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Man versus king
Obviously the outcome of this endgame depends - if not on opposition - on position. Its clear that conditions for a man on his own back rank differ from those of a man one step away from promotion. Here the focus should not only be on a man and a king in direct opposition, but more generally on the conditions - if any - under which the king can win. Lets start with the simplest structured games.
Checkers and Turkish Checkers
is the essential game in the oblique plane: it takes the simplest form of forward movement and capture and rewards promotion with the same options backward. As a result having 'the move' is everything. Having the move means being able to take opposition: in the diagram, the player to move does not have the move!
The only escape is a tric-trac corner. To put it another way: if in the above diagram the pieces were in a similar position on the light colored squares, the king would even lose (!) if he were to move. As it is he can retreat to the back rank and come up the side if black takes opposition. So a lone king in Checkers isn't very strong, and if unable to reach a tric-trac corner, it may even lose against a single man. Its strength lies in teamwork.
- Turkish Checkers
is almost the essential game in the straight plane: it takes the simplest form of non-backward movement and capture and rewards promotion with the same options backward ... and a bonus. A very understandable bonus because a promotion from 3 to 4 directions of movement and capture is a rather meager reward. So the king became long-range, moving as the rook in Chess. Good move!
Despite this it cannot win against a single man. This was perceived as a problem. A wise man was consulted and he came up with a brilliant solution: let's declare it a win! Bad move.
Draughts and Hexdame
In direct opposition a man loses if he must move. Having the move as in Checkers plays less of a role, because in the majority of cases, a king can turn the tables with a tempo move. The tric-trac corner is more than a doghole, it's an underdog hole and the graveyard of many a man. That's in fact where the above situation would end if it were white's turn.
In HexDame the king is stronger: not only can it trap a man in the above manner, it can do so till the very last moment because unlike Draughts it can cover the back rank while standing on it. In the bottom corner a white king covers both sides of the back rank up to (but excluding) the corners. If a man comes down the side, the king can trap it by taking the corner. In a race for promotion, corners are often the best option.
Dameo and Armenian
Dameo has forced forward progress, so obviously a man cannot move onto a rank covered by a king other than along the side. This eventually boils down to the situations depicted above.
Note that if it's white's turn, the situation on the left is a draw. White therefore should not take the corner while black is still on the third rank.
In Armenian the situation on the left, white to move, is also a draw, but with black to move both situations are a draw rather than a win. Black can only promote in a corner and if white prevents it in the above manner, black simply moves sideways. This man may be too strong for the game's good.