 45. Qc4+ Ke3 46. Kb5 Kf3 47. Kc6 Re4 48. Qc2 Rf4 49. Kd5 Ke3 50. Qc1+ Kf3 51. Qf1+ Kg3 52. Qe2 Rf8 53. Qe3+ Kg4 54. Qe4+ Rf4 55. Qg2+ Kf5 56. Qh3+ Kg5 57. Ke5 Rf8 58. Qe3+ Kg6 59. Qg1+ Kh5 60. Qxc5 Rf1 61. Qd5 Rf2 62. Qe4 Rf7 63. Ke6 Rg7 64. Qe3 Kg6 65. Qd3+ Kg5 66. Qd8+ Kh6 67. Qh8+ Kg6 68. Qh4 Ra7 69. Qe4+ Kh5 70. Qh1+ Kg4 71. Qg1+ Kf3 72. Qxa7 Ke2 73. Qd4 Kf3 74. Qd3+ Kg2 75. Qe2+ Kh1 76. Kf5 Kg1 77. Ke4 Kh1 78. Kf3 Kg1 79. Qg2#

tygxc

@5770
"Solved 32 piece chess game needs approximately 3 x 10^60 Bytes of data storage."
++ No. 10^44 bit is enough. Tromp has proven a 1 to 1 relationship between natural numbers 1...N and chess positions. So an array of 10^44 bit: 0 = draw, 1 = no draw is enough to store a strong solution of Chess.

MARattigan
tygxc  wrote:

@5761
I verified and the engine always plays a table base correct move as its top 1 move. Not always the fastest, but never a mistake.

And it draws from a winning position. What are you trying to say?

As I've mentioned before, you don't understand how tablebases work

 

Now please a KRPP vs. KRP that draws.

Would you like cherries on top? You are the one asserting your method to be correct, you should have checked these things at the outset. Why do you always expect others to fry their chips while you sit back.

As it happens I've kicked off a series of those too, because I knew you'd ask. Results in a few days.

In the meantime there's no reason for you not to apply your calculation to the KRBN vs KQB games I already posted. If they don't work there we can ignore your thesis.

[Variant "From Position"]
[FEN "2r5/8/8/2pP3K/2P5/3R2k1/8/8 b - - 0 1"]

1... Kf4 2. Kg6 Ke5 3. Kf7 Rc7+ 4. Ke8 Kd6 5. Rg3 Rc8+ 6. Kf7 Rc7+ 7. Kf6 Ra7 8. Kf5 Ra4 9. Rg6+ Ke7 10. Rg4 Kd6 11. Re4 Kd7 12. Kf4 Ra3 13. Re3 Ra4 14. Rc3 Ra1 15. Kf3 Kc7 16. Re3 Ra4 17. Re4 Kb7 18. Kf4 Kc7 19. Ke5 Ra3 20. Ke6 Rh3 21. Ke7 Rh7+ 22. Ke8 Rh8+ 23. Kf7 Kd8 24. Ke6 Re8+ 25. Kf5 Rf8+ 26. Kg4 Rg8+ 27. Kf3 Rh8 28. Ke2 Rh3 29. Re3 Rh4 30. Kd3 Rh6 31. Rf3 Kc7 32. Rf7+ Kd6 33. Rf8 Rh3+ 34. Kc2 Ke5 35. Re8+ Kd4 36. d6 Rh7 37. Re7 Rh2+ 38. Kb3 Rh3+ 39. Ka4 Kxc4 40. Re4+ Kd3 41. d7 Kxe4 42. d8=Q Rh5 43. Qg8 Rf5 44. Qe6+ Re5 45. Qc4+ Ke3 46. Kb5 Kf3 47. Kc6 Re4 48. Qc2 Rf4 49. Kd5 Ke3 50. Qc1+ Kf3 51. Qf1+ Kg3 52. Qe2 Rf8 53. Qe3+ Kg4 54. Qe4+ Rf4 55. Qg2+ Kf5 56. Qh3+ Kg5 57. Ke5 Rf8 58. Qe3+ Kg6 59. Qg1+ Kh5 60. Qxc5 Rf1 61. Qd5 Rf2 62. Qe4 Rf7 63. Ke6 Rg7 64. Qe3 Kg6 65. Qd3+ Kg5 66. Qd8+ Kh6 67. Qh8+ Kg6 68. Qh4 Ra7 69. Qe4+ Kh5 70. Qh1+ Kg4 71. Qg1+ Kf3 72. Qxa7 Ke2 73. Qd4 Kf3 74. Qd3+ Kg2 75. Qe2+ Kh1 76. Kf5 Kg1 77. Ke4 Kh1 78. Kf3 Kg1 79. Qg2#

Yes. Syzygy can achieve the correct result. SF15 can't.

