if $b$ is a final board state that is won, then $V(b) = 100$
if $b$ is a final board state that is lost, then $V(b) = -100$
if $b$ is a final board state that is drawn, then $V(b) = 0$
if $b$ is a not a final state in the game, then $V(b) = V(b')$,
where $b'$ is the best final board state that can be
achieved starting from $b$ and playing optimally until the
end of the game.
This gives correct values, but its
nonoperational because of case 4. That is, it is
not efficiently computable.
In general, it is very difficult to perfectly learn
$V$. We will approximate it.