[xhuhdnbi] Chess expected point outcome

While chess programs evaluate positions in centipawns, what we really want is the probability (Bayesian degree of belief) of the outcomes of win, lose, or draw.

Positions may be compared by computing expected point outcome.  Under football scoring (3-1-0) instead of the traditional (1-0.5-0), the game is NOT zero sum, so optimal play may be different.

The authors of Glaurung Stockfish comment that traditional unit pawn score cannot be used to compare between different phases of a game: +1 in the opening means something different than +1 in the middle game.  It makes me wonder how accurate it is if different portions of a tree are selectively searched to different depths.  A probability based metric would avoid this problem.

A complication: we not only want a winning position; we want to make progress toward checkmate.