Chess will never be solved, here's why

@12474

"under basic rules"
++ Without competition rules chess is not solvable.
1 Nf3 Nf6 2 Ng1 Ng8 3 Nf3 Nf6 4 Ng1 Ng8 etc.
A 3-fold, or 5-fold, or n-fold repetition rule is necessary to end an infinite sequence.
37 of the 116 perfect games end in 3-fold repetitions, usually some sacrifice to force a perpetual check.
On the contrary the 50-moves rule plays no role: the 116 perfect games end in at least 15, at most 73, average 40, standard deviation 11 moves, long before the 50-moves rule could trigger.

I agree with some of that but one part looks very incorrect.
'you always know what the best move is'.
Nyet.
There's never been such a player.
Plus - only one best move is something that comes up in tactics puzzles.
In the actual game of chess there can be multiple best moves at many points -
and if one them was or is better that doesn't mean the best players or the best chess engines would know which.

"Most of the time games will reach a tie because of equal skill level"
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That looks very dubious.
First of all it isn't qualified properly.
And as to research of what happens when players with exactly the same rating play each other - well maybe there's statistics on that - and charts of incidence of draws versus ascending rating level and determinations of at what level do draws start to exceed losses/wins.
Note that two players with the same rating may not have the same 'skill level' including because one of them is on the way up.

Posted this elsewhere and decided to post it here too.
I know tygxc is having 'fun with numbers'. Lol!
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Why are numbers always on the move?
Because they're Roamin' numerals.
How do you make 7 even?
Take away the S.
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When I told this next joke many years ago - something went wrong with the joke. It has a flaw.
But I still liked the joke anyway.
A speaker stood before a big crowd of alcoholics at an AA meeting.
He wanted to demonstrate how bad alcohol is for you.
So he first took a beaker of water and dropped a worm into it with a pair of forceps.
The worm then just swam to the side of the beaker and crawled out.
Then the speaker took a beaker of pure alcohol and dropped the worm in that.
The worm disappeared instantly! Gone. Destroyed!
So then somebody piped up from the center of the room loudly:
"I see if you drink alcohol you'll never have worms!"

Does EK know the flaw with the joke?

You can't have a repetition of natural positions, that's why FIDE needs an article to say when different positions are to be considered the same for the purposes of the triple/quintuple repetition rules (but not elsewhere - it doesn't make sense).

FIDE's use of the the term "position" is not the relevant point in any case, it's a side issue. What is relevant is your different uses of the term as basic rules forward play positions when you (mis)quote Tromp's number and nodes traversed by Stockfish (which is designed only for FIDE competition rules play) when you quote nodes/sec.

Actually Tromp's number isn't even a count of basic rules forward play positions. It counts forward play positions in a simplified version of the basic rules game where the resignation and agreed draw rules are removed and the touch move rules rewritten.

Hey that's interesting ...
three fold repetition of positions but they're 'different' with respect to the 50 move rule.
One would be inclined to think it doesn't matter though -
because there would be fewer moves left anyway.
In other words its getting more drawish that way anyway so no harm done.

hes referring specifically to a strong solution i imagine, as it is possible to guarantee no such issue will come about in a weak solution

I was reading today that in 2007 Checkers was found to be a draw with 'optimal play by both sides' but associated with that it said 'weakly solved'.
Well first - chess is not checkers - yes I know everyone knows but it seems to be forgotten sometimes ...
and there's that 'weakly solved' terminology again.
I was prepared to accept 'checkers a draw with best play' but with the factor 'weakly solved' there - not so hot.
If checkers is definitely a draw with best play - they should leave 'weakly solved' out of it instead of tainting it that way.

without some sort of invariant knowing which side wins/draws with optimal play and a weak solution are mathematically equivalent.
the checkers weak solution constructed a full game tree from the start to a known endgame tablebase, it is a full weak solution.

MEGA I appreciate that but would you care to state what you mean by 'weak solution'?
Yes I could look it up and then probably nod and say 'yeah'.
But I'm also thinking of newcomers to the forum.
'Weak solution?' Whaaa ...
I'm looking at Zemelo's theorem now ... commenting next post of mine.

weak solution means that from the start, for every possible move the opponenet could make, , you have determined a move that guarantees the desired game result. in this case it is in all likelihood a draw.

