@11043
"strategy stealing is of no detectable relevance to the solution of chess"
++ Strategy stealing is a way to prove the game-theoretic value of the initial position cannot be a black win, as white can steal the strategy of any tentative black win.
Anyway it is obvious from other considerations e.g. the initiative that Chess cannot be a black win and observed results confirm that.
On the contrary, you yourself prove that it's a Black win.
You base your Poisson distribution of blunders on the assumption that the probability of a blunder on any given move is constant throughout the game.
If you consider this game, in the final position (shown) White is theoretically losing ( you can check that here https://syzygy-tables.info/?fen=8/7P/8/8/8/5K2/7r/3k4_w_-_-_1_47).
White's probability of blundering on the next move is therefore 0 since he cannot alter the position for the worse. From your assumption, White's probability of blundering was therefore 0 throughout the game and since he only ever had a finite choice of moves it follows he made no blunders.
But if White has made no blunders and is in a losing position it follows that Chess is a win for Black.
QED as you put it.
here's the goofy part, tygxc claims that only "sufficiently strong" players match the claimed distribution. (with no justification btw)
this allows him to ignore all non zero values for his "proof" because he simply claims them as "not strong enough"
#11055
"there is no strategy stealing for chess"
1 c3 e5 2 c4 steals 1 e4 c5.
1 Nf3 d5 2 g3 c5 3 d3 Nc6 4 d4 steals 1 d4 Nf6 2 c4 g6 3 Nc3 d5.
For all tentative black wins there exists a white steal of it.
Er, were the first two lines meant to be a proof of the third? Can't help feeling something is missing somewhere.
He may be onto something. All he has to do now is to steal a set of positions so large that one of them appears in any black strategy
that's the bit I thought was missing.
(rather than the usual version of strategy stealing - stealing the first position, which cannot work). To put it another way, white has to find a set of positions one of which can be forced on black, and one of which appears in every possible black strategy (with colours reversed). This is not entirely obviously impossible, even if it seems unlikely.
Intuitively white has to find a way to waste a move in every line without black wasting a move. Thar's the rub - it seems just as easy for black to waste a move at some time, and he only has to manage it in a single strategy to stop white's valliant attempt to steal.
Note that strategy stealing by white cannot distinguish whether white has a winning strategy or a drawing strategy.
the bit that tygxc misses is that he doesnt get to choose black's response.
by definition, the strategy steal must encompass ALL possible black responses.