You must imagine that you and Elroch are sources of knowledge!
That does *not* follow. Better take the whole exam over, you might not get a good score .
Do you mean that you admit you're not sources of knowledge? Does that mean that you don't know enough to be able to make a judgement??
Exam?? Dementia?
I have a very fundamental question that I'm not sure has been answered:
Given any position in a game, does there exist, for the player about to move, an "optimal" move, such that if he makes that move, he will have a certain path to at least a draw no matter what the opponent does?
I am not convinced that such a move exists. Obviously, you can talk about percentages and data bases, but here we're looking for certainty, and I don't think we've established that it exists.
In "any position", there is one or more optimal moves which allows the forcing of the optimal result against any counterstrategy. In some positions this optimal result is a win; in others, a draw (and in some, a loss, which means all moves are optimal in the pure sense).
In "any position", there is one or more optimal moves which allows the forcing of the optimal result against any counterstrategy. In some positions this is a draw, in some positions a win (and in some a loss, which means all moves are optimal in the pure sense).
I'm not convinced. You're making an assertion that I don't agree with, but you're offering no rationale.
If we were talking tic tac toe or checkers, we'd all agree there is an "optimal" move that assures at least a path to a draw. How do we know if this is true in chess?
Also, I'm not sure how you can have one "or more" optimal moves.
Just to demonstrate that @Optimissed's projection about those who contribute to Wikipedia was not accurate:
An example peer-reviewed paper about the non-trivial ultra-weak solution of a game in the same general class as chess, checkers, go etc.
Another peer-reviewed paper listing many important games that have been weakly solved and discussing the prospects for solving others.
A milestone paper, explaining how checkers had finally been weakly solved.
In "any position", there is one or more optimal moves which allows the forcing of the optimal result against any counterstrategy. In some positions this is a draw, in some positions a win (and in some a loss, which means all moves are optimal in the pure sense).
I'm not convinced. You're making an assertion that I don't agree with, but you're offering no rationale.
I didn't, but this is a theorem from the theory of finite games, so you can be absolutely sure it is true.
The proof is not trivial but is quite easy.
In "any position", there is one or more optimal moves which allows the forcing of the optimal result against any counterstrategy. In some positions this is a draw, in some positions a win (and in some a loss, which means all moves are optimal in the pure sense).
I'm not convinced. You're making an assertion that I don't agree with, but you're offering no rationale.
I didn't, but this is a theorem from the theory of finite games, so you can be absolutely sure it is true.
The proof is not trivial but is quite easy.
OK, I'm a bit out "over my skis" here, but what is the definition of a "finite game"?
Just to demonstrate that @Optimissed's projection about those who contribute to Wikipedia was not accurate:
An example peer-reviewed paper about the non-trivial ultra-weak solution of a game in the same general class as chess, checkers, go etc.
Another peer-reviewed paper listing many important games that have been weakly solved and discussing the prospects for solving others.
A milestone paper, explaining how checkers had finally been weakly solved.
Oh come on. I've mentioned before that my late brother was a long tome Wiki editor. He very much wanted to get me involved, probably to back him up on arguments with recidicivistic Wiki editors who did not know their subjects. My brother was an historian who also had a wide knowledge of languages, religions, Occult stuff and English Literature to name but a few of his fields of excellence.
Anyway, that's beside the point, which is that although Wiki has improved somewhat over the last 10 years, anyone who imagines that they will always find correct information there is naive beyond belief.
You seem to place great faith in peer revue. Whereas, of course, it's necessary to have checks and balances in acedemia, a peer revue can only pick up on obvious errors since someone's peer is unlikely to be a specialist in the field under consideration. So peer revue isn't and cannot be a guarantee of correctness.
Also you're spouting the same old stuff about weak and strong and I've already explained that it's perfectly obvious that you do not understand the application of Games Theory sufficiently to have any authority on the matter.
In "any position", there is one or more optimal moves which allows the forcing of the optimal result against any counterstrategy. In some positions this is a draw, in some positions a win (and in some a loss, which means all moves are optimal in the pure sense).
I'm not convinced. You're making an assertion that I don't agree with, but you're offering no rationale.
