How to Crossface to Pass Half Guard
Flattening your partner with a crossface can be one of the very best techniques for passing the guard, particularly half guard (and the variations that arise from passing half guard). Whenever you're passing the guard, one way to prevent good guard maintenance is to keep your partner flat on their back, and few things do this better than a classic crossface from half guard. We'll take a look at several different variations and methods from a few different situations.
This situation provides an excellent example of two fundamentally different types of crossface, performed at different stages of the action. In the early example, your partner has built their base up and is sitting up in half guard, with their underhook intact. It's a matter of time before they sweep you or take your back. Before this happens, you have one more means of flattening your partner. If they're coming up on your right side, grab their lapel with your right hand, making sure your forearm ultimately controls their head. As you twist your grip to straighten your arm, you should find that you can turn your partner's head away from you. Lift your partner's neck up and turn them away, guiding them to the ground, and flattening them.
The second technique here is the much more fundamental "face smash" technique, or simple crossface from half guard. In this situation, simply weave your left arm around your partner's neck, gripping their armpit with your left hand in order to apply leverage to your partner's jaw and face (if you want to be somewhat nasty). Alternatively, you can utilize choking shoulder pressure.
Simple and Classic
A much more traditional method of passing half guard involves keeping your hands clasped together (as opposed to gripping the armpit). This can also work well for maintaining the crossface, especially if you're more accustomed to keeping the underhook during your half guard pass, and provided head and arm control feels best for you. As you "tripod" up in their half guard to free your leg, take care to ensure that their head is constantly turned away from you. If they're unable to look in your direction, they're going to have a very tough time executing anything offensive whatsoever. Note that you can make their head turn away, but you can also grind your shoulder underneath their jawline, pinning their shoulders very effectively.
Knee Cut Pass Variation
Another simple (but effective) application of the crossface can be during a knee cut guard pass. While on the one hand, it's great if you can manage to control their inside arm, pulling up to finish the pass, it is often not possible to grab the arm (either it's no-gi and tougher to get the grip you want, or your partner is doing a good job of hiding their arm from you). They can still have the underhook, though, meaning that they might be able to get to your back here. However, if you use a combination of flattening your partner by driving their shoulder flat, and the crossface, making them once again turn away from you, you can complete the pass in this manner.
What's more important for passing half guard?
Passing the guard is an amazingly complex thing, and yet it's a really simple thing at the same time. On the one hand, seemingly infinitely complex guard types evolve over time, and new methods of spinning, controlling, and gripping are invented almost literally every day. This makes for a perplexing outside view of passing the guard. On the other hand, human physiology hasn't changed very much over the last 10,000 years. If you can turn your partner's head away from you, you can pass their guard, and that's not likely to be affected by a new type of guard. Cracking the code of a new problem in BJJ always amounts to what the human body can and can't do, and much more fundamental rules of physics and anatomy. As always, let me know if these techniques work for you!