It is in its purest essence a function that takes the input of the game history/current board position and outputs a move as an algorithm.

in the case of chess, a weak solution does not need to know the optimal play to WIN a position if the opponent makes a mistake, only how to draw it.

of course, it needs to be proven for both sides that a draw can be guaranteed.

"In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win). An alternate statement is that for a game meeting all of these conditions except the condition that a draw is now possible, then either the first-player can force a win, or the second-player can force a win, or both players can at least force a draw.[1] The theorem is named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913."
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I object Immediately.
Not complain. Object.
" if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win)."
the first statement is automatically wrong.
Its wrong because somebody can make a mistake and not get the win.
'cannot end in a draw' is kind of Crazy.
Maybe there are positions where the only legal moves that can be made are checkmate in x moves.
I'm trying to think of a checkmate in one move that would be like that.
If it was white's move and his King is locked somewhere - and black's King is at d8 and there's white pawns at c6 d7 d6 and e6
then white's only legal moves are c7 checkmate or e7 checkmate.
Boo! Its very poorly worded in the 'theorem' ...
but it gets worse.
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"When applied to chess, Zermelo's theorem states "either White can force a win, or Black can force a win, or both sides can force at least a draw".
Yes I get the deal but I say its badly worded again.
because its not perfect and complete information as to what the moves are.
'white can force a win' if he knows what the moves are or finds out - but not if he doesn't.
same with black. Same with either side with drawing.
But how about - nobody can force a win nor a draw - because they Don't Know ... ?
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'Game-theoretic value' is also Poor.
If looked up its - reader "I have to invest an hour to see what they mean by that?
"Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition. Strongly solved is being used for a game for which such a strategy has been determined for all legal positions."
So then 'game theoretic value' leads to this:
"In game theory, we use expected value to determine the value of a game, which is the amount that each player can expect to win or lose on average. To calculate the expected value of a game, we first need to determine the payoffs for each player in each possible outcome."
Extremely poorly worded.
Even if they had made it clear they're not talking about money ...
or one argues that its obvious they're talking about probabililty -
its still very very poorly worded.
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"Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition."
Did they have to word it that way because they have to allow for different games?
If there's going to be terminology used for mathematical situations then the terminology should be as unambiguous as possible.
If they're talking about win or lose or draw - then they should use those terms instead of jargon.
In school - I was extremely strong in math and physics. And geography.
But not in history or languages. Lol!
It was a long time ago.
But one of the reasons I was so strong in math is that I didn't allow any ambiguities unless it was absolutely necessary.
Yes if you're going to have unknowns and some of them can't be solved then you might end up with a function or graph instead of a solution.
But the idea was to never do that unless you had to.

Again I appreciate that.
'in all likellihood' Lol! I don't want to complain.
Because I know you're being nice !!
Hahahaah.
Also in your post:
'if the opponent makes a mistake'.
I think some progress was made but I wonder if you see my point?
How do I do this without seeming critical or rude?
MEGA - you know me I think.
I wouldn't be obnoxious to somebody I know is being friendly and polite and patient and honest and using objectivity and is well informed. In other words ... MEGA.
So I'll try to phrase it as diplomatically as I can right now.
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Say somebody new to the forum arrives - doesn't know anything about formal game theory and we want to tell him or her what is meant by 'weakly solved' without even the slightest loose ends or fuzzy meanings and in as few words as possible but with no technical terms.
In other words only words the newcomer would know thoroughly and exactly like draw and win ....
can that be done in very few words?
I've got to be away from computer for a bit ...
but there does seem to be an opportunity for clear progress here.
And I think this could be valuable for informing newcomers more exactly why tygxc's positions are thoroughly in error.

When I posted that post MEGA I didn't realize you had re-posted already.
Please see my next post #12538.
Yes I see you replied to that previous post but I can't concentrate right now.
Lol!
Gots to Logoffsky!

@12535

"what you mean by 'weak solution'?"

'weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition' - Prof. van den Herik

Schaeffer ran 50 CPU for 2 years to examine 10^14 positions and weakly solve Checkers.
The 17 ICCF WC Finalists ran 3060 CPU for 2 years to examine 10^17 positions and in part weakly solve Chess: 116 perfect games with optimal play by both sides.

Again, you dont know the words you repeat, and thus conclude delusional takes like that a set of games are all perfect because they are draws, and that mathematical proof doesnt need to be 100% true.

please be quiet so people who are actually interested in understanding the nuance of game theory can discuss it.