The next point to cover is how to deal with their underhooking arm.
Like in the triangle, you want to cross their arm. Also like the triangle, it’s not completely necessary, but it’s best form, the cleanest technique and makes for the smoothest finish. They can use that arm to create a little space (so their shoulder doesn’t squash into their neck), or they can do Jeff’s escape of throwing the elbow back and grabbing their leg and kicking out.
I’ll show how I prevent those escapes while adjusting the choke even deeper.
Here you see them trying to escape with an underhook, grabbing my leg as they come up for a takedown. The hand on my leg is my problem, so I’ve got to kill it somehow.
A simple and natural reaction is to sprawl like you would to defend a takedown. Throw your legs back and drop your hips to the floor. You may need to turn your hips from side to side and bounce a little to shake their arm off. Stay on your toes and drive in to put pressure on their triceps with your chest to help crush their arm and prevent them from reaching up (and maintaining their grip).
You can finish from the sprawl too, but I’ve found you’re more likely to just crush their neck without choking them. As you’ll see, there’s still more adjusting you can do for a cleaner choke, and other finishing positions give you better pressure for the blood choke.
The problem I have with sprawling is that people can often hold on to my pants even with their arm stretched out. Or I’ll break their grip, but they get it again as I come back to my knees. This is why I prefer to do a mule kick. I switch my legs so the knee near their head is on the ground, then I kick my foot to the sky. I’ll keep kicking and shaking and lifting my leg until I feel their grip break and their arm fall between my legs. Put you chest on the back of their arm to press it down.
After I’ve broken their grip one way or another, I’ll come back to my knees, trapping their arm between them.
Try walking slightly towards their head, but not all the way to north-south. Changing this angle between your bodies will let you reach your choking arm deeper since you’re not stretching it so far. The reason we didn’t do this earlier is because it gives them a better angle to get to their knees, but that’s less of a threat now that they don’t have the underhook any more.
Take this moment to adjust and tighten your grips again; there is now usually an inch or two of space around their neck that you can close up now that the arm is crossed. Drop your shoulder, uppercut, wiggle deeper.
You can finish fairly well from here by crunching them into you, pressing your elbow in like you want their head to meet their belly, and dropping your shoulder to the mat.
But I like to take it even further since I’m going to sit-out to finish.
I step up with my leg near their hips to give myself space.
Then I step in with my other leg, putting my knee up past their elbow, so my thigh is pressing on the back of their arm. Their arm is now crossed all the way to the other side of my body. I may even take a second here to adjust my grips even a little deeper.
Now when I sit into them, my body (ribs, stomach, hips, thigh, knee, something) is blocking their elbow and pressing their arm across their neck. My top foot comes to their hip to prevent them from getting up. I keep scooting my hips into them, dropping my shoulder to the ground, twisting my upper body and squeezing the choke.
The “best” time to cross the arm is when you’ve got the figure-four grip, since it’s the most secure. But you can do these steps while you’ve still got other ones. It depends on what they are defending. If they are blocking your next grip in the progression, start trying to cross their arm. Either you get that or they switch to defending it and you go back to working your grips. The idea is to be aware of your multiple goals and work towards each one, intelligently switching from one to the other so they’re trying to catch up.