Why are the rules of chess regarding the king so fussy? Unlike other pieces, the king cannot be legally captured; not only is it illegal to capture the king, but also—one step further removed—it is illegal even for a player to leave their king exposed to a possible capture on the next move. The king must not move into check or through check or otherwise remain in check. The king thus enjoys a legally protected immortality. But this is not on account of his great military power or the impressive strength of his movement—rather, it is a matter of chess law. A legal prohibition against regicide might seem toothless, to be sure, if one considers that usurpers and royal enemies are not generally disposed to obey the king’s law. Nevertheless, according to the standard rules of chess, it is illegal to capture the king and illegal for a player to leave their king in check. Unlike their historical counterparts, chess kings never suffer the indignity of deposition.
Games of chess are thus weirdly truncated—one has the winning goal not of actually capturing the enemy king, but instead of placing oneself into a position in which one would be able to capture the king on the next move, no matter how the opponent plays next, if contrary to fact the moves continuing from that juncture were to be allowed. But how strangely metatheoretic and anticlimactic this is. Instead of simply continuing the game to its natural conclusion, executing what would be the main dramatic event, the game instead ends abruptly, prematurely. The anxiously anticipated king capture never actually occurs on the board. Games of chess thus seem always to end one move early—the curtains close just before the climax.
Why do we play chess like this? Why don’t we play chess with the more natural goal of simply capturing the opposing king? In what I call natural chess, we abandon the rules about check and checkmate, adopting instead the goal of capturing the opposing king. Is this simplified version of chess game-theoretically equivalent to standard chess? Are there the same game outcomes from a given position?
Think about it...
Surprisingly, the answer is no. Although natural chess is almost equivalent to standard chess, nevertheless it is not quite fully equivalent, although we shall see that it is equivalent to a nonstandard variant of chess in which some other standard rules are also changed.
To show the basic inequivalence of standard chess and natural chess, I shall exhibit two kinds of chess positions that distinguish them. Namely, (1) there are chess positions which are a win according to the rules of standard chess, but in which it would not be possible for the player to capture the king in natural chess; and conversely, (2) there are chess positions that are a draw in standard chess, but a win in natural chess. Standard chess, therefore, is not exactly the same as the necessary capture of the opposing king.
Really? Let’s discuss it.
Penultimate chess
Before continuing with that main theme, however, let me first continue to highlight what I see as a slightly comical absurdity in our standard chess rules. I should like to mock the standard rules. The basic inspiration for the standard checkmate rules, of course, is the idea that we needn’t actually capture the enemy king, but rather it should suffice for winning to be in a position such that we would certainly be able to do so on the next move.
Why don’t we take this one further step removed? Consider the chess variation I call penultimate chess. In penultimate chess, players should announce checkmate-check, when they are in a position threaten checkmate on the next move—that is, the current move is not necessarily checkmate nor even check, but they are threatening to make checkmate on their next move, unless the opponent moves so as to obstruct this. If indeed there is no way for the opponent to block the checkmate threat, then we shall say that the first player has placed his opponent in checkmate-mate—they are sure to be able to create checkmate on the next move. Of course, to make a checkmate-mate move is to create a mate-in-1 position, with the opponent to move (so it was mate-in-2 before the checkmate-mate move).
And now the point is that in penultimate chess we shall take checkmate-mate as the winning condition. You don’t have to actually capture the king, nor even put yourself in a position in which you would be certainly able to capture the king, that is, checkmate—rather, you win penultimate chess by placing yourself in a position in which you are certainly able to put yourself in a position in which you would be certainly able to capture the king, that is, checkmate-mate. Just as standard chess ends at checkmate, one step before the actual king capture, penultimate chess ends at checkmate-mate, one step before checkmate, two steps before the king capture. I would find it entirely in keeping with the spirit of the standard checkmate rules that in penultimate chess we should also make it illegal for a player to leave themselves exposed to checkmate-check (even if they are not in check), just as it is illegal in the standard chess rules to leave one’s king in check.
And why stop there? In the game of antepenultimate chess, one seeks not to capture the king explicitly, nor to create a checkmate position (in which one would certainly be able to capture the king), nor a checkmate-mate position (in which one would be certainly able to be certainly able to capture the king), but rather to create a checkmate-mate-mate position, in which one is certainly able on the next move to create a situation in which one is certainly able to create a position in which one is certainly able to capture the king on the following move. Of course, these are the mate-in-2 positions. If we think of checkmate as king-capture-in-1, then mate-in-1 is king-capture-in-2, and so one wins penultimate chess with king-capture-in-2, and you win antepenultimate chess with king-capture-in-3, or mate-in-2.
I should remark that all these games are affected by analogues of the analysis showing the difference between standard chess and natural chess, and so actually standard penultimate chess will not be game-theoretically identical to natural penultimate chess, and similarly with antepenultimate chess. Similarly, in preantepenultimate chess the goal is to make checkmate-mate-mate-mate, or king-capture-in-4, or mate-in-3.
Let’s get into it!
(A quick note regarding the phrase “one move early” is that it refers to the usual chess manner of counting moves, where one counts the moves of only one player. This is the usage in the white-to-mate-in-3 terminology, where it means that white will make three moves (or fewer if black plays poorly), so the moves will generally proceed white/black/white/black/white, ending in checkmate on the third white move. This method of counting also appears in the common chess notation such as 1.e4 e5 2.Nf3 Nc6, where each move by a player is referred to as a half move in the game.)