The question we were looking at was will @tygxc ever be able to?

 

tygxc

@5774

"it draws from a winning position" ++ Not on my computer. It checkmates in 79, see above.

"What are you trying to say?" ++ You do something wrong, or you run a bad version of SF.

"you don't understand how tablebases work" ++ I understand that very well.

 "Would you like cherries on top?" ++ No cherries, just a relevant drawn FEN KRPP vs. KRP.

"You are the one asserting your method to be correct" ++ Yes.

"you should have checked these things at the outset" ++ I did.

"Why do you always expect others to fry their chips" ++ I fry a lot of chips, and do not sit back.

"As it happens I've kicked off a series of those too, because I knew you'd ask. Results in a few days." ++ Very well, let us see. One is enough. Hopefully the interface then works again too.

"SF15 can't." ++ I did it with Stockfish 14 NNUE.

"there's no reason for you not to apply your calculation to the KRBN vs KQB games"
++ Are any of these draws? If not they cannot be reached from the initial position by optimal play from both sides, thus are not relevant to weakly solving Chess. If any is a draw, then please post the FEN and I will look at it.

Kungfucious76

You got sponsors and chess tournaments.

Where money's involved you'll have inside cheating

Lot of my games get disconnected  when I start winning

They already know who's gonna win the tournaments 

MARattigan
tygxc wrote:

@5774

"it draws from a winning position" ++ Not on my computer. It checkmates in 79, see above.

Very similar to my short think time examples (they're not all drawn from that position). Also very inaccurate. Try running it for 2048 seconds per ply. You're not guaranteed the same game or even the same result, nor even a game with fewer blunders, but I think the same result might be likely.

"What are you trying to say?" ++ You do something wrong, or you run a bad version of SF.

Not true. You just don't know how to use the Syzygy site.

"you don't understand how tablebases work" ++ I understand that very well.

If you understood very well you wouldn't keep posting that they strongly solve 7 man positions under competition rules. They do strongly solve K v K, KB v K and KN v K, but that's all.

 "Would you like cherries on top?" ++ No cherries, just a relevant drawn FEN KRPP vs. KRP.

As I said; Coming up. Any chance of you doing some work to check your own hypotheses?

You could start by applying your calculations to the KRBNvKQB games I already posted for you.

Save everybody else a lot of work. We only need one counterexample.

"You are the one asserting your method to be correct" ++ Yes.

"you should have checked these things at the outset" ++ I did.

Obviously not.

"Why do you always expect others to fry their chips" ++ I fry a lot of chips, and do not sit back.

So here is a drawn position.

White to move, ply count 0

 

Produce a series of at least 10 games with think times up to 2048 seconds for it. We'll wait.

Or if you're going to say that position is irrelevant as soon as you can't get your calculation to work, maybe this 8 man draw that you yourself posted earlier in the thread. 

White to play, ply count 0

 

We can't check how many errors in that one but we can put a lower bound on it.

Get frying. But preferably after you've applied your calculation to the 23 games I've already posted for the purpose. If you do that first we can all stop talking to you.

"As it happens I've kicked off a series of those too, because I knew you'd ask. Results in a few days." ++ Very well, let us see. Hopefully the interface then works again too.

"SF15 can't." ++ I did it with Stockfish 14 NNUE.

Versus very weak opposition (Stockfish 14 NNUE).

I should have been more precise; SF15 can't always.

 

MARattigan
Optimissed wrote:
tygxc wrote:

@5770
"Solved 32 piece chess game needs approximately 3 x 10^60 Bytes of data storage."
++ No. 10^44 bit is enough. Tromp has proven a 1 to 1 relationship between natural numbers 1...N and chess positions. So an array of 10^44 bit: 0 = draw, 1 = no draw is enough to store a strong solution of Chess.


Says you. Don't think so.

For once I agree with @Optimissed.

(I'm getting worried.)

MARattigan

Not my fault if I can't count.

MARattigan
tygxc  wrote:

...

"as the earlier version" ++ No, there are no 2 versions.

You're right; at least 27. Unfortunately none even close to being adequately described.

MARattigan
tygxc wrote:

@5765
"Why is my example irrelevant and KRPP vs KRP relevant?"
++ Your first example cannot be reached from the initial position by optimal play from both sides. That is why it is irrelevant for weakly solving Chess.

I wasn't talking about weakly solving Chess. You're obviously not going to be doing that.

I was talking about the calculation you keep posting. It would seem to be very relevant to that.

MARattigan

An hour on zoom with my wife would normally cost £30 or £40 ...

Not much use on zoom.

MARattigan

She doesn't like it either. ...

Then possibly not much use in any case.

