In any case, even in the hypothetical unreality that 2. Ba6 is winning for white, the Ke7 move would still be a blunder, since no-one would find the win. Possibly not even the strongest computer.
I found it.
To be quite honest, you may not have played black's strongest line.
In any case, even in the hypothetical unreality that 2. Ba6 is winning for white, the Ke7 move would still be a blunder, since no-one would find the win. Possibly not even the strongest computer.
You should be aware that you are engaged in a semantic disagreement. You are using the word "blunder" for an imprecise notion relating to practical chess while, in the post replied to, the word "blunder" was used for the precise theoretical concept of a move that changes the final result with optimal play thereafter.
On a very general (and very important) point, it is remarkable how often people are not fully aware whether they are debating about the truth of an objective fact or having a disagreement about the use of a label (such as "blunder" here). I am not asserting that you are not in this case.
In any case, even in the hypothetical unreality that 2. Ba6 is winning for white, the Ke7 move would still be a blunder, since no-one would find the win. Possibly not even the strongest computer.
You should be aware that this is a semantic disagreement, with you using the word "blunder" for an imprecise notion relating to practical chess, while in the post replied to, the word "blunder" was used for the precise theoretical concept of a move that changes the final result with optimal play thereafter.
On a very general (and very important) point, it is remarkable how often people are not fully aware whether they are debating about the truth of an objective fact or having a disagreement about the use of a label (such as "blunder" here). I am not asserting that you are not in this case.
You're weird. After all this time, you fail to understand that I understand it at least as well as you do. The sort of comment you make does amount to trolling, after all, since you're aware that people may exist who may not have the wit to understand what you're doing .... which is laying constant false trails. But it will make you look a bit thick, in the eyes of people who are aware that I have made a number of comments in my posts, over time, about exactly what you're confirming. You are a bit like a pianist, playing on on a sinking ship, you know.
Ke7 is very probably a blunder, except technically in the unlikely (but not logically impossible) case that the Ba6 sacrifice is winning. Even I find it difficult to be pedantic about this, but I am epistemologically obliged to be.
In your personal interpretation of epistemological obligation. If it is your belief that there's genuine doubt about the outcome of 2. Ba6, then of course it follows.
No personal interpretation involved. I have explained how the valid forms of reasoning available do not justify certainty. Some here understand this, but not all. It is a philosophically important difference but, for the man in the street, inappropriate certainty is generally pragmatically fine.
Your personal interpretation may be that no personal interpretation is involved. I know you've explained but your statement about justification of certainty depends on your personal application of relevant priorities. It cannot be an absolute and neither can you prove it true, except from axioms which can easily be challenged. Pseudo-axioms, one might call them.
I was also going to explain why game theory cannot apply to the solving of chess... [snip]
Go on, give us a treat. Perhaps afterwards you can explain why number theory does not apply to the number 213276247234766621.
I think @Optimissed might be right this time.
Under FIDE laws possible yields include but are arguably not restricted to (win,loss), (loss,win), (draw,draw), (win+draw,loss+draw), (loss+draw,win+draw), (win,win), (win+draw,win+draw) and (arbiter determined) without any ordering specified. The objective is checkmate but that cannot be forced except from positions that are already checkmate.
What part of game theory would apply?
Still thinking about 213276247234766621; don't tell me. It's not prime nor (I think) a recognisable Carmichael number, but it has fewer factors than you'd expect.
I'm very often right. I wouldn't say "all the time" though. However, I hesitate to explain why game theory is irrelevant here. Elroch won't understand and he'll probably be unpleasant as usual, instead of trying to understand it. If you don't even have the intelligence to try to ask relevant questions, but you just blunder about laying down the law as he usually does, that isn't an aid to learning. I'm still learning at 71 but not him at maybe 10 to 15 years younger.
I'll give a hint, however. When playing chess, the object is to achieve the best result you can and it isn't often necessary or even desirable to find the best moves. Therefore a player will often make moves according to a subjectively assessed probability, which will not be entirely accurate. Game theory can be applied here, although it would obviously be laborious and time-consuming, by formulating strategies to find moves based on a number of priorities, some of which will be subjective and probabilistic.
This is now the bit that Elroch won't understand. I don't think he will see the difference between playing and solving wrt the application of probabilities.
I think, rather, he will assume you're still learning (at age 71) but don't yet know what you're talking about.
