1

I am curious if there is a known position with the largest material imbalance that, no matter who it is to move, the weaker side can hold a draw.

4

One side with fully promoted pawns and all his material and the other side having nothing but his king. Just stalemate the king in the corner with a bishop, knight and rook, place your other material to block off checkmates and you have a forced stalemate.

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4

Here's a humorous, uncredited example I found in Lasker's Manual of Chess. However, a search revealed that it was created by Ludwig Meyer in 1886.

[FEN "b2b3R/1np2pp1/1p3k2/n2KN3/p7/5pN1/P1p3p1/2B2rqr w - - 0 1"]

1. Ng4+ Ke7 2. Nf5+ Kd7 3. Ne5+ Kc8 4. Ne7+ Kb8
5. Nd7+ Ka7 6. Nc8+ Ka6 7. Nb8+ Kb5 8. Na7+ Kb4
9. Na6+ Kc3 10. Nb5+ Kd3 11. Nb4+ Ke2 12. Nc3+ Kf2 (12... Ke1 Nd3#)
13. Nd3+ Kg3 14. Ne4+ Kg4 15. Ne5+ Kf5 16. Ng3+ Kf6

A draw by perpetual check, against all odds! Black has all the pieces, White only a few. Every move is forced.

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  • Great humorous problem. This may be called the “haunting knights“ XD. Just wondering, Isn’t it possible in this site to embed the chessboard position image as well through some site? Would be nice to see the position without needing to import the FEN notation. – Cedric Zoppolo Apr 7 at 5:38
  • Nevermind my comment about board rendering. I figured out the render only occurs on complete site and not mobile version. – Cedric Zoppolo Apr 7 at 6:15
2

Like @Matthew Liu said, it is possible to shove the king in corner and place all of one side’s material in a such a way that neither side can win, no matter who is to move. Going by traditional values, that means that maximum possible imbalance is worth 103 points.

8/8/8/8/6rq/5nr1/qqqqb2b/qqqqk1nK w - - 0 1

However, if you want a position where neither side is already stalemated, hete is a king-only position with an imbalance of 63 points.

8/8/8/8/8/bpp5/brrppp1n/nqqqqk1K w - - 0 1

With more than just a king, this position has a material imbalance of 68 points

7n/8/8/8/1p6/brpp4/qqkrp1K1/qqqbB2n w - - 0 1

Lastly, akin to @Raymond Hancock’s answer, here is the longest known problem in which White has minimal force against all of Black’s forces

[Title "Alexey Khanyan, SuperProblem 4/13/2009"]
 [FEN "8/ppp1P3/3p4/7n/r7/1p4p1/brpp2Kb/n1q1k3 w - - 0 1"]

1. e8=Q+ Kd1 2. Qxh5+ Ke1 3. Qe8+ Kd1 4. Qxa4 Qb1 5. Qg4+ Ke1 6. Qe4+ Kd1 7. Qf3+ Kc1 8. Qf4 d5 9. Qe3 Kd1 10. Qf3+ Kc1 11. Qf4 d4 12. Qg5 Kd1 13. Qg4+ Ke1 14. Qe4+ Kd1 15. Qf3+ Kc1 16. Qf4 a6 17. Qg5 Kd1 18. Qg4+ Ke1 19. Qe4+ Kd1 20. Qf3+ Kc1 21. Qf4 a5 22. Qg5 Kd1 23. Qg4+ Ke1 24. Qe4+ Kd1 25. Qf3+ Kc1 26. Qf4 a4 27. Qg5 Kd1 28. Qg4+ Ke1 29. Qe4+ Kd1 30. Qf3+ Kc1 31. Qf4 a3 32. Qg5 Kd1 33. Qg4+ Ke1 34. Qe4+ Kd1 35. Qf3+ Kc1 36. Qf4 b6 37. Qg5 Kd1 38. Qg4+ Ke1 39. Qe4+ Kd1 40. Qf3+ Kc1 41. Qf4 b5 42. Qg5 Kd1 43. Qg4+ Ke1 44. Qe4+ Kd1 45. Qf3+ Kc1 46. Qf4 b4 47. Qg5 Kd1 48. Qg4+ Ke1 49. Qe4+ Kd1 50. Qf3+ Kc1 51. Qf4 c6 52. Qg5 Kd1 53. Qg4+ Ke1 54. Qe4+ Kd1 55. Qf3+ Kc1 56. Qf4 c5 57. Qg5 Kd1 58. Qg4+ Ke1 59. Qe4+ Kd1 60. Qf3+ Kc1 61. Qf4 c4 62. Qg5 Kd1 63. Qg4+ Ke1 64. Qe4+ Kd1 65. Qf3+ Kc1 66. Qf4 c3 67. Qg5 Kd1 68. Qg4+ Ke1 69. Qe4+ Kd1 70. Qf3+ Kc1 71. Qf4 d3 72. Qe3 Bg1 73. Kxg1 Kd1 74. Qf3+ Kc1 75. Qf4 g2 76. Kxg2 Kd1 77. Qf1#
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1

