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Mate-in-2 situation with threefold repetition

There’s something that made me think lately: Theoretically, there could be a position where the move that normally leads to the quickest mate possible would actually be a blunder.

To show this I created a game with the following position:
http://it.lichess.org/rL5wHVn0#100

Usually 51.Rb7+ would be the right move, of course, but here it leads to a draw (in a won position for white) because then the position would repeat thrice. I know this is all very theoretical since no one would ever repeat this move thrice not realizing that they can checkmate immediately after, but I just find it funny that technically 51.Rb7+ is a blunder in this game’s position. And even the Lichess computer-analysis engine doesn’t realize that, showing full advantage for white after this move which leads to a draw.
Some genius composers have gone one better. Nikita Plaksin, in 2 of his works below, gives positions where mate in 2 is a violation of the 50-move rule (and it can be proven from the position alone.) This idea is well-known in the field of retroanalysis.

Fastest is a mate in 3 for both:
1b1K3n/2pppprp/1p4p1/1p6/b1P2B2/RP2P1R1/r1PPQPPP/NB5k
1B3K2/b1pppprp/rp4p1/1P6/b2p4/1P6/1QPPkPPP/nB1R1R2
if you give away all your pieces to a lone king, and take twenty moves to do it, the engine should segfault and uninstall itself.
What exactly does the engine limitation have to do with chess theory? :P

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