Although the chess.com engine prefers Nxa6, I'm pretty sure that black wins quicker after 2. ...ba and therefore that is the stronger capture for black.
We'll find out when @tygxc solves chess.
Um, sorry scratch that - he's not going to solve that bit.
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.
Although the chess.com engine prefers Nxa6, I'm pretty sure that black wins quicker after 2. ...ba and therefore that is the stronger capture for black.
We'll find out when @tygxc solves chess.
Um, sorry scratch that - he's not going to solve that bit.
I think that logically ba should win quicker for black than Nxa6 because it opens a file and a diagonal and the Nb8 remains nearer the centre. When I played it through against the onboard engine, I captured with the pawn.
@5312
3...Ke7?? is a blunder, turns a won position into a lost position.
You overlooked it again.
Incidentally no show yet for your calculation of the theoretical result and error rates in my games here. Are you still working on it?
But quicker is not perfecter.
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.
But quicker is not perfecter.
It might be. Unless you enjoy the hunt more than the kill.
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.
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.