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And I don't know whether it is a bug or not, but I think the crux of the issue is whether you are allowed to move through the same space twice in one move.
I would have guessed that you would be allowed to, since you aren't trying to move through a piece that you captured earlier in the turn, but I'm not sure.
The rules I've read on Wikipedia specifically say you can move over a space you've moved over before but not a piece. I guess some draughts variants don't allow this and it's been assumed for Dameo.
Would be useful to have Christian's input on this.
Well, it's a bug. The king must carry on capturing to h1. I'm puzzled as to why it appears in this particular situation. There was a prior issue regarding roundabout capture but that one was fixed.
The rule is the same as in International Draughts (but that might not help everyone ;-).
@christian the bug may be because there is also the option at that point to capture at the a column. Which is of course forbidden by the rules.
The code must be somewhere checking that capture at column a, reversing direction from previous capture, is forbidden and accidentally forbids the other capture, too, ending the move.