Recursive Chess

What is the game of recursive chess?

Consider this fascinating vision of a new form of chess—recursive chess.

This etching was created by Django Pinter, a tutorial student of mine at Oxford, who gave it to me as a parting gift upon his graduation. Django's idea was to play chess, but in order for a capture to occur successfully on the board, as here with the black queen attempting to capture the opposing white knight, the two pieces would themselves sit down for their own game of (recursive) chess. The idea was that the capture would be successful only in the event that the subgame was won. Notice in the image that not only is there a smaller recursive game of chess, but also a still tinier subrecursive game below that (if you inspect closely), while at the same time larger pieces loom in the background, indicating that the main board itself may be already several levels deep in the recursion.

The idea of recursive chess seems clear enough initially—shall we play? Perhaps upon further reflection, however, I expect that we begin to realize that the game is not actually so clear after all. How does it work exactly? What precisely is the game of recursive chess? What are the rules? How exactly does game play proceed?

In this essay I should like to offer several natural proposals, interpretations for what the rules of recursive chess might be. To my way of thinking, the question at bottom remains unsettled, and we shall ultimately have to weigh various considerations against each other. Meanwhile, the problem of deciding upon the rules of recursive chess, I find, opens up several aspects of the general theory of games that I find interesting and worthwhile to discuss.