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If there is a possible capture two or more fields away from a king like b--w- or b-----w- are those count as a compulsory/necessary jumps or not?

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It depends on the checkers/draughts variant that you are playing:

  • For American checkers / Britisch draughts (which are two names for the same game) and Italian checkers, kings are short-ranged and cannot jump over empty squares.
  • For all other variants (International/Russian/Spanish/Czech/Frisian/Thai draughts and Pool checkers), kings are long-ranged and can jump over empty squares as you indicated.

NOTE: in fact, for all but one (Thai draughts) of the long-ranged king variants, kings can also land on a sequence of adjacent empty squares behind a captured piece. In your notation, this would be patterns of the form B- - -w- - -, where the black king can land on any of the three - squares behind the white man.

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