U = 1/ Nr(1 + 2a)
Nr = 1 - K + K/ (1 - P)
U = 1/ (1 - K + K/ (1 - P))(1 + 2a)
note K ~= 2a + 1 for N> 2a + 1 etc, thus:
U = (1 - P)/ (1 + 2aP) if N > 1 + 2a
U = N(1 - P)/ (1 + 2a)(1 - P + NP) if N < 1 + 2a
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