With today's endgame tablebases, an ending like this can be analyzed perfectly. The posted position is a draw. The position after move 48, when the material is reduced to seven men, is also a draw. In between moves 48 and 108, White never had a chance for a winning move. Black had three chances to win following mistakes by White, and missed them all.
After White's 84.Qf7, Black could mate in 32 starting with 84...Rc3, but played 84...Rc5 and the position was again a draw.
After White's 87.Ke4, Black could mate in 33 starting with 87...Rh3, but played 87...R5a4+ and the position was again a draw.
On 89.Ke4 White returned to the same losing position, and this time Black played the winning Rh3. But then Black threw the win away with 90...Kd6. 90...Rc3 was the only winning move. That was the last chance for either side to win, before the game ended.
Dreaming may not be the best technique for solving an endgame, after all.
In 1956 Bobby Fischer played a game vs Hans Matthai in a tournament in Montreal, that ended up being a 108-move marathon ending in a draw. Apparently after analyzing the game later, Fischer found a way for white (Fischer) to win, but this "win" is not recorded. I've not found this solution myself, does anyone else care to give it a go? Can anyone find a win for white?
To quote the book Endgame:
"That night, in a deep but restless sleep, a dream came to him and the position appeared over and over again - seemingly hundreds of times. Just before waking, the solution came to Bobby as a kind of apparition. There WAS a win there!
Bobby woke and sat bolt upright. "I've got it!" he said aloud, not knowing that anyone else was in the room. [text deleted] "I knew I should have won!" he fairly screamed."
Here's the final position. The last move was Qb5+ by Fisher. Black to move.