@4956
"I find it quite easy."
++ I am speaking of middlegame positions of around 26 men, where most positions are.
...
So what are you proposing to solve? Chess or most middlegame positions?
There is no solution that involves two-fold repetitions being involved on the path to anywhere but a draw.
It is like in real play. A player fishing for a solution gets to a two-fold repetition and realises he needs to change his strategy from that point. When the strategies are final, this no longer occurs - two strategies that reach a two-fold repetition will reach an n-fold repetition because they are fixed.
@4960
"We have requested a detailed description of what he proposes"
++ I have explained this before.
Take an ICCF WC Finals drawn game e.g. this one.
https://www.iccf.com/game?id=1164259
It begins from the initial position and it ends in a known drawn endgame.
Take the last move 35 Be3. Look at the top 3 alternatives. Do they draw too?
Now look at 34 a5. Look at the top 3 alternatives. Do they draw too?
Now look at 33 a4. Look at the top 3 alternatives. Do they draw too?
Now look at 32 Kf2. Look at the top 3 alternatives. Do they draw too?
...
Like that all the way down until another ICCF WC finals drawn game is reached.
Throughout this thread, some have mistakenly considered extremely large finite numbers to be the equivalent of infinity....."for all practical purposes". This is a mistake. No matter how large a finite number is, it is not the equivalent of infinity....or even close.... period. And any logic or conclusions that follow that assumption are false.
You don't get any large finite numbers, they're all completely miniscule compared with practically all the rest. Come to that you don't get any large infinite numbers either.
Well, some infinite numbers (let's presume that means "cardinals" in this context) are large compared with a lot of other infinite numbers. So they can be considered large in the same way as a googol is often viewed as a large integer.
A major example would be a (strongly or weakly) inaccessible cardinal). Any inaccessible cardinal is bigger than any cardinal whose existence is provable in ZFC!
ZFC itself does not imply the existence of an inaccessible cardinal. The existence of one implies the consistency of ZFC, which itself implies that it cannot be proven that the existence of a large cardinal is consistent with ZFC (most mathematicians believe it is)).
That the linked article includes the phrase " Therefore, inaccessible cardinals are a type of large cardinal" and there is a page on said large cardinals shows mathematicians are not averse to the idea of large infinite numbers. Worse, it turns out that there is a whole litany of distinct ways in which cardinals can be large!
Yes, but they're only called large because of definitions. It's still the case that the larger they get the more minuscule (got it right this time) they get compared with almost all the rest.
@4961
"So what are you proposing to solve? Chess or most middlegame positions?"
++ Chess, but the vast majority of chess positions is around 26 men.
32 men: 1.89 × 10^33
31 men: 1.71 × 10^34
30 men: 1.64 × 10^35
29 men: 1.53 × 10^36
28 men: 5.46 × 10^36
27 men: 1.05 × 10^37
26 men: 1.08 × 10^37
25 men: 6.14 × 10^36
24 men: 3.19 × 10^36
23 men: 5.66 × 10^35
Yes. But it's worth remembering that whether these cardinals exist is not a given. You can do almost all of mathematics with ZFC set theory. The first inaccessible cardinal is bigger than all the cardinals that can be proven to exist in this model of mathematics: it has to be added via another axiom.
It is not provable that the existence of this cardinal is consistent with ZFC (but it is believed to be, like it is independently believed that ZFC is consistent).
@4966
This thread is about solving chess, not about transfinite numbers or the continuum hypothesis.
@4966
This thread is about solving chess, not about transfinite numbers or the continuum hypothesis.
But none of your posts are relevant to solving chess either.
@4969
"none of your posts are relevant to solving chess either"
++ I beg your pardon. All of my posts are relevant to solving chess.
I have calculated how long it takes to weakly solve chess: 5 years. I have shown how to do it.
Others troll with off topic.
@4960
"We have requested a detailed description of what he proposes"
++ I have explained this before.
Take an ICCF WC Finals drawn game e.g. this one.
https://www.iccf.com/game?id=1164259
It begins from the initial position and it ends in a known drawn endgame.
Take the last move 35 Be3. Look at the top 3 alternatives. Do they draw too?
Now look at 34 a5. Look at the top 3 alternatives. Do they draw too?
Now look at 33 a4. Look at the top 3 alternatives. Do they draw too?
Now look at 32 Kf2. Look at the top 3 alternatives. Do they draw too?
...
Like that all the way down until another ICCF WC finals drawn game is reached.
Yes. It doesn't work.
There's no output strategy for a start, which according to any of your posted definitions of "weakly solve" is the whole aim of the exercise.
