Chess will never be solved, here's why

@14816

"114 games all drawn does mean that the odds against the errors all occurring in pairs is astronomical"
++ If all 114 games are drawn, then all 114 games contain an even number of errors: 0, 2, 4.
The most plausible error distribution is 114-0-0-0-0.
However, a few games with a pair of errors: e.g. 112-0-2-0-0 cannot be excluded.
There can be no substantial number of games with a pair or errors, e.g. 60-0-54-0-0,
because then there would be at least 1 game with 1 unpaired error, i.e. a decisive game.

"odds for all of the errors occuring in pairs in these 114 games is necessarily tiny"
++ Assume game 115 were decisive, no clerical error, or due to illness.
Then odds of 1 error = 1/115. Thus odds of a pair of errors= (1/115)² = 0.008%.
The odds could be slightly more if there is a tendency for errors to come in pairs.

"is it more likely that the winning line found or missed by player 2 in this particular instance?"
++ Player 1 is more likely to make an error than player 2 is to miss the win after it.
The reason is player 2 has 1 ply more information: he knows the move played by player 1,
while player 1 was considering several candidate moves. Player 2 looks 1 ply deeper than player 1 did, even with equal hardware, software, and time per move.

Another issue is the time per move. They have 50 days for 10 moves, but are free to spend it as they see fit. If player spends 2 days on his move, and player 2 spends 10 days on his reply,
then player 2 is more likely to spot the error made by player 1.

ah yes tygxc, continue misconstruing statistical likelihood and intuitive probability as mathematical fact.

ah yes, continue to make a probability estimate using a "method" literally never used in any academia (why is it never used? because it is literally just BS and makes so many self contradictory fallacious assumptions it's hard to know where to begin).

the simplest error is this: you assume errors are completely independent.

if there is a winning line that requires a 60 ply machine to see, and the players only have 40 ply, both of them are going to miss it.

Glad to have some moderation here. Thanks.

"Player 2 looks 1 ply deeper than player 1 did, even with equal hardware, software, and time per move."

ah yes, a 1 ply difference, complete independence. since when?

"Another issue is the time per move. They have 50 days for 10 moves, but are free to spend it as they see fit. If player spends 2 days on his move, and player 2 spends 10 days on his reply,
then player 2 is more likely to spot the error made by player 1." - this just falsely assumes that player two will take extra time on a move they dont even know had an error yet.

"Player 1 is more likely to make an error than player 2 is to miss the win after it"

You make some relevant points here, but this sentence right here shows that you are slightly missing the point or were trying to say something else.

The first error happening is the required condition for the second error happening, so ofc player 1 is more likely to make an error than player 2 is to miss an error (meaning make a second error).

The question is ONCE the condition is true and first error has happened, is it more likely that player 2 finds it or misses it. Now this can be anywhere from almost never finds it to 50/50 to almost always finds it, but considering the similar abilities of the two players, I would tend to guess on the lower side: Player 2 rarely finds the win.

What supports my view is similar rated engines playing against each other: They make mistakes but more likely draw still. The 1 ply difference doesn't seem enough; It would require player 1 to have been exactly 1 ply away (or close to it if player 1 is slightly weaker) from evaluating the position differently. This is over simplified but the point is that being one move further isn't a big difference in terms of evaluation at this level. Of course luck is another factor, engines can follow a winning line without knowing it's winning.

This determines what on average is the expected rate for single error games vs paired error games.

But concerning that last line - tygxc is conceding 'error made'.
And he is conceding that more time is more likely to spot 'error made'.
But in other posts he is trying to claim 'perfect games'.
And trying to claim 114 Consecutive 'perfect games'.
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Issue: whoever having 'confidence' in making claims that contradict each other.
But pointing out the contradictions is not 'trolling'.
To his credit - tygxc has conceded more than once that chess cannot be solved with current technology.
But 114 games with engines of the same strength drawing each other doesn't prove anything except that those same strength computer/engines and their software are incapable of finding each other's errors - and its now been pointed out over and over again to tygxc why a claim of proof beyond that is false.
If anything - the occurence of the consecutive draws is misleading to some who ignore the context and is therefore Regression rather than progress.
To point this out - interfering with the false claims - is also Not 'trolling'.

Chess will never be solved, here's why... until Elon

@14838

"The first error happening is the required condition for the second error happening" ++ Yes.

"player 1 is more likely to make an error than player 2 is to miss an error" ++ Yes.

