Hrvoje's blog

As soon as I wrote my previous essay, I realized there are several points that require correction or further explication.  First, I checked if Stockfish would use against me the same strategy that I described for KRK and KQK, and saw that it does not, which proves I was wrong when I supposed that there are no correct strategies which are substantially different from those I described. It turns out there are, and they are faster in delivering checkmate, especially when starting position is with BK in the center and WK in the corner. The basic difference is that I assumed BK must be squeezed from the center to some edge by pushing it away from WK, by taking immediately under control the line that separates kings, using the major piece, while the engine is not afraid to push BK towards WK, and save that way a few moves needed for WK to approach BK. Second, precise and concise language in which rigorous proofs are written is known to be math. Describing KRK endgame concept mathematical...

Let me explain my point further by giving an example of what knowledge exactly are we talking about here, that engines and endgame tablebases possess, but in much more concrete form, which raises the question of software possibility to extract it from them in an abstract form, like I will present here, without using software. Pawnless endgames with major pieces, are a good start because some of them are most elementary checkmates, simplest patterns to describe, such as K+Q vs K and K+R vs K. In both cases, the lone king must be forced to the edge (or to the corner) of the board in order to get checkmated, due to a lack of other pieces (its own or its opponent’s) that could constrain its mobility additionally in sufficient way, if they were present. This can always be achieved by squeezing it from the center, by placing our king in opposition (an even simpler concept which also requires explanation/description), and checking it from the side, with the major piece. Actually, this is need...