More on flopping quads

Was just thinking a bit more about flopping quads, triggered by Shamus emailing me a screen shot of having done so again in an online hand. I wondered what the probability of flopped quads was, given that one starts with a pocket pair. I was about to dig into the math when it occurred to me that I had run through this before. So instead of pulling out the calculator, I did an archive search. Sure enough, it's all right here: http://pokergrump.blogspot.com/2008/09/three-in-row.html

If you don't feel like slogging through the math, here's the bottom line:

So, to summarize--given a pocket pair, the probability of flops is as
follows:

Set: 10.78%. (That's 1 in 9.28 times, or 8.28:1 odds against.)

Full house: 0.73%. (That's 1 in 137 times, or 136:1 odds against.)

Quads: 0.24%. (That's 1 in 417 times, or 416:1 odds against.)

So good luck to all those of you who try to hit the "flopped quads" jackpots in town (e.g., at Mandalay Bay and M Resort). You get a pocket pair one time in 17 hands on average, so you'll have to play an average of 17 x 417 = 7089 hands of poker to win. Let's say you get 30 hands an hour (taking into account some breaks). That means one set of flopped quads about every 236 hours of play. Hope you have a lot of spare time on your hands.