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Man versus King

Checkers and Turkish Checkers

   

• Checkers
  is quintessential 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 - a condition that does not depend on whose move it actually is: in the diagram, the player to move does not have the move!
  The only escape in a 1-on-1, whether with equal pieces or man versus king, is a tric-trac corner. To put it another way: if in the above diagram the pieces would be on the light colored squares, the king would 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. Black proceeds to promote and of course keeps the move, but since this 5x5 board has 4 tric-trac corners we may safely declare a draw.
  It will be clear from the above that a lone king in Checkers isn't very strong and may even lose against a single man. Its strength lies in teamwork
• Turkish Checkers
  is almost quintessential 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 obviously a promotion from 3 to 4 directions of movement and capture is too meager a reward to justify any major sacifice. So the king becomes 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. My conclusion is that these games are prolongued because of their respectability - they lived up to their task while strategy was in its infancy, but they aren't that great a weapon when differences in playing strength have really bottomed out

  

• 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 a 1-on-1 race, the seventh rank rule applies: a man wins if he can reach the seventh rank (from his point of view) before his opponent does
• 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

   

• Croda and Dameo have 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

  

It would seem clear that Checkers, Turkish and Armenian score below what one might expect of a man versus king endgame. Draughts and HexDame do reasonably well, Croda and Dameo top the list. By replacing sideways movement by diagonally forward movement, they bypass a notorious endgame problem in games on the straight plane.