"ONCE the condition is true and first error has happened, is it more likely that player 2 finds it or misses it." ++ Player 2 looks 1 ply deeper than player 1,
so player 2 is more likely to find the error than player 1 was.

"Player 2 rarely finds the win"
++ If player 1 uses only 2 days per move, then he is more likely to err than if he uses 5, or 10.
If player 2 uses 10 days on his reply instead of 5 or 2, then he is more likely to find the win. However, by taking 10 days to reply player 2 then risks to be later forced to move in 1 or 2 days, increasing his odds to err later. So player 2 can opt to increase his odds to find a win in case there is any, but at the cost of later having to move faster and increasing his own odds to err later.

"The 1 ply difference doesn't seem enough"
++ But it increases the odds of finding the win as compared to the odds of making an error.

"engines can follow a winning line without knowing it's winning"
++ Engines and humans select among the legal moves the move that they hope or believe is no error, and that they hope or believe makes it more difficult for the opponent to find the right reply, i.e. increases his odds to err.

"This determines what on average is the expected rate for single error games vs paired error games."
++ What do you mean? Can you give an example?

For the ICCF WC28 Finals of 2013 with 20 decisive games out of 136 I arrive at 114 games with 0 error, 20 games with 1 error, and 2 games with 2 errors. What do you arrive at?

For the ongoing ICCF WC33 Finals with 0 decisive games out of 114 I arrive at a probability of (1/115)² = 0.008% for a game with 2 errors. What do you arrive at?

Interesting. Looked it up.
Got this right away:
"Along with the advancement of technology, Elon Musk feels the game of chess can be fully decoded by computers in the near future. Musk seems not to be a big fan of the battle between two human brains. The Tesla CEO has predicted that the sport will be solved within a decade like checkers was."
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Can only happen with Very big improvements in the hardware and software very soon.
Big Improvements in the hardware and software have been occuring for several decades - 
but so far tablebasing only goes up to a pathetic 7 pieces on board which was a struggle of several years that was also pathetically unable to even include castling.
And now the task of 8 pieces without considering castling is even more Daunting for the 'advancement of technology' computers.

"++ What do you mean? Can you give an example?"

Yes. Again some relevant things in your post but we are not completely on the same page.

We are looking into the relationship between games with a single error and games with an error pair (which is hard but we can use the data and some logic). What information this gives us? We can look at how many decisive games there has been (0) and what does this mean in terms of expected drawn games that contain an error pair.

If we consider it reasonable that games with error pairs are more common (or similar/slightly smaller probability for that matter, as the 114 game sample is small) than games with a single error, we can't conclude from the 0 decisive games that we shouldn't expect drawn games with errors pairs in the same sample. Same goes the other way; If we imagine there were drawn games in the 114 games that contain error pairs, we can't conclude that there should be expected a decisive game (single error).

I think evidence supports error paired games being more common, like I explained in previous post.

Well this was an explanation, not an example but I could maybe write an example case later if it helps.

The bit about castling is odd. It's not that they were unable to include it, it's that they didn't bother. It wouldn't even increase the computation very much.

Syzygy acknowledges the move exists even while confirming a position with castling rights is not in its database.

one of the most egregious errors made is that these "calculations" of yours assume that chess is a draw, while at the same time you've previously used these probabilities that you've "calculated" as "proof" that chess is a draw.

circular logic.

from @Kotshmot
"and what does this mean in terms of expected drawn games that contain an error pair."
Very relevant.
I think that the following is 'understood' and perhaps discussed already somewhat but I'm mentioning it anyway.
1) An issue of whether either computer 'catches' either error when there's an error pair.
2) and whether either error is otherwise exploited by subsequent play.
3) Another issue of either error being just too deep for the current computers to catch or exploit.
And yet another issue of
4) In addition to the 'error pair' ... many other errors also in the game or games whether an odd or even number of same
and 
5) scenarios where there's an 'error' pair but many other errors where the split between which computer makes more errors is very Lopsided.
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114 consecutive draws between engines of the same strength only indicates that its very difficult for either computer to catch or otherwise exploit the very deep errors made.
Is it conceivable that in many games of 50 moves or more in such draws - that the computers averaged a combined 20% error rate in their moves?
50 complete moves is 100 plies.
How about 20 total errors in a game of 50 complete moves which is actually 100 moves in the drawn game?
Why not?
If they can't catch each others errors they can't catch them.
Its that simple.
And idea: they won't catch them - reviewing the games with the same engines.
Another thing to discuss further.

