Your assumption is ill-placed. Orcus won't make his Perception check anywhere near half the time. Actually, this is the matrix of possible methods for Orcus succeeding on the check:
I-R's Roll Orcus's Roll
1 15, 16, 17, 18, 19, 20
2 16, 17, 18, 19, 20
3 17, 18, 19, 20
4 18, 19, 20
5...