Explanation of the unique triangle

[guyhaw]

I agree with hgm that the KQQQQQK DTM EGT is of little value. The DTZ EGT is much more compact and more swiftly generated. Also, as maxDTZ =< 3 (keep sac'ing Qs), the WDL EGT with a modicum of search should suffice.
I think we have already agreed that an advantage of the WDL EGTs is that they are all that is need to generate dependant DTZ EGTs.

A requirement of an EGT is that it should be manifest, i.e. very clear, that it is correct. I am not sure that this can be said of an EGT which is underpinned by any degree of chessic logic.
g

[h.g.muller]

...
But I doubt it will on the average give better results than doing a normal alpha-beta search and relying on the hash table.

Oh yes, it will. Try finding a checkmate in a 3-men end-game by alpha-beta + hashing, for a not-too-powerful piece. I have tried this many times, even with Joker, which has a proven efficient hashing scheme (it solves Fine #70 within one second). For example, when I try King + Bison vs King (Bison is a compound (1,3) + (2,3) leaper), even when I position the attacking K+Bi in the center of a 10x8 board, it takes Joker a depth of 26 and 40 minutes to get the first mate score. When I start in a less favorable position, where the defending King is in the center and the white pieces on the edge, it has not found a mate even after 3 hours.

Compare that to the ~2 seconds it takes to build the KBiK DTM tablebase...

Forward search is an extremely inefficient way to build tablebases.

[syzygy]

...
But I doubt it will on the average give better results than doing a normal alpha-beta search and relying on the hash table.

Oh yes, it will.

Ah, I'm a bit surprised that that last sentence of mine is still there. I thought I had removed it after deciding that indeed it should help in some positions. But maybe I decided that only after posting

Forward search is an extremely inefficient way to build tablebases.

Yes, but as long as the evaluation function happens to point the way this is not a problem. For positions in which the eval does not have a clue (i.e. it knows the position is better, but it doesn't know how to proceed so the search ends up shifting around pieces without a plan), your idea could indeed make the difference.

[h.g.muller]

Well, this is where you need tablebases in the first place. For positions that engines know how to win easily by itself, even at low depth, they offer no advantage. But there are many end-games with Rooks + Pawns or Queens + Pawns, where a simple evalution based on material and piece-square tables is not better than a random guess w.r.t. WDL state.

[syzygy]

szyzygy - do you have a source/reference for that neat formula for 'Q' which enumerates the positions of like men?

I just noticed this old post in which guido gave the same formula.

While I agree with guido that the inversion process is a more complicated and less fast, it is certainly a lot easier than the general problem of solving diophantine equations in N integer variables.