Triple occurrence -- a graduate course?

In the previous triple-occurrence thread, most posters have now agreed that, in deciding whether two positions are the same for triple-occurrence purposes, it is necessary to examine not only the locations of all the pieces, but also the possible moves of the pieces, including possible future moves.

Let’s say that a player is temporarily unable to castle – for example, because the f1 square is attacked, or because there are pieces between the king and rook. Let’s say, further, that the same physical position comes up again, but now the player is permanently unable to castle, because he has moved the king or rook in the meantime.

These two positions are different. The set of moves currently available is the same in both cases, but the set of possible future moves has changed.

Even if everybody agrees with all of the above, there is still a legitimate question as to how to define the permanent loss of castling privileges. As I see it, there are (at least) two reasonable definitions:

Definition 1. Castling privileges are permanently lost if there does not exist a sequence of legal move-pairs leading to a position where the player may castle.

Definition 2. Castling privileges are permanently lost if the player has moved either the king or rook.

The two definitions are not the same. Consider the following example from the Castlemate thread (white to move):

In this position, even though white has moved neither king nor rook, there is no way white will ever be able to castle, even with cooperation from his opponent. (Please stare at the position long enough to convince yourself of this.) So white’s castling privileges are permanently lost according to Definition 1, but not according to Definition 2.

At first glance, Definition 1 seems more satisfying. It hits the nail on the head, in that it grants equal status to two identical positions if, and only if, the set of possible future moves is the same in both positions. Let’s call Definition 1 the purist definition.

But there could be practical problems. In some situations, it could be difficult for a tournament arbiter, or even a computer, to determine whether there exists a sequence of legal moves leading to castling. In the above-mentioned Castlemate thread, for example, one poster presented a position in which he believed castling would never be possible, though white could play on for 28 moves before being forced to move king or rook. That example, however, turned out to be cooked by a sequence of 16 move-pairs after which white could castle.

So there is a strong case for Definition 2. Let’s call Definition 2 the practical definition. For one thing, it’s algorithmic – to determine if a position fits the definition, just look at the move history. I’d bet dollars to donuts (hmm, that’s only about an even bet nowadays, isn’t it?), that chess engines such as Fritz would employ Definition 2. (Maybe some volunteer could set up a situation which is a triple occurrence by Definition 1 but not by Definition 2, then try to claim a draw, and see what Fritz says.)

According to some posters in previous threads, FIDE has apparently wrestled with this question, and has settled on Definition 2. Perhaps USCF should do the same, to clarify the rule and stay synchronized with FIDE.

Here’s another monkey wrench. In some situations, neither definition “feels” right:

In theory, white could retain castling privileges with Qc3, but what player in his right mind would do so, and even if he did, what opponent would play anything other than …Bxc3+, still ending white’s castling privileges?

Thorny questions, no?

Bill Smythe

One major problem with this definition is that illegal moves become legal if the opponent does not point them out in a timely fashion. So this definition would also require a change in the definition of castling itself.

Since I’m the one that started the other 3-fold line, I’ll make my suggestions. I’ll start with the easy one first. The second diagram given by Dakota above is in no way a 3-fold issue because it assumes that Bc3+ will be played. As the move is not forced, I don’t think there is any way a convincing argument can be made. It’s not the ability of the player that determines the future loss of permanent right to castle.

The first example, and the discussion I had with Bill Goichberg make me feel that the proper definition is #2 with the added words “or the rook is captured”. I think the best reason to reject definition #1 is that it requires looking at forced future moves. As a TD and player, I don’t like that the TD’s playing ability should become an issue in making a ruling. This is one of my complaints about 14H and why I don’t like adjudication.

Another reason (thanks to Martinak), is that having to consider that illegal moves should even have to be considered, rubs me the wrong way. Dakota tries to cover Martinak’s comment by inserting the word “legal”. Just because an illegal move isn’t caught in a timely way doesn’t make it legal by my definition. Is a robbery retroactively legal because no one is arrested before the statute of limitations expires? I do not want to see any rule that encourages a player to get away with illegal moves.

I’d like to take Martinak’s suggestion to an extreme. Consider that there is no way to permanently lose the right to castling illegally if after 10 additional moves it’s too late to correct it, making it therefore legal.

With definition 2, we can now repeat the static position 12 times before a draw claim would be upheld. First time en passant is legal, then repeat 2 times with it illegal, then 2 more with each of the 4 rooks having been moved and finally when all of those castling moves are illegal, the real third repetition occurs. I guess that’s better than the old rule which would allow knights of the same color to switch places and it was considered a different position.

In discussing the proper way to interpret repeated positions, I would prefer to ditch the red herring of “illegal moves”. If absolutely necessary, there could be a rule that if, after a triple occurrence claim, it is discovered that there was an illegal move any time after the first of the three occurrences, then the claim is automatically denied.

Of course, other rules regarding illegal moves would also be in force, e.g. if the illegality occurred within the last 10 moves, the position is restored, etc. etc.

I do agree with Harold S’s other reasons for preferring Definition 2.

Bill Smythe

Perhaps I didn’t express myself as well as I could have about illegal moves.

I don’t like the idea of potential illegal moves having any effect on the 3-fold claim. When I wrote “I’d like to take Martinak’s suggestion to an extreme” it was not because I like the idea. What I meant was that I’d like to show silly the idea would be if it were allowed to change the validity of a 3-fold claim.

Dakota Smythe wrote:

I think the rule about illegal moves (11A) already covers this, except when the illegality occurred more than 10 moves ago. The TD would return the game to the point just before the illegal move was made and the offending player would need to make a legal move, and with the touched piece if possible.

It is precisely the case where the illegality occurred more than 10 moves ago that might require a special rule. If it occurred, say, 20 moves ago, but after the first of the three occurrences, then (I suppose) the illegal move would not be corrected, but the triple occurrence claim should be denied.

Bill Smythe