Elroch
MARattigan wrote:
Optimissed wrote:
tygxc wrote:

@5770
"Solved 32 piece chess game needs approximately 3 x 10^60 Bytes of data storage."
++ No. 10^44 bit is enough. Tromp has proven a 1 to 1 relationship between natural numbers 1...N and chess positions. So an array of 10^44 bit: 0 = draw, 1 = no draw is enough to store a strong solution of Chess.


Says you. Don't think so.

For once I agree with @Optimissed.

(I'm getting worried.)

Maybe you should be.

The latest tablebases achieve compression of 1 bit per position with efficient access.

It's worth remembering that compression is always a tradeoff between space and efficient access. You can "store" data in the size of a program to generate it on the fly. This is in cases like this hideously inefficient in computation time.

But Syzygy and its 8 piece successor use very high compression to 1 bit per position while permitting quick access. Don't ask me how.

You could argue that 32 pieces would not permit such compression. I suspect this is not true, but even if it was, you could likely throw in a tiny factor like 4.

So storing a 32-piece tablebase of over 10^44 positions in a similar number of bits is theoretically feasible. The problem is that 10^44 (non-trivial) operations is beyond computers that can be designed today. (

10^44 trivial operations is also beyond currently feasible. Eg, the current world's fastest supercomputer can manage this number of FLOPS (simplest floating point arithmetic operations) in about 7 billion trillion years).

Elroch

A 32-piece tablebase is a strong solution of chess. You can trivially use it to make optimal strategies for each side with merely 1 access of the database per move.

[This was a reply to a post that seems to have been deleted].

MARattigan
Elroch wrote:

A 32-piece tablebase is a strong solution of chess. You can trivially use it to make optimal strategies for each side with merely 1 access of the database per move.

[This was a reply to a post that seems to have been deleted].

Reinstated in essence.

@tygxc is specifying a WD tablebase. That's not a solution. A WDL tablebase is also not a solution.

And 10^44 is not the number of competition rule game states, nor even Tromp's number.

I think Huffman codes come into it. Whether a solution could be stored in 10^44 is open to discussion.

Elroch

Syzygy and its 8-piece successor (under development) are state of the art and use about 1 bit per position, so no need to argue about WD/WDL.

Correct about the count. For practical purposes, it doesn't matter. It's too big to consider without a paradigm shift.

MARattigan
Elroch wrote:

Syzygy and its 8-piece successor (under development) are state of the art and use about 1 bit per position, so no need to argue about WD/WDL.

@tygxc says  So an array of 10^44 bit: 0 = draw, 1 = no draw is enough to store a strong solution of Chess. justifying it by postulating a WD tablebase. Are you saying I should have agreed with @tygxc in preference to @Optimissed?

Is 10^44 classical bits enough to hold a strong solution of competition rules chess without holding a generation program in the probe code? Like @Optimissed I don't think so, but you can try to persuade me (granted it's a lot of bits).

Remember Syzygy is not a strong solution of any but a few endgame positions, not even the ply count 0 positions.

But I take your point about simply storing the Syzygy generation program. That brings us back to the definition of "solution".

Correct about the count. For practical purposes, it doesn't matter. It's too big to consider without a paradigm shift.

 

DiogenesDue
MARattigan wrote:

Reinstated in essence.

@tygxc is specifying a WD tablebase. That's not a solution. A WDL tablebase is also not a solution.

And 10^44 is not the number of competition rule game states, nor even Tromp's number.

I think Huffman codes come into it. Whether a solution could be stored in 10^44 is open to discussion.

I had Huffman as a teacher once.  Have to tell you, I was not impressed with him in that capacityhappy.png.

Elroch
MARattigan wrote:
Elroch wrote:

Syzygy and its 8-piece successor (under development) are state of the art and use about 1 bit per position, so no need to argue about WD/WDL.

@tygxc says  So an array of 10^44 bit: 0 = draw, 1 = no draw is enough to store a strong solution of Chess. justifying it by postulating a WD tablebase. Are you saying I should have agreed with @tygxc in preference to @Optimissed?

Is 10^44 classical bits enough to hold a strong solution of competition rules chess? Like @Optimissed I don't think so, but you can try to persuade me (granted it's a lot of bits).

Remember Syzygy is not a strong solution of any but a few endgame positions, not even the ply count 0 positions.

Correct about the count. For practical purposes, it doesn't matter. It's too big to consider without a paradigm shift.

From the Syzygy documentation:

"Syzygy Bases consist of two sets of files, WDL files (extension .rtbw) storing win/draw/loss information considering the fifty-move rule for access during search ..."

I believe this implies Syzygy provides a strong solution for all positions. (There can be no repetitions if you aim efficiently towards a win at the first opportunity, and if you are aiming for a draw any drawing move will do.