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We assume standard (P1BN3R5Q8) value (personally I prefer 1,3,3,4.5,9 but so there).

To get a drawn position with maximum material difference, not caring about that it's illegal, we just have to plaster the field with bQs and shield the wK in the corner with a bR diagonally, plus bB or bN at the sides. This position is an immediate stalemate, no matter who has the move. (Value: 3+3+5+(64-5)*8=483)

"Improve" this position, still maximum material difference, such that the position can be played forever with help play (ignoring the dead, repetition, and 50 move rule which will cut this "play" short in this order!). This includes the possibility that Black has enough at some time and stalemates White (or self after capture) after all. Stalemate just may not be forced. Feel free to choose who has the move, but choose wisely (insert fiendish laughter). (Feel also free to give an additional position where no side can force a stalemate on self or other).

For FEN convenience, you may just omit the bQs from the diagram.

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3
  • You may get more answers if you put a chess board of your position in the question :)
    – Benjamin Wang
    Oct 5, 2022 at 22:32
  • I wonder what 1,3,3,4.5,9 means though
    – David
    Oct 6, 2022 at 17:13
  • @David: P=1,N=B=3,R=4.5,Q=9
    – Hauke Reddmann
    Oct 6, 2022 at 19:04

2 Answers 2

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If I count right we actually do a bit better than Hauke Reddmann's construction by giving White a pawn and the initiative:

[FEN "kqqqqqqq/Pqqqqqqq/qqqqqqqq/qqqqqqqq/qqqqqqqq/qqqqqqqq/qqqqqqrb/qqqqqqbK w KQkq - 0 1"]

    1.axb8=R+! Ka7! 2.Rxb7+! Ka8! 3.Ra7+

White has an immediate forced draw by 1 axb8=Q+!, but play may instead continue 1 axb8=R+! Ka7! 2 Rxb7+! Ka8! 3 Ra7(b8)+ etc. as shown, with draw by perpetual check; none of Black's (or for that matter White's) alternatives actually win, but the "!" are for the unique moves that allow the game to continue forever.

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  • 2
    Clever. The position is fundamentally different from mine in the sense that in mine, White can't even "commit suicide" if obliged so (i.e Noam's position isn't "dead"), but I never excluded that, so it's perfectly valid as answer. (For bonus points, compute how long the game maximally can go on under threefold repetition and 50 move draw rules - the rook can gobble a lot of queens before it's a forced mate :-)
    – Hauke Reddmann
    Oct 11, 2022 at 7:02
  • Why can’t you swap bKa8 with bQa1, and replace wPa7 with wQ? Then after e.g. 1.Qxb8, play can continue forever with 2 queens circulating round a8,a7,b8?
    – Laska
    Oct 12, 2022 at 5:11
  • That position is not as easily drawn (Black can try to get rid of the other bQ's on the h2-c7 diagonal and play Bg3# before wQ reaches the a1-corner), and anyway it has a smaller material difference -- we were to maximize the disparity, not the total material.
    – Noam D. Elkies
    Oct 12, 2022 at 12:31
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I don't think this position can be improved, but feel free to show me the contrary (note that the double check is retroillegal too, but who cares in an illegal position!):

[FEN "Krkqqqqq/q1pqqqqq/pprqqqqq/qqqqqqqq/qqqqqqqq/qqqqqqqq/qqqqqqqq/qqqqqqqq w KQkq - 0 1"]

Game may continue 1.Kxa7 Rb8+ 2.Ka8 Rb7+ forever, until Black selfstalemates with Ra8+ or Ra7+ at any point.

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