I don't see any particular reason to continue the discussion (and promised myself I wouldn't!
). Ed and I each had our say, I doubt Round 3 would be any more profitable than Round 2. But for the developing argument about Bayes' Theorem, it's worth distinguishing between my highly focused point, which I think is influencing Daniel, and a broader point, which prokofiev and hyperpape were elaborating with Bayes' Theorem.
Broad point: if you randomly select one of your won games and one of your lost games,
ex ante it's more likely that the lost game will have an example of any particular error you make. On inspection there may be more of a particular class of error, large or small, in the won game, but but
ex ante you wouldn't suspect this, would you? Relative proportions don't matter.
Focused point: Perfect play gains nothing, so saying that a move loses X points already assumes that the opponent will respond correctly. Errors that are part of larger sequences where the opponent screws up or doesn't notice the mistake don't affect the point total, and so don't affect who wins. To use our formal terminology, something like {bad ko threat & opponent ignores} is a mistake class that loses points and is more likely to show up in a lost game, while {bad ko threat & opponent answers} actually gains points and so is no more likely to show up in a lost game, even though the bad ko threat was an equally large mistake in either case. Similar examples: {capture in ladder instead of net & opponent plays ladder breaker}, {mess up l&d & opponent kills}, {make weak group & opponent attacks}. All of these mistakes are equally bad regardless of what the opponent does, but in some of them telling the player what the correct play is is much easier than getting him to appreciate how bad things could have gotten if his opponent had responded correctly.
I was calling these "big mistakes" in a colloquial way, but if we want feed them into a probability function we would have to specify that it is the opponent's lack of mistakes in responding to them that is making my original, point-losing move both (i) "bigger," and so more likely to be found in a lost game, and (ii) "glaring," and so easier to learn from.
Back to the broad point: here's a heuristic argument that may show that large errors
are relatively more likely in lost games. I haven't actually formalized it, so it may be garbage. Let's say I play an opponent, always taking black, hundreds of times, and we randomly vary the komi between zero, 7, and 14 in each game. Using 14 komi is like making a 14 point mistake on the first move, 7 komi is like me making a 7 point mistake. If we're even with no komi, perhaps he wins 70% of the games with 7 komi and 90% of the games with 14 komi. So while I make this particular 7 pt. mistake with pr=.33 and the 14 pt. mistake with pr=.33, the pr(14 komi game | i lost)= .43, while pr(7 komi game | i lost) = .33. I don't think this relies on the fact that pr(14 komi |7 komi)=0. So the relative frequency of large mistakes should be higher in lost games.
But I'm not trying to say that I think errors of large magnitude are necessarily more important, and this doesn't affect any argument about which games to review.. My point was always narrowly about how palpable the consequences of the error are, which depends on independent events later in the game. In fact, I think that one thing prokofiev has shown is that a lost game is much more likely to contain multiple cases of the same error, which would make it much easier to correct common small errors in lost game. (Again, this goes back to making things manifest: when you can point out that someone made the
same endgame mistake four times, he'll understand why the game suddenly turned against him, and won't do it again.)
