Draw Meister

PRIOR to this round-seven game in the 'Paignton' premier, my opponent had drawn five games and taken a half-point bye in his remaining one.
The finish of this game may help explain why he is such a 'solid' player.

White has just played 23.Ra1-d1 and offered a draw in Adrian Pickersgill (1948/170) - Spanton (1881/168)

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AP explained in the postmortem that he offered a draw because he thought the position was equal, which is confirmed by the analysis engines Stockfish10 and Komodo10.
23...Qd6?
Playing on in this type of position helps explain, on the other hand, why so few of my games end in draws. Sometimes it seems I will play any move, just to keep the game going.
Here it would have made sense to play 23...h6 or 23...g6, to avoid back-rank mate problems, or 23...a6 to give the b5 pawn more protection. The problem with the text is that it unblockades the white isolani, and that is a problem because, as a general rule, isolated pawns become stronger the further they advance (provided they do not just become easily capturable).
24.a3?!
White is better after 24.d5, which takes the pressure off his isolani and drives Black's knight to an unfavourable square, eg 24...Na5 25.b3.
24...Rd7 25.Qh4
Pushing the d pawn is not so clear-cut now as Black replies 25...Ne7.
25...f6?!
This solves Black's potential back-rank mate problem, and restricts White's knight. But, to a certain extent, the knight is restricted anyway by being tied to the d pawn, and the text creates a new problem by weakening the e6 square.
26.Qh5 g6??
The best moves, it is said, contain more than one threat. Well, I saw that 26.Qh5 threatened to invade with a rook at e8, but I completely missed the other point of the move.
27.Qxb5
In one move the game has gone from equal material, but with White having the only isolani, to White being a pawn up, and Black having two isolanis against White's one.
27...Kf7?
I wanted to give extra protection to the e6 square to stop a white rook landing there, but there were more pressing problems. I rejected 27...Rb8 because after 28.Qc4+ Qd5 29.Qxd5+ Rxd5, White has 30.Re6, which is indeed good for White, although the engines reckon 30.Rc1 is even stronger.
28.b4?
White wins a second pawn after 28.Qc4+ Qd5 29.Qxd5 Rxd5 30.Rc1, eg 30...Rd6 31.d5 etc.
28...Rfd8 29.h3
29.d5 may be even stronger, but Black has no meaningful counterplay, so guarding against a back-rank mate (and doing so in a sensible manner) cannot be bad.
29...Kg7?
Setting up a white knight-fork at e6 does not help, but Black was in a bad way in any event.
30.Re3?
This time d5 was definitely stronger, and if 30...Ne5, then 31.Nd4 (with Ne6 to come), as 31...Qxd5?? loses to 32.Qxd5 (best) Rxd5 33.Rxd5 Ne6+.
30...Ne7 31.Rde1 Nf5 32.Re6?!
AP pointed out that better was 32.Re4, but the text should also win.
32...Nxd4 33.Nxd4 Qxd4 34.Re7+ Kh6 35.R7e4
White is better after the text, thanks to Black's weak queenside pawns and exposed king. But even stronger is 35.Qc6, when best, according to the engines, is 35...Rxe7 36.Rxe7 Qd1+ 37.Kh2 Qd6+ 38.Qxd6 Rxd6 39.Rxc7 Ra6 40.Rc3, with what I am sure is a technically winning rook-and-pawn ending.
White accompanied his last move with his second draw offer of the game, and this time even I could not find a (spurious) reason to play on.