@8236
"Where did Euler say that?"
++ He wrote that on June 30, 1742 in a letter to Goldbach:
'Dass ... ein jeder numerus par eine summa duorum primorum sey,
halte ich für ein ganz gewisses theorema, ungeachtet ich dasselbe nicht demonstriren kann.'
Chess will never be solved, here's why
Sort:
@8234
"YOUR CALCULATIONS DON'T WORK."
++ They do. You do not understand.
@8235
"This topic is not about whether chess is a draw.
It's about whether it can be proven to be a draw."
++ The topic weakly solving chess is about finding out how to draw.
We already know chess is draw.
@8240
"Let’s say chess is solved by a super computer. Does it change anything for us?"
++ A player knowing part of the solution has an advantage.
@8242
"If it turns out to be forced win in say less than a hundred moves it would be possible to follow and we may as well all give up playing."
++ It cannot be a forced win, it is a forced draw.
It is indeed a forced draw in less than about 100 moves.
Assuming 4 non-transposing choices per move
4^100 = 10^60.
There are only 10^44 legal positions of which 10^38 with promotions restricted to either a queen or a previously captured piece and of which 10^34 resulting from reasonable play.
That is why weakly solving chess to a draw needs 10^22 positions the stupid and dumb way with no restrictions, 10^19 positions with restricted promotions and 10^17 positions in the smart and clever way.
Feb 2, 2023
0
#6067
tygxc wrote:
@8234
"YOUR CALCULATIONS DON'T WORK."
++ They do. You do not understand.
no its that YOU dont understand that they dont work.
Feb 2, 2023
0
#6068
tygxc wrote:
@8235
"This topic is not about whether chess is a draw.
It's about whether it can be proven to be a draw."
++ The topic weakly solving chess is about finding out how to draw.
We already know chess is draw.
we dont already know chess is a draw. i have asked a dozen times and you have failed every single time to give actual evidence for this.
@8252
"errors in your logic" ++ There are no errors. What you fail to understand is no error.
"the decisive game/ time per move" ++ The more time / move, the less decisive games and the less mistakes. At unlimited time zero decisive games and zero errors.
"1 error per decisive game" ++ Every decisive game has an odd number of errors.
At higher rates of decisive games there are games with 1 error, with 3 errrors, with 5 errors...
As the error rate and the rate of decisive games goes down like in Tata Steel Masters 2023 there are only decisive games with 1 or 3 errors. As the rate of decisive games goes further down,
like in the ICCF WC Finals, decisive games have 1 error only.
"comparison between alphazero and your '10^9 nodes' thing"
++ AlphaZero provides some peer reviewed conclusions of extensive calculations.
10^9 nodes/s is the present state of technology of existing cloud engines.
It mainly serves to convert positions to time needed.
"there were pre set starting openings" ++ No, in that table AlphaZero was free to open.
"your program could catch any errors made"
++ No. The program only calculates to the 7-men endgame table base.
If a white win were reached, then some black move was an error and has to be retracted.
If a black draw or win is reached, then the black moves need not be questioned, but alternatives for the white moves need to be explored.
"different nodes are of comparable strength"
++ Does not matter. The calculation just hops from the initial position to other drawn positions until it reaches a 7-men table base draw or a prior 3-fold repetition.
"the 'top 4' are going to have equivalent individual chances of finding the correct moves"
++ probability (all 4 top engine moves are errors) = (probability top 1 move is error)^4.
"a pre existing set of positions" ++ The task of the good assistants i.e. (ICCF) (grand)masters is to work out suitable starting positions of preferably 26 men for the calculation by the modern computers i.e. 3 cloud engines of 10^9 nodes/s (or 3,000 desktops of 10^6 nodes/s).
"jump to the 10^9 nodes" ++ There is no jump. 10^9 nodes/s is the state of the art speed of existing cloud engines now. That is to convert positions to time needed.
"what you erred" ++ I did not err, you failed to understand.
