Armbar grip breaks (and general maintenance of the armbar finish position) make up the key to being able to finish the armlock on more than twice as many opponents. As you go further down the rabbit hole, you start to notice that a technique that works to deal with one particular style of defense doesn't work at all to deal with another defense. As such, having excellent maintenance is as important as knowing the right techniques to break the grips. Unfortunately, that part is 100% up to you, as you need to be in the Armbar Finish position as many times as possible and for as long as you possibly can. The good news is that which grip break to use is pretty easy to figure out.
The particular rabbit hole we're going down today involves the "middle finger defense", when your partner hides their hand behind their biceps, but not underneath your leg (we'll cover that next time). While this isn't always as good of a grip as the lapel grab or the "rear naked choke" defense, it's still formidable, and comes up frequently in transition. Generally speaking, it's better to have the "pocket" grip than the Kimura grip for this finish sequence, so if you got to the armbar with a Kimura grip, go ahead and switch to the "pocket" grip. Make sure that you are "elbow deep" with the pocket grip, not shallow! From here, you can try the simplest, least energy option: just lean in the direction of your partner's feet. If their grip isn't incredibly committed, you can often generate enough leverage to strip their hand free. One detail, though: make sure you lift your elbow up away from your body, straightening their arm completely (as opposed to giving them the opportunity to re-grip their biceps or palm).
Another grip break that works extremely well from the "middle finger" defense is the swimming grip break. Starting with the pocket grip, you actually want to make your pocket hand shallower for this one, so you allow room for your other arm to swim through. If your left hand is in your pocket, your right hand is going to swim under, but not from the side that feels most comfortable and natural; instead, you're going to swim through from the same direction your first hand is fed through. This will feel (in scientific terms) wonky, but it's going to pay off when you have the leverage to shoulder lock your partner and strip their grip along the palm that's trying to grab. Your left hand can now come free, and then clasp your right hand over the top, dropping your elbow down to help with the leverage. As you wrench their arm free, be careful not to inadvertently shoulder-lock your partner. If they straighten their arm to defend, you can finish the armlock with their arm trapped under your armpit.
The hip bump option is probably the simplest one, conceptually, but there are a few tricks to it. Start with your patented pocket grip with your left arm in your hip pocket. Next, base with your right hand behind and to your right, and plant your left foot on the ground as though you are going to stand up in base. Now, act like someone is calling your name behind you, turning to your right in order to break the grip. This can be a dynamic, fast technique, so be careful with your partner during this transition. Once again, flare your elbow out so that your partner's arm stays straight.
All three of these options will frequently work with the "middle finger" defense, and possibly for some other defenses as well, although they work best with this particular grip. Remember: maintaining the position is everything, so be sure that you are able to do this before worrying too much about breaking the grip (you'll get there eventually, but if your partner is able to come up on top immediately every time, you'll never get good at breaking their grips). As always, please do let me know how these techniques are working for you! Have fun with your training partners, and know that there are plenty more options for breaking grips from the armbar.