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Peter, I think that the freer capturing is really more in line with your rationale for the edge sqaures in the first place: to keep pieces from using the edges to hide from Long Leapers. So how about: A piece may not move to an edge square except to capture a piece which it could not capture by moving to a non-edge square. This applies even if the starting square is an edge square. The Swapper's swap move is a capture for this purpose whether the piece swapped is friendly or hostile, as is a Chameleon's swap with a Swapper whether friendly or hostile.
For the sake of posterity, here is a link to the game in question.
I see two logically independent questions here:
1) What should the rules be?
2) What is the correct interpretation of the rules as written?
The first question is relevant to future games of Rococo and should be answered by the inventors, taking input from the rest of us if they wish to. For the particular case of the present game, I think that the second question is relevant, and that ideally it should be answered by consensus.
The rules as written contain a general statement describing the concept of edge squares and their role in the game, and a specific statement for each type of piece, describing how that piece behaves with respect to edge squares.
The general statement:
These marked squares on the edge of the board are edge squares, and a move may only end on an edge square if necessary for a capture. Or in other words, a piece may only end up on an edge square by making a capturing move that would not be possible without landing on the edge square. This includes moves that start on edge squares.
The specific statement for the Long Leaper:
It may end its move on an edge square only when that is the only way to make a particular capture.
As I read these rules, the only thing that could be construed to forbid my move to x0 is the definite article in the second sentence of the general statement. It's worth noting that David's interpretation, based on this definite article, is paradoxical (as Mike Nelson has pointed out), and that the definite article only appears in a sentence which is presented as a rephrasing of the previous sentence. The first sentence of the general statement and the specific statement both imply (in my opinion; there may be some room for debate) that one edge square is as good as another. Since I can't capture the black Leaper by moving to an interior square, x1 and x0, both being edge squares, should be equally permissible under the rules as written.
Peter's emendation of 'landing on' to 'landing on or passing over' does produce a well-defined rule, but in my opinion it is inconsistent with the intention of the edge squares. If the black Leaper were on x3, then this rule would say that I can capture only by moving to x2, not x1. But a piece on x1 is no safer from a Leaper than a piece on x2. On the other hand, a piece on x0 is safer, so it would seem reasonable to forbid capture on x0, not because it is not the first square beyond the victim, but because it is on two edges rather than one.
In fact, I think this was Mike Madsen's understanding of the rules. (I hope he'll correct me if it wasn't.) While I maintain my belief that this is not the rule as written, it seems sensible, and in my opinion would be the best rule for the game. It could perhaps be stated most easily by defining three classes of squares (interior, edge, and corner), and forbidding a piece to move to an edge square except to make a capture which cannot be made by moving to an interior square, or to move to a corner square except to make a capture which cannot be made by moving to an interior or edge square.
I have read the rules, very carefully, a great many times, and I remain convinced that my original interpretation was the correct interpretation of the rules as they were written before yesterday's revision. I have explained my analysis in gory detail, and of those who disagree, only Greg Strong has provided reasoning based on the text of the rules in response.
You say that under my interpretation the Long Leapers would have too much power. That may be so, but that is a subjective assessment which can only be made based on experience with the game (or perhaps experience with similar games and an intuition superior to mine). The fact (if that word can be used) that a particular set of rules does not yield the best of all possible games does not mean that that set of rules was not written down. As it happens, I think that the Long Leapers in Rococo may be too powerful regardless of which rule is used for capture along an edge. But one's opinions of the merits of a game are not relevant to interpretation of the written rules. The rules are what they are, not what you, or I, or anyone else, think they ought to be.
Also, the fact that some anonymous player once played a move which was not the best move under my interpretation (which you call the 'wrong' interpretation) cannot be taken as evidence for or against any of the three interpretations. It is not even evidence that the player interpreted the rules one way or another, unless the annotations (which I have not seen) contain some discussion of the matter.
Peter,
Regarding game design, I agree with Michael Nelson's last comment, but after your last comment I understand your position much better. I now see this as a question, not of logic, but of taste. And it's not my game, so I'll shut up about that.
I'm glad to see that the rules have been revised to reflect your intentions (although I had hoped that the tournament issue would be resolved first), and I believe that the revised rules are equivalent to what you have indicated in recent comments. But, if you're interested, I have a few suggestions as to how I think they could be written better, so as to avoid future misunderstandings.
The sentence that was most controversial in the original rules was this one:
Or in other words, a piece may only end up on an edge square by making a capturing move that would not be possible without landing on the edge square.Before the revision this sentence threatened to break the game; now I think it's just unnecessary and possibly confusing.
The section labeled 'Rules' seems unnecessarily complex and extremely redundant. The same statement is made at least four times, and if I were unfamiliar with Rococo, I would have to read this section three or four times to be sure I had it right.
You've now included a precise mathematical definition of the term 'capturing move'. This is good, because I now understand what you mean by the term, but I'm not sure that this is the best term for this definition. To see what I mean, consider this example: A Long Leaper on a4 could capture an opposing piece on a3 by moving to a2 or a1 (assuming both of these squares are vacant). In the absence of a definition of the term 'capturing move', I would regard these as two distinct capturing moves, since they are two distinct moves. But it seems natural to say that they result in the same capture. The rules would be clearer (to me, at least) if the term 'capturing move' were replaced everywhere with 'capture'.
The inclusion of the clarifying example is perhaps helpful, but it is not the best possible example, since it does not fully distinguish between the three interpretations of the original rules. A better example can be formed by placing the piece to be captured on x3 rather than x2, so that under the revised rules the Long Leaper can capture by moving to x2, but not to x1 or x0. Also, the example breaks up the flow of the redundant rules; perhaps it could be moved to its own paragraph. And if the rules refer to the square x9, the ASCII diagram should be modified to refer to the last rank as 9, rather than 00.
The formal statement of the edge-square rules is unambiguous, but statement 4 is completely unnecessary. It follows from the first three statements, and should therefore be treated as a theorem rather than a rule. If I'm not mistaken, the entirety of the edge-square rules could be stated in one sentence, something like:
A piece p capturing a set P of opposing pieces may land on or pass over only the minimal number of edge squares necessary for p to capture all the pieces in P.
The piece descriptions of the Long Leaper and the Withdrawer should include statements that these pieces, when moving along an edge, may move only the shortest possible distance for a particular capture. In fact, since each piece description contains the edge-square rules applying to that piece, I wonder whether it would be better for the 'Rules' section simply to introduce the general concept of edge squares, and leave the details to the individual piece descriptions.
Finally, I've noticed some typos: 'mininal', 'Moves that captures', and 'fewist'.
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