Take the 2-minute tour ×  If you wanted to measure the strength
of, say, a chess player, the best way would involve knowing the
true value of each position: then you could compute the
frequency $W$ with which the player finds a winning move in a
won position, and $D$ of finding a drawing move in a drawn
position.  Even without a perfect evaluation algorithm, perhaps
mathematics offers the possibility of saying something about a
player's $W$ and $D$? So I ask, do there exists tools in
probability theory, if not for chess then at least for some
class of idealized games (only the morphology of the game tree
would matter) that would would allow prediction of one player's
winning percentage over another given just the two players' $W$
and $D$ frequencies?  If yes, then the distribution of winning
percentages in a population of players might serve as data for
an inverse problem allowing the statistical estimation of $W$
and $D$ frequencies (or at least associated derived quantities,
or relative quantities).  Also w