How many white-to-move positions are required to prove this endgame a draw?
2
100Ṁ74
2100
9%
< 10^3
34%
< 10^5
50%
< 10^7
66%
< 10^9

Inspired by this question.

This question will proceed on the assumption that the position depicted is a draw, and that it's possible to prove this by enumerating a set of white-to-move positions that:

  1. Includes the above

  2. Includes all one-ply follow-ons with colors flipped

  3. Is such that for any position in the set, there is a move for white such that any response to the move by black leads back to a position in the set.

This question asks, what is the minimal size of a set with this property?

Note that "position" includes castling and en passant data, but not half-move counter data.

Individual answers resolve when proof is provided in the comments that they should resolve a particular way.

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