I noticed in Matt Brown's fight last night in UFC 139, that unlike Joe Rogan kept sayin, Matt was not actually doing everything right to escape the guillotine choke while in his opponent's guard. The things he was doing required a lot of strength vs strength, hoping he could forcibly break his opponent's hold on his neck, or that he could loosen the choke by force enough to slip out. I have noticed this in the overwhelming majority of UFC fights when someone if caught in a guillotine. Sometimes it works (especially when the opponent does not have the choke sunk in very deeply, of if he is tired), and sometimes it doesn't. I explained a simple guillotine escape in the UFC 139 Spoilers thread, and I found some youtube videos that I will link here that show the simple escapes, which I will link here. The only difference between what I described and these videos is that in the videos, you wind up passing guard and going to side control, which is much better than what I had been doing. My method would work for someone stuck in a super good guard, or for someone who didn't care to pass, but instead just wanted to posture up & ground and pound.
3 minute long video:
8 minute long video with detailed explanations:
Bas Rutten video, defending the guillotine as opponent is rolling back into guard: