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If you look at a position where one player has a minor piece over his opponent and the other has no attacking combination, opportunity to queen a pawn, etc. the other player has a 0% 'chance' of winning using this model. Unless you can calculate that even though you are down material you will be either to a) gain back more material than you lose or b) mate your opponent and there is no combination of moves to prevent this, you have lost the game. Of course if this was the case, you weren't really 'down' to begin with. There is no 'chance' or probability involved here unless you are playing with faulty tactics and hoping that your opponent won't find the correct defense. The attack either works or it doesn't... purely objective.
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One has to be very careful with throwing in the absolute, so you'll see how it's reasonable not to be so absolute in ones statements.
Your statement is (mathematically speaking) busted. Here, black can not get back material(with perfect play), nor can he mate his opponent, yet he will not lose the game.
Here is the same for white, he is down material, and he can not win, yet he does not lose:

They don't bother me, I love statistics. They just don't apply.
"Chances are, that winning position occurred because one of the players played some bad moves along the way."
Not chances, absolutely that is how it occured. One player played better moves than the other: luck, probability, chances, etc. had nothing to do with it.
You are diluting the discussion, I just pointed out that a winning position probably occurred because one of the players played imperfect moves.
So, your debate about perfect continuation came to life because players are imperfect.
I still don't know why you oppose linking probability theory to chess, it's completely standard branch of mathematics.