From memory, I think a set of 7 rules and brute force (but the brute force served only to show that the 7 rules were in all circumstances sufficient).
One rule would be enough for either connect4 or chess because any number of rules can be combined into a single rule.
@4756
No. The definition is:
'Weakly solved means that for the initial position a strategy has been determined
to achieve the game-theoretic value against any opposition.'
You turn it into strongly solving.
Your memory appears to be getting a bit flaky if you claim to be referring to the standard definition of strong solution.
A strong solution is able to find a best move IN ANY POSITION. Any competent person can see that is different to what I said.
However, a strong solution is not relevant to solving chess in any meaningful way.
Any competent person should be able to see that.
Amusing semantic joke there.
A STRONG SOLUTION is something that STRONGLY SOLVES chess. So it is rather relevant to that variant of "solving chess".
Here we have focussed on WEAKLY SOLVING chess, which requires a WEAK SOLUTION.
Being clear about what words refer to is so important, especially when they are used in two different ways in different contexts.
@4761
++ You do not understand.
If you require "against ALL responses" and for both sides, then you end up with all legal moves and thus all legal positions and thus a strong solution of chess.
No. You do not. Not by a million miles.
This is like saying if you want an opening strategy at chess you need to learn every opening. Do you think that is true? The truth is that if you want an opening strategy at chess to get you to move 10, you need about the square root of the number of moves in the complete opening book of legal games to move 10. You can manage with a bit less perhaps by careful selection, but not much less (on a logarithmic scale, of course).
(Chess is not entirely directional, so this is not a very precise notion for full strategies, but there is quite a lot of directionality, since pawn moves, captures, promoting, castling and loss of castling rights cannot be reversed).
What do you really mean by solving chess?
Are you trying to solve it like a puzzle, putting the pieces together?
Are you trying to find out which move is the most accurate and will guarantee no disadvantage and improve your position as much as it can?
Actually, if you refer to the second question, then chess will not be fun anymore.
If each side cancels out each other's moves, it will be a draw repeatedly like tic tac toe games.
Of course, it could also be a game in which one position is always guaranteed to win.
All theorems applying to this class of games apply to chess.
In particular, you have condemned anyone who uses inductive thinking in this matter and yet what is that but a glaring example of inductive thinking, which is entirely inappropriate, as you yourself have pointed out?
I am bemused how you could think that is any sort of example of inductive thinking. It simply isn't.
In mathematics and related subjects there are theorems which start with a set of axioms and end with a proposition. They say that when the set of axioms is true, the proposition is true. I stated that chess satisfies a certain set of axioms defining a class of games, and thus all theorems that can be proven from those axioms are true about chess.
None of this involves induction: it is a very fundamental fact about deductive knowledge in general. It could itself be proven in a formal manner, as a theorem of mathematical logic.
What do you really mean by solving chess?
Are you trying to solve it like a puzzle, putting the pieces together?
Are you trying to find out which move is the most accurate and will guarantee no disadvantage and improve your position as much as it can?
Actually, if you refer to the second question, then chess will not be fun anymore.
If each side cancels out each other's moves, it will be a draw repeatedly like tic tac toe games.
Of course, it could also be a game in which one position is always guaranteed to win.
Solving chess, as for solving any game, is already defined. There's no ambiguity, choice or interpretation involved.
What do you really mean by solving chess?
Are you trying to solve it like a puzzle, putting the pieces together?
Are you trying to find out which move is the most accurate and will guarantee no disadvantage and improve your position as much as it can?
Actually, if you refer to the second question, then chess will not be fun anymore.
If each side cancels out each other's moves, it will be a draw repeatedly like tic tac toe games.
Of course, it could also be a game in which one position is always guaranteed to win.
It is actually a good question, I'll post a fuller answer later.
For the present, you say
Are you trying to find out which move is the most accurate and will guarantee no disadvantage and improve your position as much as it can?
No.
Accuracy is not generally required in chess. If you take forty nine moves to mate with king and queen against a king, the rules don't reward you any less than if you do it in the minimum number of moves (so long as you don't run out of time, but that, together with the tide, can wait till I post a fuller answer).
Also, you cannot make a move that theoretically improves your position; only your opponent can do that.
What do you really mean by solving chess?
Are you trying to solve it like a puzzle, putting the pieces together?
Are you trying to find out which move is the most accurate and will guarantee no disadvantage and improve your position as much as it can?
Actually, if you refer to the second question, then chess will not be fun anymore.
If each side cancels out each other's moves, it will be a draw repeatedly like tic tac toe games.
Of course, it could also be a game in which one position is always guaranteed to win.
It is actually a good question, I'll post a fuller answer later.
For the present, you say
Are you trying to find out which move is the most accurate and will guarantee no disadvantage and improve your position as much as it can?
No.
