Yeah 1 in 17 sounds right. Odds
of any particular pair are 1 in 220 so that would be 13 possible pairs, 13/220 is about 1/17.
That doesn't mean you wont have long streaks. Sometimes you'll not see any for far longer than 17 hands, sometimes you'll 2 or 3 in a row. Just that on average it should be 1/17.
On a related note someone on fulltilt once became convinced that it was rigged and I was a hacker or superuser when I got AA 3 times in ten hands and a total of 10 pocket pairs in about 30 hands. Sometimes you just get lucky. More often you remember the bad streaks but that was a pretty memorable good one.