When you get to "Look at the top 3 alternatives" there's nothing to say how you determine what they are.
When you look for the sub function "Do they draw too?" it isn't there.
No mention of a computer, so what are the cloud cuckoo computers all about?
Not much point in going any further, it's a joke.
@4973
"There's no output strategy" ++ The output are the 3 alternative lines per white move.
"there's nothing to say how you determine what they are"
++ The top 4 moves of the cloud engine running for 17 s, (or a desktop running for 4.7 h). As previously shown the real good move is always among the top 4 moves with 1 error in 10^20.
"When you look for the sub function "Do they draw too?" it isn't there."
++ Either a table base draw, or a 3 fold repetition, or a humanly known draw, adjudicated by the good assistants.
"No mention of a computer" ++ Of course the 3 computers serve to do that. 1 computer looks at 1 e4, 1 computer at 1 d4, and a 3rd computer at 1 c4 and 1 Nf3 lines that do not transpose.
There is no solution that involves two-fold repetitions being involved on the path to anywhere but a draw.
It is like in real play. A player fishing for a solution gets to a two-fold repetition and realises he needs to change his strategy from that point. When the strategies are final, this no longer occurs - two strategies that reach a two-fold repetition will reach an n-fold repetition because they are fixed.
Perfectly understood.
But a solution is not the same as a process for finding a solution. The tablebase approach avoids any problems by associating any position with on ordered pair (b,n) where b is a basic rules position and n is an increasing distance from some objective and never repeating a "b".
SF doesn't. It happily moves into repeated positions whether it evaluates its position as positive or otherwise and whether it is actually winning or otherwise (which it doesn't know). So a process for solving chess using SF with a twofold repetition rule would not produce the same results as a process using a threefold repetition rule. The GUI is arbiter and would terminate games under a twofold repetition rule that would continue under a threefold repetition rule. SF has a triple rule avoidance routine that will fire in many circumstances.
@4976
"SF has a triple rule avoidance routine that will fire in many circumstances."
++ Yes that is right. It might be modified to 2-fold. It may also be left 3-fold, when some 2-fold repetitions may get into the lines, but that does not harm.
"Extrapolation"? Not a concept that seems to fit in here.
That's because you believe that all other people's inductive reasoning is inductive but that most of your inductive reasoning is deductive. You don't seem to understand the difference. This is taken from page 4, this January, post #79 in reply to my post #77. At the time, it was less clear that you don't know the difference.
Or, if you do, your interpretation of your own inductive thinking as deductive is notable.
@4960
"We have requested a detailed description of what he proposes"
++ I have explained this before.
Take an ICCF WC Finals drawn game e.g. this one.
https://www.iccf.com/game?id=1164259
It begins from the initial position and it ends in a known drawn endgame.
Take the last move 35 Be3. Look at the top 3 alternatives. Do they draw too?
Now look at 34 a5. Look at the top 3 alternatives. Do they draw too?
Now look at 33 a4. Look at the top 3 alternatives. Do they draw too?
Now look at 32 Kf2. Look at the top 3 alternatives. Do they draw too?
...
Like that all the way down until another ICCF WC finals drawn game is reached.
Yes. It doesn't work.
There's no output strategy for a start, which according to any of your posted definitions of "weakly solve" is the whole aim of the exercise.
When you get to "Look at the top 3 alternatives" there's nothing to say how you determine what they are.
When you look for the sub function "Do they draw too?" it isn't there.
No mention of a computer, so what are the cloud cuckoo computers all about?
Not much point in going any further, it's a joke.
The entire idea of strategy as applied here and in those definitions is incorrect and "strategy" is referred to because it seems classy and also it refers to the definitions and seems to support them.
"A different move" is the non-obfuscatory way to refer to the procedure, not that anyone here, who is on the wrong side of a discussion, is interested in being non-obfuscatory.
@4973
"There's no output strategy" ++ The output are the 3 alternative lines per white move.
Which is not a strategy, so according to your definition(s) not a solution. What is it exactly that you are posting?
"there's nothing to say how you determine what they are"
++ The top 4 moves of the cloud engine running for 17 s, (or a desktop running for 4.7 h).-Which? It could affect any timescale.-As previously shown the real good move is always among the top 4 moves with 1 error in 10^20.
Well you didn't say that. When are you going to produce a usable description of your method?
But cloud engines don't produce moves; you need software, e.g. an engine and a GUI. And which cloud computer anyway?
When you say "previously shown" were you referring to my post here (I reproduce the screenshot) or one of the other half dozen examples I posted where SF blows half a point with all its top 4 moves?
