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In regular chess no piece can checkmate the opposite king alone (i.e. without the help of his allied king). But a Maharajah can.

  • Is there a piece weaker than the Maharajah, of course invented, that can force checkmate on the opposite king alone?

  • Is there a piece weaker than the Maharajah, of course invented, that can checkmate the opposite king alone (but optimal play from the opposite king can hold a draw)?

To calculate the power of a piece:

  1. Take sum of squares attacked in all corners as $x$,
  2. Number of squares attacked when in any of 4 centre squares as $y$.
  3. The power of the piece is then $\frac{x+y}{5}$

For example the bishop: $7 \times 4$ for the corners, $13$ for the centre. $\frac{28+13}{5} = 8.2$

A piece is weaker than another if its power is lower.

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  • $\begingroup$ According to your definition the weakest piece that can force a checkmate by itself is the long-range teleporter. This piece, which I just invented, controls any square that is more than 4 but less than 7 squares away in any direction, but no other squares. When it is in the centre of the board it controls no squares and thus has a power of zero, the lowest possible power, and is therefore as weak as it's possible to be. However, if the long-range teleporter is on one side of the board and the opposing king on the other, it is checkmate in the next move. $\endgroup$ – Nathaniel Oct 19 '14 at 14:24
  • $\begingroup$ @d'alar'cop I created a new way to asses score, do you think I should keep the old one for reference? $\endgroup$ – Caridorc Oct 19 '14 at 14:27
  • $\begingroup$ @Caridorc I don't see any reason to keep the old one as well... especially since the answer has incorporated the current system $\endgroup$ – d'alar'cop Oct 19 '14 at 14:48
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    $\begingroup$ The division by 5 is pointless, since it's a constant multiple to all "powers". The result would be the same if it were just x + y. $\endgroup$ – BlueRaja - Danny Pflughoeft Oct 19 '14 at 15:44
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    $\begingroup$ I think "invented" chess questions need to be in check to keep this site interesting $\endgroup$ – skv Oct 19 '14 at 17:01
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This all assumes that one cannot have conditional-attack pieces. Like "only attacks iff the enemy king is on the left."

  1. I'm pretty sure that one piece cannot force a mate without at least power 8. A queen that attacks the squares containing white pawns:

enter image description here

  1. A queen with power 1.2 that can checkmate: She may attack only squares that 6 or 7 square "ahead" (side-wise) of her, and of those only those that share her column and the columns immediately to the left. She will attack 4 squares when on D1: C8,D8,C7,D7. In fact, the checkmate must occur with the king in H8 and the queen is in H1.

By the way, the piece you call a "Maharajah" is also known as the "Amazon".

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  • $\begingroup$ A queen with power 1/64 that *can* checkmate if the opponent king is 'smothered'. This piece does not follow the rules: quoting from the question: the opposite king alone $\endgroup$ – Caridorc Oct 19 '14 at 14:31
  • $\begingroup$ Good answer, I will wait a little in case someone else wants to answer, I will then accept. $\endgroup$ – Caridorc Oct 19 '14 at 14:49
  • $\begingroup$ thanks. I would wait a while too. There's some other people around who are really good as these chess puzzles. Joel Rondeau for example. $\endgroup$ – d'alar'cop Oct 19 '14 at 14:51
  • $\begingroup$ I think this has power 2.4..( 2+2+4+4+0)/5 $\endgroup$ – ev3commander Jul 26 '16 at 11:30
  • $\begingroup$ queen attacking 6/7 squares ahead and 1 square to the right have attack power of 0.8 but still can mate the king. (queen attacks 4 squares in left bottom corner, and none when queen is in other 3 corners or in centre). In this case, if King is in H8, and queen is at F1, queen attacks G8, G7, H8, H7; thus checkmate. $\endgroup$ – Shaun Jul 26 '16 at 16:15
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A piece with power 0 by your definition of "power": On the third rank, it attacks the entire board. On any other square, it attacks nothing.

If instead you change "power" to "sum of all spaces attacked on every square of the board", then the provably-minimal piece would be: On one square it attacks one corner in a 2x2 area. On every other square, it attacks nothing.

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    $\begingroup$ A better definition of power for this purpose maximum number of squares controlled from any square of the board(because we are free to define our pieces the way we like, and we are only interested in control from a single square). Your 4 squares in the corner is still the minimal though. $\endgroup$ – Taemyr Oct 21 '14 at 14:26
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Feel this got some more hate than it deserved, but somewhat understandable due to the flexibility of what is a new piece.

One cool one I thought of would a knight bishop where the king is in the corner and the knightop is in the third square of the diagonal. The bishop applies check and blocks a move along the diagonal and the knight traps.

Another cool variant is a pawn, rook, knight. The roownight has two options, king in the corner with the roownight checking via the knight. The rook blocks the 2 in a line and the pawn covers the other escape (this is independent of which knight check you chose). The if the king is on the top wall, you can just check with the rook from 2 squares below. Knight blocks off the escapes along the wall, pawn the diagonal escapes and rook the towards you escape.

I admit this is an openly phrased question, but I think it was cool. Interestingly I have thought of few cases where a king would give advantage over a pawn.

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