2

Consider this (illegal) position.

[FEN "5n1k/3p1p1p/3PpPpP/4P1P1/1p1p4/pPpPp3/P1P1P3/K1N5 w - - 0 1"]

If we do not consider the position's illegality, and the fact that it is clearly unwinnable by eiter player (and therefore an automatic draw even if either of the players resgined, ran out of time, etc), then this position has an interesting property. Regardless of what move every player does (which is obvious in this case, since there is always only one legal move), the position results in forced threefold repetition in 4 moves.

Now here arises a question, basically a problem creation: Which legal position has the least amount of moves to make threefold repetition, assuming no player wants to repeat the positions?

3 Answers 3

4

This legal position should fit the bill for the least amount of units needed and the least amount of moves. There is one king, one bishop, and four pawns for each side - a total 12 pieces. The threefold repetition is forced no matter what moves the players make since they only have one legal move each time. It's basically your idea in a legal and lighter setting.

[FEN "5b1k/4p1p1/4P1P1/8/8/1p1p4/1P1P4/K1B5 w - - 0 1"]
2

The questioner invited us to ignore illegality or dead position rule.

Title: question: which legal position has the smallest number of moves in a "forced loop"?

Forced draw by repetition in the shortest number of moves. Well that's 4 single moves = 2.0 double moves. Same number of units as Rewan Demontay, but slightly lighter position:

[FEN "5b1k/4p1p1/4P1P1/5pP1/5PpK/6P1/8/8 w - - 0 1"]

Eventual draw by repetition, also ignoring 50/75 move rules Well just two kings on the board is enough. There are 3,612 (= 3655 + 2458 + 4*60) arrangements of the two kings. Each might be achieved with either white or black to play, and appear twice. So after at most 14,448 single moves (=7,224.0 double moves) a position will occur for the third time. Does the connectedness of the position graph allow this value to be achieved "in practice"? Can the draw be postponed this long? I don't know, but I guess yes.

1

This is an even lighter position that's sure to eventually produce a triple repetition if the 50- or 75-move rule doesn't end the game sooner:

[FEN "4k3/8/8/1p2p2p/1P2P2P/8/8/4K3 w - - 0 1"]

one can also mix and match:

[FEN "5bk1/1p2p1p1/1P2P1P1/8/8/8/8/4K3 w - - 0 1"]

(Without the b-pawns it's still a dead draw but the game might end by stalemate instead of repetition.)

1
  • It seems the OP isn't looking for the most economical position but for the one with the least moves before a repetition inevitally occurs (4 moves, as per the other answer, obviously cannot be beaten).
    – Evargalo
    Feb 1, 2022 at 15:11

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