I think, rather, he will assume you're still learning (at age 71) but don't yet know what you're talking about.
It's absolutely true, though, and it happens when I talk to people on this thread. It's a case of having to work out wtf they're talking about and whether it's their ego, their anger or what little's left of their brains that's directing them. And then trying to translate in the light of my surmises regarding their intentions, which isn't a very bright or beckoning light. One or two people excepted, of course.
But I can very clearly see that game theory isn't applicable to solving chess, as he assumes it is and apparently so do the World's leading intellectual human lanterns. At least those who are engaged in trying to work out strategies to solve chess, since the only strategy available is to find the best moves and then a few others which might be good.
I was also going to explain why game theory cannot apply to the solving of chess... [snip]
Go on, give us a treat. Perhaps afterwards you can explain why number theory does not apply to the number 213276247234766621.
I think @Optimissed might be right this time.
Under FIDE laws possible yields include but are arguably not restricted to (win,loss), (loss,win), (draw,draw), (win+draw,loss+draw), (loss+draw,win+draw), (win,win), (win+draw,win+draw) and (arbiter determined) without any ordering specified. The objective is checkmate but that cannot be forced except from positions that are already checkmate.
What part of game theory would apply?
Still thinking about 213276247234766621; don't tell me. It's not prime but it has abnormally few factors.
While I understand that you are being light-hearted, you understand that "solving chess" refers unambiguously to the abstract game of chess (or, to be precise, a version of it defined by the relevant rule set), which has no time limits, nothing happening off the board, but may include well-defined rules such as the option (or obligation) to claim a draw in an n-times repeated position, or when the 50 move rule applies.
No arbiters ever the chance to get involved any more than they do in the solution of tic-tac-toe - the only laws involved are those that govern legal moving and results.
If I recall, the only appeal to game theory that has taken place in this forum was to a general theorem that applies to a class of games to which chess belongs. Given the definitions:
then there exists an optimal strategy for each side and these strategies achieve the same result.
I'd like this theorem to be trivial, but when trying to show it was, I convinced myself it is not quite! The theorem seems to rely on the fact that every game is finite, for example.
He's being serious, since the result can't be quantified in between the win/draw/loss. Therefore it can't be scored on the probabilistic outcome basis that game theory uses. Anyway, it can be assumed that he has intelligence and an intelligent person who can USE it well will be in agreement with me.
As I explained, GT can be applied to the playing of chess but not to the solving, since the playing more/less goes from move to move and the moves can be chosen on the basis that if enough traps are set, the opponent will fall into one.
Game theory does not deal with probabilistic outcomes in games like chess (deterministic, perfect information).
Tablebase results are discrete.
Perfect play can be clearly defined in a tablebase.
This is true for a (hypothetical) 32-piece tablebase.
(The only place probabilities have arisen here is as states of belief for unresolved propositions).
I was also going to explain why game theory cannot apply to the solving of chess... [snip]
Go on, give us a treat. Perhaps afterwards you can explain why number theory does not apply to the number 213276247234766621.
I think @Optimissed might be right this time.
Under FIDE laws possible yields include but are arguably not restricted to (win,loss), (loss,win), (draw,draw), (win+draw,loss+draw), (loss+draw,win+draw), (win,win), (win+draw,win+draw) and (arbiter determined) without any ordering specified. The objective is checkmate but that cannot be forced except from positions that are already checkmate.
What part of game theory would apply?
Still thinking about 213276247234766621; don't tell me. It's not prime but it has abnormally few factors.
While I understand that you are being light-hearted, you understand that "solving chess" refers unambiguously to the abstract game of chess (or, to be precise, a version of it defined by the relevant rule set), which has no time limits, nothing happening off the board, but may include well-defined rules such as the option (or obligation) to claim a draw in an n-times repeated position, or when the 50 move rule applies.
No arbiters ever the chance to get involved any more than they do in the solution of tic-tac-toe - the only laws involved are those that govern legal moving and results.
Yes and no. What are the abstract rules? The complexity of solving one set of abstract rules may be very different from another, so it seems to me that question needs to be addressed before commenting on OP's question.
It could be that an abstract game based on basic rules will eventually be solved by human ingenuity while an abstract game based on competition rules proves too difficult.
And if you plan to use a GUI/Stockfish combination in solving, you do have an arbiter; it's the GUI. You also have a concrete set of rules.
