After posting the above post I realized that QR is obviously a mate that can be done in the center of the board because the rook can pretend it marks the edge of the board, then the Q and K perform a mate on that invisible "edge" in the middle of the board, like so:
So if I skip all the intervening piece combinations and just add QR and QQ to the end of my table I get:
I'm still looking to find the transition point where "any side" becomes "anywhere" per the right-hand column.
Similar to the previous post, I realized it is *possible* to get a mate with RR in the same manner by using one rook as an "edge" down the middle of the board, but I realized that if I want to add more cases I will eventually need to distinguish between two situations: whether a mate in the middle part of the board is *possible* versus *forcible*. That will require another column of the table. Here's an example where it's possible, but I'm not sure if White can choose the square where the mate will occur.
Based on one mate pattern used as an example of a "pure mate" (https://www.chess.com/forum/view/game-showcase/pure-mate), I realized QB also allows a mate in the center of the board, although in practice I'd have a hard time forcing the king out of the edges to produce this mate, so I modified the last column to read "with worst defense". Here is one way such a central QB mate could occur:
That means I can add another row to my table:
Since the modification of the table's last column now means we can include ridiculous selfmates, the remaining entries are pretty easy to fill in. Here's a QN central mate, for example...
So--after making a correction for NN after learning about HGMuller's discovery that NN can occur on the side as well as in the corner (https://www.chess.com/forum/view/general/two-knights-vs-king-for-checkmate)--the table now looks like:
I was able to complete the above table with a little experimentation.
It's pretty clear to me that RB cannot mate in the center of the board because there always exist escape squares that are not covered. Here are some examples of RB non-mates:
The same is true of RN. Here are some examples of RN non-mates:
Since R alone can mate on the edge, then adding N or B does not enhance the mate power in the sense of the right column, therefore RN and RB qualify as edge mates at best.
In addition, it seems that the word "superior side" is used by at least one chess author (Pandolfini) to mean the player with the superior material...
(p. 233)
Though mate cannot be forced in this manner, perpetual check
prevents the superior side from proceeding with his plans.
Pandolfini, Bruce. 1988. Pandolfini's Endgame Course. New York, New York: Fireside.
After posting the above post I realized that QR is obviously a mate that can be done in the center of the board because the rook can pretend it marks the edge of the board, then the Q and K perform a mate on that invisible "edge" in the middle of the board, like so:
So if I skip all the intervening piece combinations and just add QR and QQ to the end of my table I get:
I'm still looking to find the transition point where "any side" becomes "anywhere" per the right-hand column.
Why not 1.Qd4 Ke7 2.Qe5 # ?
Above is a little table I made to answer the frequently-asked question about whether it's possible to mate with two knights (NN). I think it's a really insightful summary. In fact, I'm finding it so interesting that I feel like adding more rows to the end of it just out of curiosity so as to fill in that last column completely until it says "anywhere".
Specifically, I know it's possible to mate on any arbitrarily chosen square on the board with two queens (QQ), so that would be the last line in the table, but that raises the question as to which information comes between for RN, RB, RR, QN, QB, and QR. This is all purely academic at this point, not practical, but if anybody feels like working on this problem, please let me know what you discover, show your logic, and I'll fill in the rest of the table.
An example of how to mate in the center of the board ("anywhere") with two queens (QQ):
And the second check mate with two queens is 1.Qc6 Kd3 2.Qe4 # or 1.Qe6 Kd3 2.Qc4 # This is also possible in the middel of the board.
Based on one mate pattern used as an example of a "pure mate" (https://www.chess.com/forum/view/game-showcase/pure-mate), I realized QB also allows a mate in the center of the board, although in practice I'd have a hard time forcing the king out of the edges to produce this mate, so I modified the last column to read "with worst defense". Here is one way such a central QB mate could occur:
That means I can add another row to my table:
Why not 1.Qd4 Ke7 2.Qe5 # ?
Yes, that works, too, thanks. I admit I didn't see that faster mate, but then I was just illustrating a point, not trying to find the fastest mate.
By the way, after I changed my right-hand column to specify "with worst defense," the problem became much easier since all I had to do is find one example of a mate in the middle of the board. If I were to add another column for location "with best defense," that would require looking at a large number of possibilities, possibly all possibilities within certain constraints, which is a much harder problem, therefore I think I'll skip creation of such a column. Another tempting study is to study which mates can be done without a king, which has some practical applications, such as knowing that a certain group of four pieces can mate the opponent with nonstop checks so that a queen sacrifice becomes feasible, as in Fischer's Game of the Century (https://www.chess.com/article/view/bobby-fischers-breakthrough-the-game-of-the-century). However, there is no end to such questions, so the above table is a good stopping point, I believe, at least for the time being.
Above is a little table I made to answer the frequently-asked question about whether it's possible to mate with two knights (NN). I think it's a really insightful summary. In fact, I'm finding it so interesting that I feel like adding more rows to the end of it just out of curiosity so as to fill in that last column completely until it says "anywhere".
Specifically, I know it's possible to mate on any arbitrarily chosen square on the board with two queens (QQ), so that would be the last line in the table, but that raises the question as to which information comes between for RN, RB, RR, QN, QB, and QR. This is all purely academic at this point, not practical, but if anybody feels like working on this problem, please let me know what you discover, show your logic, and I'll fill in the rest of the table.
An example of how to mate in the center of the board ("anywhere") with two queens (QQ):