No matter whether you are a hawk or a dove, you may disregard all meetings with doves, for you won't be killed. Also, whatever happens to doves doesn't affect your chances. So, you may consider the world to be populated only by N hawks and you. (N=H if you are a dove, and N=H-1 if you are a hawk.)
If N is odd, you'll be killed no matter what you are.
If N is even, it also makes no difference if you are a hawk or a dove; you'll be alive only if you are the last one standing, with odds 1/(N+1).
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