Try it another way.
If today's engines review draws between engines of ten years ago -
do they find 'errors' by those engines?
How many? What percentage of moves on average?
How does the percentage of errors correspond to how many years back the old draws occurred?
If this has been discussed here already I missed it.
Point: if such research has already been done then that could be useful here.
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I expect that ten years from now the engines of that time (including the engines that Elon Musk expects) will find various errors in the 114 consecutive ICCF draws.
Point: the engines reviewing games whether present or future don't have to be set to any '5 days per move' limitation.
But engines of the same strength reviewing their own games looks suspect though.
And - there would still be practical limitations on how many days per move even on reviewing games.
But if they're as strong as Musk expects then they're more likely to find the ten year old errors made by today's computers.
The stronger they are - the more likely that happens.
Am I 'presupposing' there are errors?
No. tygxc is presupposing there aren't any apparently.
The more engines advance the more they prove that the engines of yesteryear are error prone.
Otherwise - how could they be advancing?

@14843

"We are looking into the relationship between games with a single error and games with an error pair" ++ Yes. For example in the ICCF WC28 Finals of 2013 I expect 20 games with a single error: the 20 decisive games, and 2 drawn games with an error pair.

"We can look at how many decisive games there has been (0) and what does this mean in terms of expected drawn games that contain an error pair." ++ OK. I expect 0 games with an error pair, but I cannot exclude a few games (2-3) with an error pair, but I do exclude a substantial number of games (20-30) with an error pair, as then at least 1 game with 1 error, i.e. a decisive game should be present as well.

"games with error pairs are more common than games with a single error" ++ Maybe.

"conclude from the 0 decisive games that we shouldn't expect drawn games with errors pairs in the same sample" ++ At least not more than a few (2-3).

"If we imagine there were drawn games in the 114 games that contain error pairs, we can't conclude that there should be expected a decisive game (single error)."
++ A few error pairs (2-3) OK, but a substantial number of error pairs (20-30) should show at least 1 single error game, i.e. decisive game.

"evidence supports error paired games being more common" ++ Maybe.

Multiple error pairs per game.
Even more likely.

reminder to all that these arent just hypothetical probabilities that tygxc is claiming. tygxc actively 'uses' his made up numbers to claim that the iccf chess games are perfect with mathematical rigor and that they can be used to discard positions in proof with impunity.

If I've got Elroch's point right - its that if there's an error there has to then be an error pair for the game to draw.
An even-numbered number of errors.
But its easy to misinterpret that and think/say ...
'But doesn't that mean an odd number of errors would cause a win?' and then further misinterpret from there.

The point is that the other computer would have to exploit the error - and if there's 'failure to exploit' that makes an 'error pair'.
Its potentially very misleading.
Because of types of 'error'.
Game-losing or potentially game-losing error versus 'not playing strongly enough to exploit that error' being also classified as an 'error'.
Pitfalls and minefields in the terminologies of the word 'error'.
and then Enter: invalid claims.

"++ A few error pairs (2-3) OK, but a substantial number of error pairs (20-30) should show at least 1 single error game, i.e. decisive game."

why tygxc? theres literally no reason why there arent a lot of lines that are being missed. after all, the engines are all about the same level, with a few ply difference here and there.

and again, your 'calculations assume' perfect independence, while the concession you make here contradicts that vastly.

another reminder yall:

@tygxc tries to make claims of hard fact, (often mathematical), but then when confronted with the fact that he literally has no grounds or definitive logic, he starts speaking in softer terms and acts like its a grey area discussion.

This entire probability calculation discussion started because tygxc tried to justify an objectively false claim with his 'probabilities' as mathematically rigorous logic. And, as mountains of doubt have since been cast onto his 'probabilities', tygxc is now trying to argue his 'probabilities' from a heuristic estimation perspective.

Since it is part of a claimed proof by tygxc, is not enough for tygxc to justify his numbers as heuristical approximations (disregarding the errors he makes in his heuristics). he must prove that his probability is the ONLY probability that can be reached (or better) no matter what additional available information we may incorporate.

and THEN, even if he did justify his calculations rigorously, It would still be a fallacy because high probability is not mathematical proof of a game solution of a turn-based game of perfect information.

hey tygxc, if you want to see more examples of you making claims of fact and then backpedaling, just downvote my post like the others instead of arguing with it. i aleady have a handful of examples in mind.