Regarding wins, and not draws, I remember a joke problem by Otto Blathy where black has their entire army, but the pawns trap all the pieces and black can only play Qa1 and Qa2 repeatedly. White promotes their single pawn to a knight, forces black to make a move that strips their king’s protection, and then checkmates black.

[Title "Otto Blathy, The Chsss Amateur 1922"]
[FEN "8/8/8/2p5/1pp5/brpp4/qpprpK1P/1nkbn3 w - - 0 1"]

1. Kxe1 Qa1 2. h3 Qa2 3. h4 Qa1 4. h5 Qa2 5. h6 Qa1 6. h7 Qa2 7. h8=N Qa1 8. Nf7 Qa2 9. Nd8 Qa1 10. Ne6 Qa2 11. Nxc5 Qa1 12. Ne4 Qa2 13. Nd6 Qa1 14. Nxc4 Qa2 15. Na5 Qa1 16. Nxb3#

Entry #270 in Tim Krabbe’s Chess Diary shows a problem which is pretty close to what you're asking for, but it's a win and not a draw. It is a problem is which White faces nearly all of Black’s forces.

[Title "Marek Kwiatkowski, The Problemist 1992, Mate In 29 Moves"]
[FEN "3n4/rBp1p3/2P5/2PK4/k2N4/pp2R3/bppB2Rp/q1n1r1b1 w - - 0 1"]

1. Rg4 h1=Q+ 2. Nf3+ Kb5 3. Rb4+ Ka5 4. Rbe4+ Kb5 5. Nd4+ Ka4 6. Ne2+ Kb5 7. Nc3+ Ka5 8. Nxa2+ Kb5 9. Nc3+ Ka5 10. Ne2+ Kb5 11. Nd4+ Ka4 12. Nf3+ Kb5 13. Rb4+ Ka5 14. Rbxb3+ Ka4 15. Rb4+ Ka5 16. Rbe4+ Kb5 17. Nd4+ Ka4 18. Ne2+ Kb5 19. Nc3+ Ka5 20. Na2+ Kb5 21. Ba6+ Rxa6 22. Nc3+ Ka5 23. Ne2+ Kb5 24. Nd4+ Ka4 25. Nf3+ Kb5 26. Rb4+ Ka5 27. Rb6+ Ka4 28. Rxa6+ Kb5 29. Ra5#
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1

For a draw by insufficient mating material (rather than stalemate), one possibility is king and nine bishops, all on squares of the same colour (eight of them promoted) versus bare king.

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0

Using a different idea, it is trivial to generate a stalemate that is 26 pawns in material behind for one side by forming an indestructible pawn chain (with only one piece to capture a pawn and white with a defender for that).

[FEN "r2qkb1r/4p3/3pPp2/2pP1Pp1/1pP1B1Pp/pP5P/P7/4K3 w - - 0 1"]

Really, either idea (isolated bare king against the world or indestructible pawn chain) requires cooperation from the other side. There is no way for these formations to happen unless the opponent is being very, very helpful. I think a much more interesting question would be, "What is the biggest material imbalance for a position that is drawn for either side that happened in a real game?"

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  • 2
    Black can take on e3 here and open up the chain. This is not a draw. – fuxia Jun 30 at 2:30
  • 3
    It seems that Black wins with 1...Qc8, 2...Qxe6 and 3...f5 or 3...d5 depending on how White captures the queen. – Evargalo Jun 30 at 6:27

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