Well, the probability of getting a particular pocket pair on any given hand is 1 in 221.
Then the probability to flop a set with it is 1 - (48/50)(47/49)(46/48) = 0.117551
So the probability of this exact event happening on a single given hand is:
(0.117551)/221 = 0.0005319 = 1 in 1880.
For it to be back to back to back in only 3 hands of play: (1/1880)^3 = 1 in 6.64 billion.
But, before we start saying, "zomg, poker is rigged!", we need to consider a couple of things. One, you play more than 3 hands of poker in your lifetime.
So in this case the probability nearly scales with the number of hands you have played since the event is a rare occurrence. Exact calculations may be done using a streak calculator like this one:
http://www.pulcinientertainment.com/...tor-enter.html
So if you have a sample of 1,000,000 hands, he chances of seeing exactly 99 3 times in a row and flopping a set 3 times would become 1 in 6649.
Now the other thing to consider is that you would have made this post with any pocket pair where you would have flopped a set 3 consecutive times. So considering this would increase the overall probability of this occurring by a factor of 13 [(1/17)*(1/221)*(1/221)*(0.117551)]^3. So for a sample of 3 hands, it would become 1 in 511 million. For a sample of a million hands, 1 in 511.5.
So this is still a rare occurrence and virtually all live poker players won't see it in their lifetime, but some of the online grinders will definitely be seeing it.
Last edited by tringlomane; 06-18-2012 at 11:15 AM.
Reason: add more math detail