"When you look for the sub function "Do they draw too?" it isn't there."
++ Either a table base draw, or a 3 fold repetition, or a humanly known draw, adjudicated by the good assistants.
Well you didn't say that. When are you going to produce a usable description of your method?
You don't appear to have fixed which ICCF game we're talking about yet, you say, "Take an ICCF WC Finals drawn game e.g. this one. [my italics]
https://www.iccf.com/game?id=1164259".
When do you expect to decide on a definite first step? Will that be within five years?
But mainly you say, "do they draw too?". Your example appears to be an agreed draw, so the alternatives will draw too if you assume an agreed draw will follow. Are you just intending to prove that any moves will draw if a draw is agreed? I think you should be able to do that without too much investment.
"No mention of a computer" ++ Of course the 3 computers serve to do that. 1 computer looks at 1 e4, 1 computer at 1 d4, and a 3rd computer at 1 c4 and 1 Nf3 lines that do not transpose.
The last 3 are going to be a bit stuck if they're trying to follow your explanations with the example game you've given. And I could have sworn White has more first moves.
@4960
"We have requested a detailed description of what he proposes"
++ I have explained this before.
Take an ICCF WC Finals drawn game e.g. this one.
https://www.iccf.com/game?id=1164259
It begins from the initial position and it ends in a known drawn endgame.
Take the last move 35 Be3. Look at the top 3 alternatives. Do they draw too?
Now look at 34 a5. Look at the top 3 alternatives. Do they draw too?
Now look at 33 a4. Look at the top 3 alternatives. Do they draw too?
Now look at 32 Kf2. Look at the top 3 alternatives. Do they draw too?
...
Like that all the way down until another ICCF WC finals drawn game is reached.
Yes. It doesn't work.
There's no output strategy for a start, which according to any of your posted definitions of "weakly solve" is the whole aim of the exercise.
When you get to "Look at the top 3 alternatives" there's nothing to say how you determine what they are.
When you look for the sub function "Do they draw too?" it isn't there.
No mention of a computer, so what are the cloud cuckoo computers all about?
Not much point in going any further, it's a joke.
The entire idea of strategy as applied here and in those definitions is incorrect and "strategy" is referred to because it seems classy and also it refers to the definitions and seems to support them.
"A different move" is the non-obfuscatory way to refer to the procedure, not that anyone here, who is on the wrong side of a discussion, is interested in being non-obfuscatory.
A model of clarity I must say. How the hell can "a different move" refer to a procedure?
I'm using the word "strategy" because that's exactly the word that @tygxc has used in his definitions. I don't have any problem with the word; try a dictionary.
@4960
"We have requested a detailed description of what he proposes"
++ I have explained this before.
Take an ICCF WC Finals drawn game e.g. this one.
https://www.iccf.com/game?id=1164259
It begins from the initial position and it ends in a known drawn endgame.
Take the last move 35 Be3. Look at the top 3 alternatives. Do they draw too?
Now look at 34 a5. Look at the top 3 alternatives. Do they draw too?
Now look at 33 a4. Look at the top 3 alternatives. Do they draw too?
Now look at 32 Kf2. Look at the top 3 alternatives. Do they draw too?
...
Like that all the way down until another ICCF WC finals drawn game is reached.
Yes. It doesn't work.
There's no output strategy for a start, which according to any of your posted definitions of "weakly solve" is the whole aim of the exercise.
When you get to "Look at the top 3 alternatives" there's nothing to say how you determine what they are.
When you look for the sub function "Do they draw too?" it isn't there.
No mention of a computer, so what are the cloud cuckoo computers all about?
Not much point in going any further, it's a joke.
The entire idea of strategy as applied here and in those definitions is incorrect and "strategy" is referred to because it seems classy and also it refers to the definitions and seems to support them.
"A different move" is the non-obfuscatory way to refer to the procedure, not that anyone here, who is on the wrong side of a discussion, is interested in being non-obfuscatory.
A model of clarity I must say. How the hell can "a different move" refer to a procedure?
I'm using the word "strategy" because that's exact the word that @tygxc has used in his definitions. I don't have any problem with the word; try a dictionary.
I can't help it if you aren't great at English.
Intuitively solving chess with 2-fold repetition draw is equivalent to solving it with 3-fold repetition.
Not true.
A solution of chess with 2-fold repetition draw is equivalent to a solution with 3-fold repetition, but whether solving the two are equivalent depends on the method of solution.
So far as @tygxc's method is concerned the latter equiivalence would appear not to hold. We have requested a detailed description of what he proposes, but I doubt if he can manage to produce one in five years.