Thirdly, although I’ve been talking about the “value” of a position as if it’s a well-defined concept, it mostly isn’t. Stockfish’s value calculations are grounded in the likelihood of it winning from that position when playing itself. But there’s no clear way to translate from that to the likelihood of winning against one’s actual opponent, which is what we’re interested in. I won’t discuss this further here, but trying to pin down how to estimate a position’s value in that sense seems potentially fruitful.
I’ll take a shot. If EAlice(mvs,Bob) is the expected return (1 for win, 0.5 for draw and 0 for loss) for Alice given that she’s playing Bob, she knows Bob’s source code, and the moves mvs have been played so far, then the value of a position for Alice is ∑pϵSEAlice(mvs,p)∗P(p|mvs) where S is the set of programs that Alice’s opponent is drawn from.
I’ll take a shot. If EAlice(mvs,Bob) is the expected return (1 for win, 0.5 for draw and 0 for loss) for Alice given that she’s playing Bob, she knows Bob’s source code, and the moves mvs have been played so far, then the value of a position for Alice is ∑pϵSEAlice(mvs,p)∗P(p|mvs) where S is the set of programs that Alice’s opponent is drawn from.