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We're considering basics, so let's put two opposing men on the boards:
- The straight plane has no forced progress and has one-sided opposition: the player to move cannot get out of it, while his opponent can either keep opposition or move forward.
- The oblique plane has forced progress and absolute opposition: the player to move must sacrifice the man.
- The hexagonal plane has forced progress too, but has no opposition whatsoever: the player to move cannot be stopped.
The diagrams above represent the situation in Turkish Checkers (left), Anglo-American Checkers, Shaski and Draughts (middle) and HexDame respectively.
To enlarge the field, we'll show one-on-one in games that employ both planes: Dameo and Armenian.
The existence or non-existence of 1-on-1 opposition is not a criterion for quality but an indication of character. Games that have it, naturally offer less freedom of movement and more emphasis on blockade as a means to win. Games that don't, are not devoid of opposition in a wider sense but they tend to rely more on breakthrough and promotion and usually require weak men and strong kings to prevent drawishness.
Here we can label a quality aspect: a lone king should at least be able to trap a lone man.