What is the theoretical maximal material difference of a dead draw which is not a stalemate?

I have noticed the following example, which should be a dead draw:

I am wondering what is the theoretical material difference of a dead draw which is not a stalemate? (I am not asking about agreed draws.) Apparently we could not add more rooks to the diagram as all white pawns have not been promoted.

By the way, the game above is not drawn by the insufficient material rule, as white can theoretically win the game if black makes a blunder such as capturing the rook.

• I believe if you add a white queen on a1 or b1 or b2 and a black knight on b5 it would still be draw (if you capture on a3 or c3 I am going to recapture with the knight). Jan 15, 2019 at 20:31
• dead draw = Impossibility of checkmate? Why would it be a dead draw? a checkmate is possible black just does not blunder, this would be draw on agreement or threefold repetition or fitfy-move-rule. Or do you mean fifty-move-rule by dead draw? Jan 16, 2019 at 14:34
• @KamiKaze, I agree that the phrase "dead draw" is not ideal here. What I mean is that the game is clearly a draw, except if one side purposefully make a suicidal move such as capturing the rook in the diagram above. Jan 16, 2019 at 15:42
• I think the term should be "forced draw" rather than "dead draw". In a dead draw, no legal sequence of moves could result in a victory by either side, but with White to play in the above example [or Black to play, making an arbitrary king move], 1. Re1? bxf2+ 2. Ka1 fxe1=Q++ would be a victory for black. Jan 16, 2019 at 16:00
• @CedricMartens: it couldn't have got there. Usually with construction problems it is required that the position would actually be reachable by a series of legal moves from the starting position. Jan 17, 2019 at 9:43

With white to move the following position is a draw with the maximum possible material difference. The position is not currently stalemate but will be with correct play from white. If white plays Kh1 any move from black will result in stalemate.

``````8/7b/8/3n4/q3k3/8/qqqq1rKn/qqq1qrb1 w KQkq - 0 1
``````

(Another possibility would be a position utilizing a forced draw due to the 50 move rule)

``````[fen ""]

1. a4 b5 2. b4 bxa4 3. c4 c5 4. d4 cxb4 5. e4 d5 6. f4 dxc4 7. g4 e5
8. h4 exd4 9. Ba3 g5 10. Nc3 gxh4 11. Qb3 f5 12. Kf2 h3 13. Kg3 h2
14. Bd3 Qa5 15. Kh4 dxc3 16. Kg5 h5 17. Kg6 cxb3 18. g5 Rh7 19. Ra2 Rc7
20. Bc4 Rxc4 21. Kh7 Bd6 22. g6 fxe4 23. Kg7 hxg1=Q 24. Kh7 h4 25. Kg7 h3
26. Kh7 h2
27. Kg7 bxa3 28. Kh7 bxa2 29. Kg7 Qgb6 30. Rg1 hxg1=Q 31. Kh7 Nc6
32. Kg7 Nd8 33. Kh7 Nf6+ 34. Kg7 Nd7 35. Kh7 a1=Q 36. Kg7 c2+ 37. Kh7 Qab1
38. Kg7 Qb8 39. Kh7 Q1b7 40. Kg7 c1=Q 41. Kh7 a2 42. Kg7 a1=Q+
43. Kh7 Qab1 44. Kg7 Qb1b6 45. Kh7 a3 46. Kg7 a2 47. Kh7 a1=Q 48. Kg8 Qab1
49. Kg7 Q1b5 50. Kh7 Nf6+ 51. Kh8 Bd7 52. Kg7 Nc6 53. Kh8 Be7 54. Kg7 Bd8
55. Kh8 e3 56. g7 Ne4 57. Kh7 Qab4 58. Kh8 a5 59. Kh7 a4 60. Kh8 a3
61. Kh7 a2 62. Kh8 Qxf4 63. Kh7 a1=Q 64. Kg8 e2 65. Kh8 Nc5 66. Kh7 Re4
67. Kh8 Re6 68. Kh7 Qf4b8 69. Kh8 Ra6 70. Kh7 Qb6a7 71. Kh8 Nd4
72. Kh7 Rad6 73. Kh8 e1=Q 74. Kh7 Qg1e3
``````

White can force a draw from this position with 75. g8=Q+ and perpetually check the black king. The end position given above (before the pawn promotes) is the moment of maximum material difference in this forced draw.

• This should be the maximal material difference. Unless there is a dead draw which is not a stalemate where black has all the pieces as above and white has only the king. I don't believe it is possible though. Jan 16, 2019 at 3:35
• I don't see why would it be a draw. There is a risk of stalemate, but black could win. Maybe you could add a bit of explanation. Jan 16, 2019 at 7:13
• It's a draw because White can promote and give a perpetual, but the position before the promotion is given because that's when the material difference is biggest!
– JiK
Jan 16, 2019 at 12:10

With white to move, the following position is a draw:

I think it's reachable from the original position, although it would be difficult. I'll let you know if I can.

• Heh, that idea works too, but I'm not sure if the OP wants to include perpetual check or not. Jan 15, 2019 at 20:51
• Yeah, I'm not sure, either, but since he didn't specify, I felt obligated. Jan 15, 2019 at 20:52
• I am the OP and I am not sure as well. Since I am not sure, theoretically no one knows for sure whether the OP wants to include perpetual check or not. Jan 15, 2019 at 20:56
• hahaha this could get awkward Jan 15, 2019 at 21:00
• You could improve this by replacing the rook with a minor piece. A possible perpetual could be for instance: black Bf8, Ng7, Kh8; white: Nf7+, Kg6 and the knight is shuffling between h6 and f7. I am sure you can place 9 queens and the rest of the material somewhere on the board so that it does not interfere with the perpetual. Jan 15, 2019 at 21:34

``````1q3r1k/2b1Nn1r/5K2/qqn5/qqb5/qq6/q7/8 w - - 0 1
``````

The knight gives a perpetual. I think this position is possible, but I have not verified it.

This position, with a material difference of 1 queen, 2 rooks, a bishop and a knight, is (quite easily) reachable from the starting position:

``````7k/8/8/1n6/1p1p1p1p/pPpPpPpP/P1P1P1P1/RQNKNB1R w - - 0 1
``````

You could add a white bishop on g1 and a black knight on f5, but the material difference remains the same.

• Assuming white only moves its rook back and forth, black could play Nd6, Nc4, and Nb2. From there the (strange) line Qxb2 Kg8 Qb1 is also a draw with one less knight. Jan 15, 2019 at 20:57
• @Brandon_J: Without the black knight, white would play Qb2 and then Qxa3 (or Qxc3) and then it s not a draw anymore. Jan 15, 2019 at 21:35
• Ahhh...would never have seen Qb2 for white Jan 15, 2019 at 22:14
• 1. Qb2 followed by 2. Qxc3 avoids the draw. Hmm. So does 1. Resigns. Oh, never mind.
– bof
Apr 3, 2020 at 2:02
• @bof Black recaptures with the knight and the blockade is in place again. Apr 3, 2020 at 5:36