Wednesday, March 10, 2010

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:

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

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.


DuggleBogey said...

On my second time ever playing in a casino I flopped quads twice in a row, and flopped a set on the very next hand.

I remember thinking "this game is easy!"

I made the most money off the set because it was a $2/4 limit game with a full kill.

Keiser said...

Meanwhile I've lived in Vegas for 2 and a half years and have never won a high hand jackpot. Probably somewhere in the 15-20,000 hand range. Only time I had anything in a casino was 5 years ago visiting here, got flopped quad Jacks at Bellagio (no jackpot).

Oh last time I played at Imperial Palace I did see quads five times (one guy got quads twice in one orbit). As you can imagine, it was a bad session, lost with a few boats and nut flushes that day.

Anonymous said...

1/2 nlhe. I flopped quad 5's and had 2 people bet into me on T55 flop. I just called with the deck crushed. Turn is a beautiful T. 1st guy bets, 2nd guy calls, I just call. River is a blank low card. So the board is 55TTx and I have 55. 1st guy bets, 2nd guy raises, I shove. 1st guy folds his T putting me on quads! 2nd guy calls with his T. Ship the $800 pot.

Anonymous said...

arent the odds of flopping a set or better more than grump stated? his figures seem lower than what I have seen in many books