problem, but I can't see it at present.
I have run a Monte-Carlo experiment for this problem and the result
from that is the average number of cards that needs to be turned over
to find two aces is 21.21+/-0.02 (2 sigma).
OK, I can confirm that the expectaion is 21.2, but the computation is a
but long winded and fiddly to type here at present.