On translation of games

At Language Log recent discussion has gone on about how you can translate from one language to another, but you can't translate from one game to another. For example, you can't take a game of chess and translate it into poker.

I'm reminded of the Subjunc-TV in Douglas Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid, which has characters tuning into a baseball game that has been made to look like a football game. Of course this doesn't work perfectly, which is intended to illustrate Hofstadter's points about the imperfection of analogies.

At Language Log, I learned that there are certain "logical games" for which a notion of translation is possible. These are apparently of interest to logicians; you can read more at the Stanford Encyclopedia of Philosophy.

But in combinatorial game theory, we can associate each position in certain games with a "number"; is it meaningful to say that positions in different games which have the same number are the "same position"? In this case, translations between games would become possible, except that those numbers are apparently difficult to calculate.