A move which can be seen to change the result by half a point deserves "??" for a sufficiently strong player. Check with any GM.
The eccentric view that blunders only occur from winning positions rather than drawing ones is a random obfuscation by you.
Huebner points out that from a detached viewpoint there are no brilliant moves, merely correct ones, since no move positively changes the theoretical result.
By contrast, blunders do exist.
@6310
https://www.iccf.com/event?id=85042
136 games = 119 draws + 17 decisive games.
Assume chess a win.
Fit a Poisson distribution with 119 / 136 probability of an odd number of errors / game.
It is impossible, thus Chess is a draw.
Fit a Poisson distribution with 17 / 136 probability of an odd number of errors / game.
It is possible with average 0.143 error / game.
Games with 0 errors: 118
Games with 1 error: 17
Games with 2 errors: 1
Notice there is an anomaly in the games of SIM Bock, Steffen.
Strike the 16 games of SIM Bock Steffen.
120 games = 116 draws + 4 decisive games
Assume Chess a win, it is impossible to fit a Poisson distribution of errors / game with 116 / 120 probability of an odd number of errors / game. Thus Chess is a draw.
Fit a Poisson distribution with 4 / 120 probability of an odd number of errors / game.
It is possible with average 0.0345 error / game, i.e. 1 error / 29 games
Games with 0 errors: 116
Games with 1 error: 4
The above game is 96.6% certain to be an optimal game without any error by either side.
This misses most of the detail in the calculation, and is:
(1) Taken from games that are played under different rules from the nebulous game you offer to solve.
(2) Not played by the vehicle (Stockfish, version yet to be documented) you say you plan to use.
(3) From a position where none of the results can be reliably checked.
(4) Verifiably wrong in numerous positions that can be checked from tablebases.
It's based on the assumption that the occurrence of blunders in a game is a Poisson process. So you're postulating e.g. that SF? will make as many blunders in KNNvKP positions (where it normally blunders) as in KRvK positions (where it normally doesn't).
Moreover the material on the board enters nowhere into your "reasoning", so it should apply irrespective of material. Your assumption is also that the probability of a second half point blunder in any position is the same as the first, so unless you're asserting that only full point blunders occur (which invalidates your Poisson process assumption straight away) your reasoning should apply equally to drawn or winning positions.
For the above reasons I have posted some games (reproduced below) where your "calculation" can be checked against perfect play by reference to tablebases and invited you to apply your calculations to those games. I've added the blunders both with and without the 50 move (resp. CRblunder and BRblunder) in the last game to start you off.
You've been pretending not to notice the first set for the best part of a year and you've been pretending not to notice the rest for at least the last dozen pages, though I've reminded you several times.
I'm inclined to guess, possibly unkindly, that you've already tried and failed to get your calculations to work in these positions, but having convinced yourself that your proposed "solution" is a non-starter, are ignoring these reminders because you just get a perverted pleasure from posting as much misinformation as you can on the internet.
You can prove that guess wrong by either successfully showing that your calculation works in those games or acknowledging that you've been posting so much BS and ceasing to plug your "solution". I challenge you to do one or other.
If you disregard the terminology...... obviously there are many kinds and degrees of mistakes, referred to as blunders in chess. Are we suggesting that all mistakes are equal, or can we say, "Although a blunder is a blunder is a blunder, and they all make the forced result worse for the blunderer, there are degrees. Some blunders change a win to a draw, some change a draw to a loss, and some change a win to a loss." So, tygxc's differentiation kind of makes sense to me.....even though I don't see those definitions as pertinent to whether chess can be solved.
@6332
"solving chess is purely mathematical" ++ Agree
"with zero consideration of such things as confidence levels or statistical treatments"
++ Solving itself is different from arguments about it.
"If someone solves chess to the point of being 99.99% confident" ++ The proposed method makes 1 error in 10^20 positions, while there are only 10^17 relevant positions.
@6337
"tygxc's differentiation kind of makes sense to me" ++ Of course it makes sense, it is the only sensible definition. It is not even mine, it stems from GM Dr. Hübner.
"I don't see those definitions as pertinent to whether chess can be solved"
++ Chess can be weakly solved, the question is in what time. In the arguments about that it is pertinent to define error. The definition calls for both players to play optimally. Playing optimally is play without error.
...
I'm inclined to guess, possibly unkindly, that you've already tried and failed to get your calculations to work in these positions, but having convinced yourself that your proposed "solution" is a non-starter, are ignoring these reminders because you just get a perverted pleasure from posting as much misinformation as you can on the internet.
You can prove that guess wrong by either successfully showing that your calculation works in those games or acknowledging that you've been posting so much BS and ceasing to plug your "solution". I challenge you to do one or other.
@tygxc hello... hello... hello... hello...hello...hello... hello... ...
...
...
...
...
Then, silence. Some fancied they heard in the air
A weary and wandering sigh
That resembled a sum but the others declare
It was only a breeze that went by.
