It's better to let your opponent to keep his hands up instead.Most important thing ever when dealing with striking. Keep the hands up. It's the basic skill but even the professionals forget this.
You can use "stiff arm" and put your fist in front of your opponent's face. You then ready to throw your cross anytime you want to. When you use stiff arm, you will get the same result (even better) as to use your arm to protect your own head. Since your stiff arm is in your opponent's striking path, he has to deal with your stiff arm before he can punch to your head. You are still using your arm to protect your head. It's just in a more aggressive way.
The moment that your arms are up and guard your own head, your opponent knows that you are in "defense mode". He can then put himself in "offense mode". This is not good for you. IMO, it's better to fight in your opponent's territory than to fight in your own territory.
In sword fight, do you want to extend your sword toward your opponent, or do you want to use your sword to guard your head?
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