If you are a math student, then you should be able to understand. It is only basic math.
@8269
"we dont already know chess is a draw" ++ We know Chess is a draw.
"give actual evidence" ++ I have given evidence several times.
1 tempo < 1 pawn. A pawn can queen, a tempo cannot. White cannot win.
Each move dilutes the 1 tempo, so if a forced win existed, then it must be short.
Chess has 10^44 legal positions, meaning < 73 non-transposing choices between 4 moves.
Strategy stealing shows Chess cannot be a black win: for every presumed forced black win there exists a corresponding forced white win by losing a tempo.
The strongest Chess we have is the International Correspondence Chess Federation World Championship Finals: games last 2 years at a rate of 50 days per 10 moves, engines allowed, played by pre-qualified ICCF (grand)masters.
We have 1469 such games, of which 292 are decisive and 1177 are draws.
Assume chess a white win or a black win. Then there must be a probability of 1177 / 1469 of an odd number of errors. Try to fit a Poisson distribution of the errors per game with that outcome. It is impossible. That shows chess is a draw.
Now assume Chess is a draw. Then there must be a probability of 292 / 1469 of an odd number of errors. Try to fit a Poisson distribution of the errors per game with that outcome. It is possible. It shows that over 1000 of the draws are perfect games with no errors i.e. optimal play from both sides. All decisive games are lost by 1 error.
Some of the draws especially from earlier years have 2 errors that undo each other.
Feb 2, 2023
0
#6071
tygxc wrote:
@8252
"errors in your logic" ++ There are no errors. What you fail to understand is no error.
"the decisive game/ time per move" ++ The more time / move, the less decisive games and the less mistakes. At unlimited time zero decisive games and zero errors.
"1 error per decisive game" ++ Every decisive game has an odd number of errors.
At higher rates of decisive games there are games with 1 error, with 3 errrors, with 5 errors...
As the error rate and the rate of decisive games goes down like in Tata Steel Masters 2023 there are only decisive games with 1 or 3 errors. As the rate of decisive games goes further down,
like in the ICCF WC Finals, decisive games have 1 error only.
we dont know that. you just made more assumptions.
"comparison between alphazero and your '10^9 nodes' thing"
++ AlphaZero provides some peer reviewed conclusions of extensive calculations.
10^9 nodes/s is the present state of technology of existing cloud engines.
It mainly serves to convert positions to time needed.
and you made some BS conversion between the two, thats the whole point.
current 10^9 cloud engines would run alphazero on 10^6 nodes.
"44,000,000 * 60 Seconds = 2,640,000,000 Nodes per Move for Stockfish 8
50,286 * 60 Seconds = 3,017,160 Nodes per Move for Leela"
(google)
"there were pre set starting openings" ++ No, in that table AlphaZero was free to open.
no, for that table IT EXPLICITLY SAYS THE OPPOSITE.
"As AlphaZero is approximately deterministic given the same MCTS depth
and number of rollouts, we promote diversity in games by
sampling the first 20 plies in each game proportional to the
softmax of the MCTS visit counts, followed by playing the
top moves for the rest of the game."
"your program could catch any errors made"
++ No. The program only calculates to the 7-men endgame table base.
If a white win were reached, then some black move was an error and has to be retracted.
If a black draw or win is reached, then the black moves need not be questioned, but alternatives for the white moves need to be explored.
theres no method of exploration defined in your program. after all, YOU said 10^17.
"different nodes are of comparable strength"
++ Does not matter. The calculation just hops from the initial position to other drawn positions until it reaches a 7-men table base draw or a prior 3-fold repetition.
yeah strength matters. the alphazero evaluations dont take the same space as a stockfish node. your math is therefore off by a factor of at LEAST a thousand.
you are putting a brute force amount of calculations onto a neural network, that isnt able to be done.
