When escpaing the triangle choke, it is natural--and sometimes effective--to move away from the trapped arm. I've seen no gi fighters get out of triangles this way.
Clearly, the lack of friction is a plus for this escape--which explains why it is more effective in bare-chested no gi and MMA competition than in gi or real-world situations. If there is one mistake I have seen in triangle chokes over and over again, then that mistake has been when the attacker has gotten "too much shoulder" into the choke."
I was watching an IFL mixed martial arts fight with Fabio Leopoldo and another guy, a tough, wrestler-type with good slams. Leopoldo won the fight, though it was closer than it needed to be because while Leopoldo achieved excellent submission positions--especially involving the triangle--he failed to finish any of them.
In particular, Leopoldo missed with numerous triangle chokes. His mistake was attacking straight on, and not getting an angle--something I think of as being able to look down the line of your choking knee. His opponent was powerfully built in the shoulders and was never in any danger because too much of his shoulder was involved in the choke. This prevented the necessary arm-to-neck pressure that makes the triangle a finishing move.
Attempting to escape the triangle choke by "pulling the arm out" actually gives the attacker a chance at getting an even better position because in pulling your arm out, you are taking your shoulder out of the equation and making it easier for a proper triangle choke to be set.
It seems counter-intuitive ("If I give him more arm, then he'll just transition to an armbar!"), but I think this is why the CC Grinder triangle choke escape is effective. As long as you remember to keep the hips in check, you can create a lot of pressure on the attacker's legs as you circle around in the direction of the arm, keeping the guy's hips low enough to ward off a realistic armbar attack, smashing the triangle.
