user16626: 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.

user7297: 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.

user18311: 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)

user307: How about this? 
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.

user18168: 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.

user15238: [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.  

16626: <p>I have noticed the following example, which should be a dead draw:</p>

<p><a href="https://i.stack.imgur.com/PPb6X.png" rel="noreferrer"><img src="https://i.stack.imgur.com/PPb6X.png" alt="enter image description here"></a></p>

<p>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.</p>

<p>By the way, the game above is not drawn by <a href="http://www.e4ec.org/immr.html" rel="noreferrer">the insufficient material rule</a>, as white can theoretically win the game if black makes a blunder such as capturing the rook.</p>
 7297: <p>This position, with a material difference of 1 queen, 2 rooks, a bishop and a knight, is (quite easily) reachable from the starting position:</p>

<pre><code>7k/8/8/1n6/1p1p1p1p/pPpPpPpP/P1P1P1P1/RQNKNB1R w - - 0 1
</code></pre>

<p>You could add a white bishop on g1 and a black knight on f5, but the material difference remains the same.</p>
 18311: <p>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. </p>

<pre><code>8/7b/8/3n4/q3k3/8/qqqq1rKn/qqq1qrb1 w KQkq - 0 1
</code></pre>

<p>(Another possibility would be a position utilizing a forced draw due to the 50 move rule)</p>
 307: <p>How about this? </p>

<pre><code>1q3r1k/2b1Nn1r/5K2/qqn5/qqb5/qq6/q7/8 w - - 0 1
</code></pre>

<p>The knight gives a perpetual. I think this position is possible, but I have not verified it.</p>
 18168: <p>With white to move, the following position is a draw:</p>

<p><a href="https://i.stack.imgur.com/0mnkC.png" rel="noreferrer"><img src="https://i.stack.imgur.com/0mnkC.png" alt="enter image description here"></a></p>

<p>I <em>think</em> it's reachable from the original position, although it would be difficult. I'll let you know if I can.</p>
 15238: <pre><code>[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
</code></pre>

<p>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.  </p>
