Like Ray, I'd like to point out that if the PINs are not chosen randomly but selected by humans and there is no rejection of the easiest pins, the same rules as for passwords apply: some are very, very, very common.
This analysis of 4-digit pins shows that 3 tries will allow you to break over 18% of 4-digit pins, not the 0.03% you would expect from the maths:
PIN Freq
#1 1234 10.713%
#2 1111 6.016%
#3 0000 1.881%
#4 1212 1.197%
#5 7777 0.745%
#6 1004 0.616%
#7 2000 0.613%
#8 4444 0.526%
#9 2222 0.516%
#10 6969 0.512%
#11 9999 0.451%
#12 3333 0.419%
#13 5555 0.395%
#14 6666 0.391%
#15 1122 0.366%
#16 1313 0.304%
#17 8888 0.303%
#18 4321 0.293%
#19 2001 0.290%
#20 1010 0.285%
I strongly suspect that even if you expand to 8 digits, you'll still have 12345678, 11111111 and 00000000 representing way more than 10% of the PINs in actual use, a lot more than the 0.000003% the maths tell you.
So if you want to select a pin as postulated by the question, start by avoiding the usual suspects (repetitions, sequences, alternating digits).
Also avoid anything that looks like a birthdate (in any of its permutations). The space for this is pretty large (probably over 100K combinations), but if the attacker knows you (rather than just a random attack), then this reduces to a dozen or so useful combinations.
The next one (in no particular order) is to avoid use any digit multiple times in the same PIN (even if not consecutive), or at least reduce the number of repetitions as much as possible. This way, even if there's any dedicated physical input system for that PIN, you'll have wear/traces on 8 different digits (out of 10), which reduces the chances anyone will be able to trace back the PIN from that.
Next, avoid any patterns (like the 2580 in the analysis linked to above), as not only they will be in the "usual suspects" list, but they are easier for someone to catch when you enter the PIN.
Of course, all of this will make memorising the pin more difficult (especially if it changes often!), so as always, it's a trade-off between security and ease. It all depends on what the pin protects: don't burden the user with impossible-to-remember pins that change every week, or the only thing that will happen is that they will write it down right away!