Checkmating Applet

This page allows you to practice your technique for checkmating a bare (orthodox) King with a King plus one other piece. (For checkmating with a King plus two pieces, go here.) Just move a piece of the side you want to play with, and the computer will reply with the best move for the other player.

BEWARE! When the worst-case distance to mate is larger than 115, the applet might not select the correct move in positions where the mate is still more than 100 moves away, due to overflow problems.

Majors and minors

A 'major' is defined as a piece that, together with its own royal, can in general force a win against a bare royal of the opponent. Pieces that cannot do that are 'minors'. In orthodox Chess the situation is clear: KQK and KRK are always won when the strong side is on move, so R and Q are definitely majors. On the other hand, KBK and KNK are draws by 'insufficient mating material': no checkmate positions are possible at all, even not with the poorest possible moves of the bare King ('help mates'), so B and N are minors.

With some pieces there can be mate positions that cannot be enforced. With orthodox King the necessary and sufficient condition for existence of a checkmate position is that the piece can capture to two orthogonally adjacent squares. A Wildebeest (NC) can do that, but it cannot force checkmate; there aren't even any mate-in-2 positions. The number of won positions for such pieces is thus extremely small, and although it is non-zero, we count them as minors.

Coincidentally the major/minor division in orthodox Chess correlates perfectly with piece values, but this doesn't have to be the case in general. The lowest-valued major I could conceive on 8x8 is a leaper with only 5 moves (the Deva, fbrFflW, from Maka Dai Dai Shogi), which in a FIDE context probably would not be worth more than 2 Pawns. (Try it here!) And minors can be more valuable than a Queen. (Think of a color-bound universal leaper, which can teleport to any dark square.)

Whether a piece has mating potential of course depends on how the royal moves: in Knightmate (where the royal moves as a Knight) the Rook is a minor. Board size matters too: a non-royal King is a major up to 14x14, but a minor on 15x15. And on a cylinder board the Rook is a minor, as to force checkmate with a Rook requires a corner. The stalemate result also matters: in Xiangqi even a Pawn is a major, because stalemate is a win.

It can also be a bit vague what generally won means. A piece that moves as Rook in one dimension, and as Dababba in the perpendicular one (e.g. vRsD) can force checkmate on boards of any even size, except that there is a fortress draw when the bare King is on the edge that the piece cannot reach. So it depends on whether you can cut off the King from reaching that edge. (Try it!) With the perpendicular move a Dababbarider (vRsDD) you have even better chances to achieve that, and a relatively small fractions of the possible start positions is draw. (But many more than the 0.5% or so that you typically see in a generally won end-game.)

Majors that have a sub-set of the King moves (such as the Shogi generals) can often not survive on their own against a King approaching them from a vulnerable side. They cannot outrun the King, and can eventually be chased up to the edge and captured there, when they cannot find shelter near their own King. This can cause some 5-10% of the possible start positions to be draws. Even with faster pieces, such as the range-2 Rook, there are drawn positions where the R2 is cut off from its King, and 'dynamically trapped' in a corner area by the bare King on the same diagonal. There is then no way to outflank the King; it can always get on the diagonal where the R2 moves to, and will approach and eventually attack it when it doesn't move. Although the piece cannot be captured as long as it keeps moving, this will eventually lead to a draw by repetition. So there exists a continuous spectrum between minor and major.

Cornering and Stalemate

There are few chess variants where you can also win by stalemating the opponent, and none that I know where you win by driving his King to a corner. But these options provided by the Applet are useful for figuring out the reason that a given piece cannot force checkmate. If the problem lies in the tactics for delivering the final blow, such as with the Wildebeest (NC), it is usually possible to force a stalemate in or near the corner.

But even if this is possible it does not prove the piece is able to drive the King into the corner when stalemate would not be a win. Because stalemates are usually also possible along an edge, and the threat of winning by stalemate can be a great help in driving the bare King along an edge to a corner. So to know if the piece is powerful enough to drive the bare King into a corner under normal rules (i.e. stalemate being a draw), the option is provided where you win by forcing this King onto one of the corner squares.

Last revised by H. G. Muller.