White to move.
This is a famous Frisian draughts endgame. In 1976, H. Walinga even wrote a little book about this endgame, with the tentative conclusion that it was a draw. Now you might wonder how such a ridiculously simple looking endgame might be worth more than a few lines of analysis, let alone a whole book. Isn't this a simple draw?
Not so fast! In Frisian draughts, 2 kings win against 1 king since the majority side can always trap the lone king owing to the orthogonal and diagonal captures. So it must be a simple win then?
Not so fast again! There are 2 little rules that make it a lot harder for the majority side to actually win this endgame. The first rule is that a side with both kings and men cannot move the same king more than 3 consecutive moves. After that, a capture with that king or a move by any other piece is mandatory. This allows for some subtle delaying tactics by the minority side. E.g. if the majority side has just played 3 consecutive moves with the same king, then an attack on that temporarily immobile king can often not be answered. The second rule is that as soon as a 2 kings against 1 king endgame appears, the majority side has exactly 13 plies to win. In rare cases this can not be enough to win.
My universal engine <Mistral> (still experimental but supporting every legal draughts variant) does not know these 2 little rules yet, but it does know the orthogonal capture rule. So it should analyze this position to be a simple white win. Right?
Not so right after all. Even without the 3 consecutive move rule and the 13 plies rule, black has a lot of subtle delaying tactics that it took <Mistral> 10 minutes and a nominal search depth of 39 plies to resolve the above diagram to a win! Here's the longest line of defense:
[FEN "W:W28,K46:BK43"]
1. 28-22 43-38 2. 46-41 38-16 3. 41-10 16-2 4. 22-18 2-35 5. 10-14 35-8 6. 14-28 8-30 7. 28-37 30-35 8. 37-26 35-2 9. 26-31 2-30 10. 18-12 30-48 11. 31-13 48-43 12. 13-19 43-25 13. 19-46 25-34 14. 12-8 34-1 15. 46-10 1-29 16. 8-3 29-15 17. 10-23 15-42 18. 23-1
18... 42-26 19. 1-12 26x8 20. 3x12 *
You might wonder why 18... 42-26 if forced in the second diagram. Just look at it carefully and see what all the orthogonal captures can do! E.g. 18... 42-15 19. 3-12! 15x11 20. 1x21.
Note that it took white 11 king moves to actually promote his man when it was only 4 moves away from the promotion line. In particular, the 5 consecutive white king moves (moves 5-9) are not allowed under the 3 consecutive king moves rule. If we write Frisian(K) as the Frisian rules with K allowed consecutive king moves, then we know that the above endgame is a win for Frisian(5) and higher K. It's an open question whether the endgame is won for the official K=3 rules.
Given the hardness of the partial analysis of this deceptively simple looking endgame, the full analysis (with the 3 consec. and 13 plies rules) might take far too long for a normal forward search. So I would have to build an endgame database. In this case, one actually needs to build 4 endgame databases, with the white king having 3, 2, 1 or 0 moves left. Still very doable and it should take only a few minutes to generate them once I have that programmed. But larger databases need 16 different versions if both colors have both a man and a king. That would probably limit the Frisian draughts databases to 6 or 7 pieces with current technology.
