I see you have been busy! You might have noticed that after generating the tablebase, the last thing the program prints before asking you to enter a position is two octal numbers. These are codes for 'maximin' positions, the longest forcible mate. For instance with N+F this is 36 moves. (For these elementary end-games DTC is the same as DTM, of course). Actually the mating sequence from this position is a pretty interesting one:
The black king can just be trapped in the deadly corner by the dynamic enclosure
5B2/8/8/8/8/3K1N2/8/2k5 b - - 3 2
1... Kb2 {make a run for the open} 2. Nd4 Ka3 3. Nc6 Ka4 4. Kc4 Ka3
{the knight and king are just able to close the trap again, and cut off black's escape to the safe corner, by mirroring their original position in the diagonal}
5. Fe7 {white has one free move now, which he uses to approach the Ferz}
5... Kb2 {next futile try for the open} 6. Nd4 Kc1 7. Nf3 Kd1 8. Kd3 Kc1 {and history repeats...}
9. Fd6 {next free white move}.
Apparently N+F are to weak to drive the bare King from the safe corner to the deadly one, which precludes this from being a general win. With K+W there is no safe corner, so I guess forcing your own K+N to the center by definition traps the opponent King in some corner on 8x8, and you can use this dynamic enclosure to approch the Wazir, making it generally won.
Note that when playing by octal numbers, it is possible to just enter a two-digit number in which case it moves the black King there, and leaves the other pieces where they are.
I could not find your video on general mating principles with two fairy pieces anymore! Did you remove it? I thought it was quite useful (although perhaps not complete). I am searching for a simple algorithm to decide if pairs of fairy pieces have mating potential (and if so, in which corner), for use in a general (configurable) variant-playing engine, other than building the entire tablebases. Based on your video I had formulated the following heuristics:
*) to be able to give a corner mate, you must have a piece that can move from c1 to a1 (or symmetry-equivalents) in 3 moves. To account for divergent or asymmetric pieces this would have to be made more specific in one uncapture, one non-capture and one capture.
*) In doing so it must not go over b3 (where the attacking King is supposed to be). If it must go over b3, but not a3, the other piece must be able to attack b1 (for checking) and c2 at the same time. (Or the first piece should cover c1 and c2 at the same time, but this presumably would equip it with mating potential by itself.)
*) The other piece mustbe able to attack b2, from a point that wouldnot interfere with the 3-move tour.
*) If both pieces cannot do both, and one of them is color bound, that determines the color of the corner where a corner mate is possible.
Note that in general simple leapers cannot make the 3-move tour, because they are color or meta-color alterators, and a1 and c1 have the same meta-color. Except for pieces that are both color-bound and meta-color bound, like Dababba, but then their high-order of color-binding makes them useless in the driving process. So the prospect for corner mates is in general a bit bleak. Some compound leapers are of the same general strength as simple leapers, however, because both steps they can make fall on symmetry axes, and result in only 4 moves in stead of the usual 8. Of these the King and Woody Rook have mating potential by themselves, which leaves WA, FA and FD as the interesting ones. All of these can make the 3-move tour needed to force a corner mate (and the latter two are color-bound).
Then we have the edge mates, subject to the following conditions:
*) One piece must be able to attack ('fork') a1 and c1 at the same time.
*) The other piece would have to be able to go from c1 to b1 with in 3-moves (again uncapture + non-capture + capture)
*) Neither piece must need to be on b3 for this. (This is where a pair of Knights fails.)
*) If the forking piece eeds to be on b3, it would still be possible if it could attack c2 on the move before, (or, unlikely, the piece coveri.g c1 woud do that), and it would also attack c2 from b3, (unlikely), or the piece checking b1 should do that. And either should have to be on a3 for that. (This is what makes it possible for N+W.)
Now the mate of Zebra+Ferz falls in neither category, but is a kind of 'double-edge' mate peculiar to Ferz, where you put the King on c3 and the Ferz on b2, because a Ferz can fork a1+c1 and a1+a3
at the same time. This prevents stalemate by trapping the bare King on a2-b1, and thus voids the assumption you now need to be able to mate in a single move. In stead you have all the time in the world to position your second piece, but the condition is that it should be able to attack both a2 and b1 at the same time, (and not do it from c3). But the Zebra can do this.
An interesting corollary is that in the endgame of WA and AJ (=(2,2)+(3,3) compound leaper) the mate can only be performed in the corner of
opposite color as the color-bound AJ: none of the pieces can fork a1-c1, so the only hope is a corner mate, but the AJ cannot go from c1 to a1 in 3 moves. So you are dependent on the WA, which indeed can do this. So the AJ must perform the mate on b1. This shows that the fact that you have to be on Bishop color is not so much due to the Bishop being color bound, but more to the Knight not being able to do the 3-move tour.
Of course whether the ability to perform the actual mate on a properly trapped King is a necessary condition, but not a sufficient one for the end-game to be generally won. So the bove heuristics can rule out mating potential (and then by giving the opponent a Pawn to break stalemate it might becomepossible again, as in KNNKP), but to determine general drawishness additional heuristics are needed. I get the impression that the following holds:
Two pieces with 8 move targets have no problem driving a bare King anywhere. When pieces with 4 move targets, like Ferz and Wazir are involved it, is more tricky. A Wazir is in general quite adept in driving the bare King along an edge to a corner, but a Ferz is too clumsy to do it. So if mate is not possible in all corners and you have Ferz, the end-game is not generally won. When oneof your pieces has higher-order color binding, it is hopeless.
With two 4-movers it is not always hopeless, although Ferz+Wazir only has a small number of forced mates: apair 'omni-directional paws' (cFmW) or their Berolina counterparts (cWmF) domake a generally won end-game! Could divergence be an asset in this respect?