I didn't, but this is a theorem from the theory of finite games, so you can be absolutely sure it is true.
The proof is not trivial but is quite easy.
OK, I'm a bit out "over my skis" here, but what is the definition of a "finite game"?
He's trying to blind us with theory. A finite game is one that is not infinite. Thet is, it ends at some point and does not have an infinity of permutations or positions. Chess might as well be infinite, for all the possibility there is in tracing all the possible games.
<<I didn't, but this is a theorem from the theory of finite games, so you can be absolutely sure it is true.>>
I stopped accepting Elroch's judgement many years ago.
In "any position", there is one or more optimal moves which allows the forcing of the optimal result against any counterstrategy. In some positions this is a draw, in some positions a win (and in some a loss, which means all moves are optimal in the pure sense).
I'm not convinced. You're making an assertion that I don't agree with, but you're offering no rationale.
I didn't, but this is a theorem from the theory of finite games, so you can be absolutely sure it is true.
The proof is not trivial but is quite easy.
OK, I'm a bit out "over my skis" here, but what is the definition of a "finite game"?
A finite two player game is where there are two players, they move alternately, there are a finite number of alternatives at each move and every game ends in a finite number of moves. An example of a game that fails to meet the definition would be noughts and crosses on an infinite plane. Chess only meets the definition if you assume draws are forced by the 50 move rule or a repetition, rather than needing to be claimed.
[Also, I don't think my adjective "easy" was really appropriate. Rather it is a concise proof!].
In "any position", there is one or more optimal moves which allows the forcing of the optimal result against any counterstrategy. In some positions this is a draw, in some positions a win (and in some a loss, which means all moves are optimal in the pure sense).
I'm not convinced. You're making an assertion that I don't agree with, but you're offering no rationale.
I didn't, but this is a theorem from the theory of finite games, so you can be absolutely sure it is true.
The proof is not trivial but is quite easy.
OK, I'm a bit out "over my skis" here, but what is the definition of a "finite game"?
A finite two player game is where there are two players, they move alternately, there are a finite number of alternatives at each move and every game ends in a finite number of moves. An example of a game that fails to meet the definition would be noughts and crosses on an infinite plane. Chess only meets the definition if you assume draws are forced by the 50 move rule or a repetition, rather than needing to be claimed.
[Also, I don't think my adjective "easy" was really appropriate. Rather it is a concise proof!].
What if there were two players and they each had two moves alternately?
Do you mean that you admit you're not sources of knowledge? Does that mean that you don't know enough to be able to make a judgement??
Exam?? Dementia?
Lol, when you don't like your test results you just take the test over and over until you do...I would have expected you to pick up on that.
I have not much idea of what you're rabbitting on about unless it's inspired by jealousy regarding something or other.
Kennel!!
Come to think of it, I know you seem to have obsessive-compulsive disorder and it may be that you're talking about the IQ tests I did years ago. It's the second time you've mentioned "tests" in a couple of days and I haven't taken any Covid tests. I was a Wolf Cub, for a while and we had to take tests to get badges but I doubt it's that. Must be the IQ thing you're still obsessing over.
I have not much idea of what you're rabbitting on about unless it's inspired by jealousy regarding something or other.
Kennel!!
I was not addressing the general "you", but the specific you.
If you still don't get it, I don't know what to tell you, it's your own past anecdote I'm referring to.
When I was 9, my IQ was officially tested by the county education people, as was everyone else's. I was told I had scored the second highest result **ever** in the county but they wouldn't give me the exact score. All they would tell me was "over 140" and I knew that already. It was bound to be a long way North of that but by how much? So I didn't have an official result, unless we can discover the third highest score ever in 1960 and it's higher than that. Otherwise, can't help you further regarding the one official test result.
That's why I did the battery of Eysenck tests under exam conditions, when I was recovering from infectious hepatitis in 1977. I scored either four or five 169s but never made 170, so my dad beat me by two points.
But then I had been extremely ill. Does that help? I was taught always to behave in a kindly fashion towards obsessives, because it's partly the result of insecurity.
I could fly to Pluto in five years if I had the money and three chess grandmasters to help. Nobody will believe me. How come tygxc believes Sveshnikov?