#2766
"My impression is that a 1 pawn advantage gives an expectation of about 0.7"
Expectation is a notion of imperfect play, linked to probability of error.
No, probability of result. There is no guarantee that there is merely one error. If errors can occur, multiple errors surely can too, for either or both sides.
A position is either a draw, a win, or a loss.
There are no intermediates.
It's nice that some of your statements are true. The above is an example.
I feel you have entirely missed a crucial fact. Suppose it is the case that a position is evaluated +1 pawns by a super-duper computer (and let's assume one side is actually a pawn up), Then suppose if you play two super-duper computers against each other in this position (or a set of such positions), the score is 70%, most of the results being draws and almost all the rest being wins for the side with the extra pawn.
You claim the mixed results are due to inaccuracy. This is correct from a game theoretic point of view if there are mixed results for a single position. But you also claim the true result is a win. This is not only unjustifiable, it is also likely to be wrong a lot of the time. If the true result was a win, why does the winning side make so many blunders to give away the draw, while the side with a pawn less makes fewer cancelling blunders?
You can be very confident that a lot of +1.00 positions are draws. The evidence is that it is most of them, but regardless of this the notion that all of them are wins is absurd.


Statistically, the claim that a win of a pawn wins a game is not only unsupportable, it is dubious whether the win of a pawn suffices to make the expectation of the game greater than 75% (which would be the expectation if the probability of a win was the same as the probability of a draw.
Strong evidence for this comes from Stockfish evaluations collated with results and with neural network expections. My impression is that a 1 pawn advantage gives an expectation of about 0.7. Note that a 1 pawn advantage from Stockfish is what you have if you are 1 pawn up but it evaluates the positional factors to be balanced (positional factors adjust the material balance indicated in the evaluation).
Certainly this needs to be checked empirically in a more systematic way.
How would such a check tell you anything about perfect play?
If you try a statistical check on the result of KQKNN positions, SF14 with NNUE or human, will tell you they're generally drawn under basic rules, but Nalimov says they're 98% won by the queen.
I think all you get from looking at practical play is information about practical play.