White to play - Draw* (instead of Fine's White Wins)

*Many of the positions in this ending including the starting position are objectively winning for White, but are drawn because Black will be able to claim the 50-move rule. I've tweaked the Nunn convention a bit for this ending.
(!) indicates the only move that would win or draw in the absence of the 50-move rule.
?! indicates a move that would change a draw to a loss or a win to a draw in the absence of the 50-move rule.
! for Black indicates the only drawing move with the 50-move rule.

1.Kf4 1.Nd4 is the fastest mate (in 87), but Black will hold by the 50 move rule before then. 1...e5+ 2.Kg4?! 2.Ke3 (!) is the only move that leads to a win (this time mate in 105!), but again the 50-move rule will come into effect. After the text, the position is an objective draw. 2...Ke6?! Without the 50-move rule 2...d5 (!) is the only drawing move. Black will play 3...e4 and even if the position wasn't drawn on its own, the pawn on e4 is beyond the second Troitsky line, so Black should even have the 50-move rule to fall back on if he didn't play precisely. 3.Ng5+(!) Kf6! 4.Nce4+ Ke7! 5.Kf5 d5! 6.Nc5(!) Kd6! 7.Nge6 e4! crossing the 2nd Troitsky line 8.Kf4(!) Ke7! 9.Ke5 Fine stops here claiming a win for White. It is mate in 75 per the tablebase, but after White collects the c- and d-pawns it will take him more than 50 moves before Black will have to play ...e3. Playing down the optimum line for both sides 9...Kf7! 10.Nf4 Ke7 11.Ng2 Kf7 12.Ne3 Ke7 13.Ne6 Kd7 14.Nf5 Kc8 15.Kd6 c5! 16.Kxd5 c4 17.Ne3(!) c3 18.Nd4 Kd7 19.Kc4 c2 20.Ndxc2 Here it is mate in 64, but Black won't have to move his pawn until the very end. 20...Kd6 21.Nd4 Ke5 22.Ne2 Kd6 23.Kb5 Ke5 24.Kc5 Ke6 25.Kd4 Kd6 26.Nf4 Kc6 27.Ke5 Kd7 28.Kd5 Kc7 29.Ke6 Kc6 30.Ne2 Kc5 31.Kd7 Kb6! 32.Kd6 Kb7 33.Nd4 Kb6! 34.Kd5 Kb7 35.Ke6 Ka6 36.Ne2 Kb7 37.Kd6 Kc8 38.Nd4 Kd8 39.Ne6+ Ke8! 40.Ng5 Kd8 41.Nf7+ Ke8! 42.Ke6 Kf8 43.Nd6 Kg7 44.Kf5 Kh7! 45.Kf6 Kh6! 46.Ndf5+ Kh5! 47.Ng3+ Kh4! 48.Ne2 Kh5! 49.Kf5 Kh6! 50.Nf4 Kg7! 51.Ke6 Kf8! 52.Nh5 Ke8! 53.Ng7+ Kd8! 54.Kd6 Kc8 55.Ne6 Kb7 56.Kc5 Ka6 57.Kc6 Ka5! 58.Nd4 Kb4 59.Nb5 Ka4 60.Kc5 Kb3 61.Kd4 Kb4 62.Nc7 Ka5 63.Kc5 Ka4 64.Ncd5 Ka5 65.Nb4 Ka4 66.Nc6 Ka3 67.Kd5 Kb3 68.Kd4 Ka3 69.Kc3 Ka4 70.Kc4 This position is mate in 14, but the last capture was on move 20, so 50 moves have been reached without a capture or pawn move, so it is a draw.

Analysis using chess endgame tablebase

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