Accuracy is not generally required in chess. If you take forty nine moves to mate with king and queen against a king, the rules don't reward you any less than if you do it in the minimum number of moves (so long as you don't run out of time, but that, together with the tide, can wait till I post a fuller answer).
Also, you cannot make a move that theoretically improves your position; only your opponent can do that.
What if one side is guaranteed to win simply because of who moves first? Your last statement technically means that.
@SpaceVoidSuperEvil
If you're winning you can't be any better off whatever you move; if you have a move that wins that means you were already winning and if all moves leave you in the sh*t that means you're in the sh*t already.
If, as you postulate, one side is guaranteed to win simply because of who moves first, that's the first case.
But it's usually quite easy to theoretically improve your opponent's position. That's what practical chess is all about. Also in practical chess it is quite often possible to improve the perceived evaluation of your position by a move. That's because nobody's perceived evaluations of win draw or loss consistently match the theoretical evaluations (excepting @tygxc and @Optimissed, of course).
@4775
"What if one side is guaranteed to win simply because of who moves first?"
++ The extra tempo of the first move is worth 0.33 pawn and is not enough to win.
In a drawn position you have at least one good move that keeps the draw,
and errors (?) that turn the draw into a loss.
In a won position you have at least one good move that wins,
errors (?) that turn the win back to a draw,
and blunders or double errors (??) that turn the win into a loss.
@4775
"What if one side is guaranteed to win simply because of who moves first?"
++ The extra tempo of the first move is worth 0.33 pawn and is not enough to win.
Q: do engines ever evaluate a position that is winning as 0.33?
A: yes, certainly. Even in tiny samples you can find examples of where engines get it wrong, by losing from a position with evaluation 0.33 (or -0.33)
@4782
"Even in tiny samples you can find examples of where engines get it wrong, by losing from a position with evaluation 0.33 (or -0.33)"
++ Engines err, otherwise they would draw 100% and not 99%. Whenever an engine game from the initial position is decisive, it is a decisive game starting from +0.33. It is rare for an engine game to be decisive. That is why in TCEC they now impose slightly unbalanced openings, so as to start around +0.5 or -0.5.
@4775
"What if one side is guaranteed to win simply because of who moves first?"
++ The extra tempo of the first move is worth 0.33 pawn and is not enough to win.
Q: do engines ever evaluate a position that is winning as 0.33?
A: yes, certainly. Even in tiny samples you can find examples of where engines get it wrong, by losing from a position with evaluation 0.33 (or -0.33)
Not to mention drawing from a position with evaluation -25.5.
If you can't see why you were using inductive thinking, I suggest not to take your own word on the matter but to try to think about it for a year or two. Something might click. It may even take you longer.
Thanks for making me smile.
My statement was an example of a fundamental rule of logic. The general version is:
If (all things with property P have property Q) and (X has property P) then (X has property Q)
P was the set of finite deterministic games of perfect information, X was chess, and P was any chosen theorem about games of class P.
Am I right to give you the credit for being able to see this is deductive reasoning, not inductive reasoning?
That is because you're relying on the deductive part to carry you through but the deductive part is very simple and straightforward, seemingly indicating that your thinking is also simple and straightforward.
The important thing is that you're arguing from an ideal. That's basically something that you've constructed mentally but it doesn't mean that your syllogism is an accurate representation of the reality we're trying to discuss. You're only asserting that it is.
It ain't.
The game of basic chess is a mathematical object (indeed a finite, combinatorial object describable as a sort of directed graph of all legal positions), an example of a class of games about which there are theorems.
There is no approximation at all in the application of theorems of the theory of finite games. I feel you should be able to understand this.
is there a cheating happening here? cause i had disconnection problem several times specially when winning . .. blitz 5 mins
Yes. Somehow replaced it with a new response and didn't think it worth reinstating since you'd copied it anyway.
I think, after a moment's reflection, that you believe that you have the answer to everything. Even I don't try to teach you statistics but you try to teach me my subject.
I would put your IQ at around 145 to 155 at a guess. I have a good record of guessing these things. According to btickler, in a moment of honesty perhape, I got his within about 3 points. What I am trying to say is that you're used to being right. Used to being the cleverest in the bunch.
If you can't see why you were using inductive thinking, I suggest not to take your own word on the matter but to try to think about it for a year or two. Something might click. It may even take you longer.
Ummm, no. I posted it well beforehand, you forgot it later, then predicted it back to me (which I neither confirmed nor denied, by the way, 3pts or otherwise).
This is probably why you also believe you have psychic predictive powers.
@4763
"it doesn't matter"
++ It does matter. After chess is weakly solved, a human can memorise say 10,000 perfect games corresponding to a certain repertoire. Then that human would have a tremendous advantage over his peers.
It may also turn out possible to summarise the weak solution of chess into a set of say 1000 rules that can be memorised.
Allen has solved Connect Four by brute force,
but Allis independently solved it with a set of 7 rules.