King versus man+king

If two kings can trap a lone one, as in Checkers, in Turkish, in Armenian and in Dameo, then the key question concerning the above endgame, is whether it can be converted to a 2x1 kings endgame.

King v. man+king checkers
diagram 1
It will be clear from diagram 1 that black - to move - has the choice between losing and reaching a draw, so saying that the endgame is unconditionally won is stretching it a bit.
On the other hand, you might have trouble working your way into such a predicament, having the benefit of two pieces for 'keeping the move'. Usually, it would seem, the conversion and thus the win can be secured.
If in doubt, consult your local Checkers site - I'd hardly be breaking new ground here.

The same holds for Turkish Checkers. A man can move sideways, and can move onto a rank covered by the opponent's king along the side columns. The king therefore must oppose the man to have a chance. It would seem that - black to move - the situation in diagram 2 is one white might want to avoid, and the situation in diagram 3 one black might want to avoid.
So lets assume for argument's sake that it's white to move in both diagrams.

King v. man+king turkish
diagram 2
King v. man+king turkish
diagram 3

Diagram 2
White moves say dc1 and black can progress with 1... d54: white cannot move back to d1 but he can block the man with 2.c13.
Black moves 2... d68. Now white must allow the man access to either d3 or c4. This is the general idea of progress towards the side column and down, with the black king either attacking its opponent or covering its man. Clearly this is a win.

Diagram 3
White moves say 1.da1 and the black king must vacate the d-column or 2.a16 would trap the man and force a draw.
After 1 ... dh5 however black has his own threat: white cannot move a15 or a16, and any move on the back rank except 2. ad1 will result in the black king moving to h8 to cover the man from behind. Since this allows promotion, white is forced to keep attacking the black man.
The black man thus can allow itself to be driven to a6 after which black interposes the king again: 5... ha5, see diagram 4.

King v. man+king turkish
diagram 4
King v. man+king turkish
diagram 5

White moves anywhere on the back rank, say ah1, and black takes the corner, diagram 5. Now nothing can prevent the black man from promoting on a1 or b1. Usually, it would seem, the conversion and thus the win can be secured.

Armenian is Turkish with diagonal movement: capture remains straight only. In the above example, it's black rather than white who may profit from this additional freedom, so in Armenian the conversion is even less problematic.

The 'Armenian' king, but with a different man, one for which the option to move sideways has been replaced by the option to move diagonally forward. In terms of initial appreciation of the positions in diagram 2 and 3, nothing much changes. The black man usually needs access to a corner to promote. New are the facts that:

  • it cannot reach one, once it has crossed both main diagonals.
  • unless covered, it must approach via b2 or g2 or it will be trapped by the king in the corner.

King v. man+king dameo
diagram 6

To illustrate the some of the consequences, consider diagram 6, where the black man is beyond reaching a corner, white to move.

  • 1.da1?-d32 (threatening d4a1) and now 2.ad1-d48, while other moves are followed by either 2... d4a1 or indeed promotion, either way securing a black win.
  • 1.dh1?-d32, 2.ha1-d4h8! and black wins.

So allowing black access to the second rank isn't such a great idea. White can keep a draw by:

  • 1.d1c2-d4a1, 2.cb2-a12, 3.b2c1 and the black man cannot move to d2(e2) because of 4. cd1(e1).

Draughts, Shaski, Spanish and Hexdame do not even qualify, so in this category they're the most drawish. In Checkers and Dameo draws are possible but rare. In Turkish and Armenian the endgame is an unconditional win, which is ironically due to sideways movement.