Field
Particular games
Hackenbush, Nim, Domineering, Toads and Frogs — the specific games the general theory was built to explain.
Hackenbush is a numeral
Draw a stalk of coloured edges. Read it as a string, blue for one and red for zero, and the string is the binary expansion of what the position is worth. Not approximately — exactly, and the site computes it both ways and refuses to build if they disagree.
Domineering
One player places dominoes vertically, the other horizontally, on a shared grid. The rules take one line, the values are a mess, and that mess is the point — this is what the theory looks like applied to a game nobody designed for it.
Toads and Frogs
Toads shuffle right, frogs shuffle left, and either may jump over one of the other. A strip six cells long is worth exactly up. Another six-cell strip is worth exactly down. Nobody has a formula for which.