I like the suggestions that medevac suggested for improving the guard, and as fireplug said, you must be active from the guard (or any position for that matter).
Some other ideas are to
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find a tree (preferably one that you can get your legs around into a closed guard position, but just barely) and hang from your guard for time. Or if you really want a challenge, hang on with your legs while doing sit ups.
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get into a closed guard position and have your partner stack you. Go up on the top of your head. Then have him apply forward pressure (the level of force will depend on the strength of your neck muscles) while you do bridges.
This will not only increase the strength of your legs having to hold onto him but also the strength of your neck and make it harder to “steam roll” you (don’t know if that’s the popular term).
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go out and find a tree (as in #1) but instead of hanging for time practice climbing the tree (like a bear, not by using the tree limbs). You’ll need to find a tree that doesn’t have low branches (oaks are good). This will help to strengthen up your inner thigh muscles.
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instead of climbing the tree just get into a closed guard on it and try to crush it. You won’t be able to do so, but the attempt will strengthen your inner thigh muscles (along with your hip extensors and knee extensors depending on what mechanics you use). Like other isometric exercises this is a great way to develop maximal strength.
As for opening the guard, well that depends on the rules you’re abiding by I guess. The single most effective guard breaker I’ve ever found was just a simple thumb in the hollow of the throat while attempting to stand up and disengage.
If you’re looking for a more “sport oriented” technique I too would suggest a can opener. Only don’t just crank the head straight down, as some people have good neck flexibility and the chin will actually limit the heads ROM. Instead turn the head to the side and then crank it forward. Slight modification, but, at least for me, it noticeably increases the effectiveness of the technique.
There are numerous others that I (and I’m sure others) could suggest. But try the can opener and see how it works for you.
As for open guard, I always just felt that this was fairly easy to deal with and that the opponent had basically done a step for me. You can also break the legs further apart using the point of the elbow and applying pressure into the nerve on the inside of the leg near the knee.
However, you must place your thigh under the leg to brace it, kind of like your leg is the anvil and your elbow is the hammer.
If you were to try to just hold a piece of metal out in the air and pound it into shape with a hammer it wouldn’t be very effective. However, if you put that piece of metal on a solid surface, like an anvil, now you can pound it into shape. The leg acts in the same way, and greatly improves the effectiveness of the technique.
From there you can fall back into a heel hook/straight ankle/toe push back (although with an open guard it’s often possible to do this anyway). You can pin the leg to the ground with your elbow, then drag your shin across the inner thigh (further pinning it) while transitioning into side control (or sit through).
With the leg pinned you could bring your leg through his legs and spin to a knee bar/toe hold/wrapping knee bar.
Hope this gives you some ideas to work on.
Good training,
Sentoguy