[bigpooch]

It is quite clear that P has a +EV: this is just a
generalization of the two envelope paradox: use a more
intricate switching type function. Normally, picking the
last (unseen) number as in the middle all the time will
yield an EV = 0 but using a modified switching function
based on the maximum when thinking of picking the last
number as higher and similarly for the opposite direction
(when the probability functions say to pick last as min
and max choose middle).

Of course, one can generalize this for more than 3 numbers;
again, pick max or min accordingly depending on the
switching functions. I didn't work out technical details
but the idea seems quite clear. On the other hand, more
precise analysis would be required for maximizing EV. Did
you happen to find an answer for this maximization?