I was also going to explain why game theory cannot apply to the solving of chess... [snip]
Go on, give us a treat. Perhaps afterwards you can explain why number theory does not apply to the number 213276247234766621.
I think @Optimissed might be right this time.
Under FIDE laws possible yields include but are arguably not restricted to (win,loss), (loss,win), (draw,draw), (win+draw,loss+draw), (loss+draw,win+draw), (win,win), (win+draw,win+draw) and (arbiter determined) without any ordering specified. The objective is checkmate but that cannot be forced except from positions that are already checkmate.
What part of game theory would apply?
Still thinking about 213276247234766621; don't tell me. It's not prime but it has abnormally few factors.
While I understand that you are being light-hearted, you understand that "solving chess" refers unambiguously to the abstract game of chess (or, to be precise, a version of it defined by the relevant rule set), which has no time limits, nothing happening off the board, but may include well-defined rules such as the option (or obligation) to claim a draw in an n-times repeated position, or when the 50 move rule applies.
No arbiters ever the chance to get involved any more than they do in the solution of tic-tac-toe - the only laws involved are those that govern legal moving and results.
Yes and no. What are the abstract rules?
Correct. We have discussed the difference in this problem for various rule sets.
The complexity of solving one set of abstract rules may be very different from another, so it seems to me that question needs to be addressed before commenting on OP's question.
The first point is true. I have referred to a relatively simple version of chess which has a 50 move rule and no 3-fold repetition rule. This is the least complex (using FEN positions which are only moderately more numerous (factor of 50) than basic chess. I have also discussed the huge state space of chess with a repetition rule but argued that this can be sidestepped for the purpose of solution as optimal strategies with basic chess rules only repeat positions when they are not trying to win).
It could be argued that there is a simpler purely abstract version of chess with no 50 move rule or repetition rule where games can be infinite and an infinite game is a draw. This is slightly less complex as the half-move count can be omitted from the state space. Of course, the lack of a 50 move rule may change the optimality of strategies, but I confidently believe (without proof) there are single strategies that are optimal for this version and the two others.
It could be that an abstract game based on basic rules will eventually be solved by human ingenuity while an abstract game based on competition rules proves too difficult.
I believe not for the reasons expressed above.
And if you plan to use a GUI/Stockfish combination in solving, you do have an arbiter; it's the GUI. You also have a concrete set of rules.
But do you have a point? 
[And why would you think I would do that??]
Game theory does not deal with probabilistic outcomes in games like chess (deterministic, perfect information).
Tablebase results are discrete.
Perfect play can be clearly defined in a tablebase.
This is true for a (hypothetical) 32-piece tablebase.
(The only place probabilities have arisen here is as states of belief for unresolved propositions).
You're not following, as usual.
It seems as though you don't know what game theory is.
Game theory uses a simplified model of an RLS (real life situation) of which chess may be considered to be one. It explores strategies of dealing with the situation by scoring outcomes.
Logically, if an RLS isn't probabilistic and the information display is perfect, game theory is not required since outcomes can be worked out logically. Chess displays full information but not in a way that can be used. If it could be used easily, we wouldn't need to solve it. But the existing, full information display is insufficient to calculate the outcomes except by the method of solving we're discussing.
Nevertheless, we know that chess has a fixed outcome with best play. It is either a draw or a win for either side and it only remains to discover what best play is. It follows that the only way of discovering best play is by analysing all moves in reply to all moves with the intention of revealing a set of game trees to be considered as best or optimum play. Obviously, the game tree will be huge but since probability only applies to playing, rather than to solving, as already explained, and since game theory uses a simplified model of an RLS and since such a simplified model of chess is impossible without producing the very inaccuracies we are trying to avoid, then GT does not apply to the solving of chess and the various experts you are relying on are in error.
It's really rather simple but you, Elroch, can't follow it because you don't like being out-argued by a lay person, irrespective that I'm far more intelligent than you are. And I don't apologise for reiterating that because your behaviour in this discussion has been extremely poor in general. You have tried every dishonest trick you can find to avoid the spectacle of losing an argument and no doubt that will continue. But you have failed to reply to the arguments.
Due to the fact that you are completely out of your depth.
But quicker is not perfecter.
It might be. Unless you enjoy the hunt more than the kill.