I'm just suggesting that there are different degrees of blunders, so I don't have a problem, per se, with tygxc's differentiation of them.
But a true solution of chess would treat all blunders the same......i.e. avoidance.
I'm just suggesting that there are different degrees of blunders, so I don't have a problem, per se, with tygxc's differentiation of them.
But a true solution of chess would treat all blunders the same......i.e. avoidance.
Wrong
I'm just suggesting that there are different degrees of blunders, so I don't have a problem, per se, with tygxc's differentiation of them.
But a true solution of chess would treat all blunders the same......i.e. avoidance.
There's nothing wrong with @tygxc's differentiation between errors that change a theoretical win into a theoretical loss and errors that either change a theoretical draw into a theoretical loss or a theoretical win into a theoretical draw.
There is a problem with his terminology, exactly as @Elroch points out here.
A practical consequence is that I have in the past been using the term "error" to mean "half point blunder" and "blunder" to mean "full point blunder" when responding to @tygxc and reverting to standard in other responses. This is likely to cause confusion all round, so I've lately reverted to standard in some of my responses to @tygxc - no doubt causing even more confusion.
@tygxc is, I would judge, unlikely to change his terminology, so the best thing is probably to ignore his posts altogether. I would say he has comprehensively demonstrated that he is deliberately trolling.
So I would suggest that all should use the terms "half point blunder" and "full point blunder" in the sense generally used by game theorists, to avoid talking at cross purposes.
Note that the terms represent different moves depending on whether the 50 move and 3-fold repetition rule are in force or not. In the first set of games (KNNvKP) that I posted for @tygxc, SF made 30 basic rules blunders and 28 blunders with the rules in force, but only 4 of those were blunders in both games. Similarly in the last game that I annotated there were 2 blunders with the rules in force and 1 without that was neither of those.
The degrees of blunder you mention certainly bear examination and I'll come back to that, but if they're not actually theoretical blunders I think we should refer to them as errors of varying severity. The level of severity very much depends on the level of play.
E.g. In this game the analysis gives me
Moves 68B (the unique most accurate move) and 72W are flagged as blunders. These are not blunders at the level of Javitotwit, newbie4711, Syzygy or Nalimov, but they are blunders at the level of Coach (with my subscription).
@Optimissed, I know Contact has pi in it, but this was way too late and not consistent with my memory! It has to be a novel published by the mid-1970s.
I think you are thinking of a Heinlein novel, I just don't know which one has it.
Wrong
Somebody got unmuted. Congrats.
@tygxc, someone buys a lottery ticket in a one in a thousand lottery. Do you think you can prove the ticket will not win?
If you can answer that correctly you will see the error with your reasoning:
"The proposed method makes 1 error in 10^20 positions, while there are only 10^17 relevant positions."
@Optimissed, I know Contact has pi in it, but this was way too late and not consistent with my memory! It has to be a novel published by the mid-1970s.
I think you are thinking of a Heinlein novel, I just don't know which one has it.
I eliminated "Space Cadet" by scanning 159 pages. Just a few more novels to go.
someone buys a lottery ticket in a one in a thousand lottery. Do you think you can prove the ticket will not win?
I can....based on the fact that he has previously bought 10^17 lottery tickets and never won. And several Lottery Masters have agreed that he can't win. 
Q.E.D.
In that case I think a court might accept it as proof the lottery was fixed.
@Optimissed, I know Contact has pi in it, but this was way too late and not consistent with my memory! It has to be a novel published by the mid-1970s.
I think you are thinking of a Heinlein novel, I just don't know which one has it.
I've just read the first third of "Time for the Stars". It probably isn't that one, but it was one of my favourites as a teenager. There was an early chapter called "the natural logarithm of two".
No it wasn't Flowers for Algernon, an exceptionally good short story and well-deserved Hugo Award winner.
someone buys a lottery ticket in a one in a thousand lottery. Do you think you can prove the ticket will not win?
I can....based on the fact that he has previously bought 10^17 lottery tickets and never won. And several Lottery Masters have agreed that he can't win.
Q.E.D.
What if he had a team of lottery masters work with supercomputers for five years? Could he win then? Maybe the expense would be greater than prize?
No it wasn't Flowers for Algernon, an exceptionally good short story and well-deserved Hugo Award winner.
While you boys are busy working out the exact extent of @tygxc's logic I'm back to looking at 213276247234766621.
Are you guaranteeing it's theoretically significant?
It looks more like a conundrum - the chances of an 18 digit number missing 4 or more digits is only about 1¾%.
@6324
"non-standard terminology"
'I have attached question marks to the moves which change a winning position into a drawn game, or a drawn position into a losing one, according to my judgment;
a move which changes a winning game into a losing one deserves two question marks
There are no exclamation marks, as they serve no useful purpose. The best move should be mentioned in the analysis in any case; an exclamation mark can only serve to indicate the personal excitement of the commentator.' - GM Dr. Hübner