"the 'top 4' are going to have equivalent individual chances of finding the correct moves"
++ probability (all 4 top engine moves are errors) = (probability top 1 move is error)^4.
yeah. thats an assumption. one that isnt necessarily true.
"a pre existing set of positions" ++
The task of the good assistants i.e. (ICCF) (grand)masters is to work out suitable starting positions of preferably 26 men for the calculation by the modern computers i.e. 3 cloud engines of 10^9 nodes/s (or 3,000 desktops of 10^6 nodes/s).
engines can find the suitable starting position better.
"jump to the 10^9 nodes" ++ There is no jump. 10^9 nodes/s is the state of the art speed of existing cloud engines now. That is to convert positions to time needed.
"what you erred" ++ I did not err, you failed to understand.
If you are a math student, then you should be able to understand. It is only basic math.
im literally a math student. you are just having a dunning kruger moment, thinking you know something that the rest of the world hasnt figured out yet.
your "top 4 engine moves" is also self contradicting to your own claims. to find the top 4 engine moves would be 4^50 * 10^17 to calculate, as a heuristic.
Feb 2, 2023
0
#6072
tygxc wrote:
@8269
"we dont already know chess is a draw" ++ We know Chess is a draw.
"give actual evidence" ++ I have given evidence several times.
1 tempo < 1 pawn
and theres your error.
not even 1 sentence in you make an assumption.
it doesnt matter that a pawn could queen.
Strategy stealing shows Chess cannot be a black win: for every presumed forced black win there exists a corresponding forced white win by losing a tempo.
white cant lose tempo in that way, its physically impossible.
in fact, i can prove it.
@8272
"Chess is not won my material advantage." ++ It is.
'Other things being equal, any material gain, no matter how small, means success' - Capablanca
"Do you need to be ahead in material to win a game of chess?"
++ The answer is YES! A direct checkmate of the opposing king is only possible if the opponent defends badly, i.e. does not play optimally.
Feb 2, 2023
0
#6074
whatever move white makes, black COULD follow this pattern: do the same move but replace a 1 with 8, 2 with 7, 3 with 6, 4 with 5, and vice versa. after blacks move things are symmetrical, after whites move things arent. therefore in the case of a symmetrical position black win, it is impossible for white to reach that position with a tempo lost, at least without a check or piece capture.
however, your argument makes no such check or piece capture provision.
hence, your argument must be wrong.
Feb 2, 2023
0
#6075
"the strategy-stealing argument cannot be applied to chess" - wikipedia
Feb 2, 2023
0
#6076
heck, its so obvious that the source wiki cites just has it as a side note.
@8271
"im literally a math student" ++ Then you should be able to understand.
"you know something that the rest of the world hasnt figured out yet"
++ GM Sveshnikov had it figured out long before me.
"top 4 engine moves is also self contradicting" ++ No. It is not.
"to find the top 4 engine moves would be 4^50 * 10^17 to calculate"
++ That is nonsense. As a math student you should know.
There are no more Chess positions than there are Chess positions.
@8276
"the strategy-stealing argument cannot be applied to chess - wikipedia"
++ It cannot be applied to prove a draw, but it can be applied to disprove a black win.
Feb 2, 2023
0
#6079
"""the strategy-stealing argument cannot be applied to chess - wikipedia"
++ It cannot be applied to prove a draw, but it can be applied to disprove a black win."
you do realize that they are talking about that you cant disprove a black win?
LITERALLY THE NEXT SENTENCE "It is not currently known whether White or Black can force a win with optimal play, or if both players can force a draw" - wikipedia
@8279
"I guess sacrifices in chess do not work"
++ Read the Capablanca statement carefully: 'Other things being equal'
Sacrifices can work if material is restored or gained after x moves.
Checkmate is an infinite amount of material up.
Sacrificial attacks only work if the opponent has defended badly: neglected the safety of his king, neglected the center, neglected development..., i.e. has not played optimally.
and also it was tygxc who brought euler's statement up.
i was responding to tygxc but clicked ur message by mistake