Probability of getting a pocket pair

[AlamedaMike]

We all know the odds of being dealt a specif pocket pair are 220-1 or 16-1 for any pocket pair.

Well, talk about variance - I moved over to Poker Stars awhile back and I have 6008 of my hands in the database.

I have had KK - 27 times which is the right number but TT - 29 and QQ - 42 times. AA - 24 and 22 - 22.

Okay variance - in a million hands it might even out.

At .25/.50 with 650 hands I have had AA 1 time and TT - 11 times?

Does anyone else have more stats for poker stars?

Overall it is 16-1 for any pocket pair.

[janeg]

Alameda, what's the point of this post? Do you think you're not getting pairs dealt to you the appropriate number of times?

There are 13 pair hands (AA to 22), each of which can be made 6 ways. There are 1,326 starting hand possibilities. (13 x 6)/1,326 = 5.8% chance you'll be dealt any pair. Over 6,008 hands that's 348 pair hands. Looking at your pair list for 6,008 hands, they are basically converging around the expectation of 27 hands (6,008 x 0.45%) with QQ running very high.

Looking at my own recent play on Stars, I've got 9,287 hands and 553 of them have been pairs. 553/9,287 = 5.9%. Exactly what probability would predict.

If I look at my recent play across all sites, I've got 26,677 hands; 1,572 of which have been pairs. 1,572/26,677 = 5.9%. Again, just what I should expect although they aren't spread evenly, I've had 55 153 times, QQ 131 times, AA 118 times, KK 114 times when the expectation for any specific pair is 120 times( 26,677 x 0.45%)

I've played 1,278 of those pairs and flopped sets with them 152 times. 152/1,278 = 11.9% which is exactly what I would expect (odds of flopping a set are 12% or 7.5:1).

I've been on a bad run for the last month (10/8-11/7). If I look at my pairs I'm actually running a little behind expectation; 3,400 hands x 5.8% = 197 when I've only had 182 although I've actually run a little hot with AA (18 times vs expected 15). What's really hurt me over this period are my 2pr, straights, and boats being beaten more often than usual. I usually average an 84% win rate with straights but have only managed 77% over the last month. I've also had 7 boats and only won with 4 of them!

Hope that helps

[AlamedaMike]

thanks - just to show the short term flux of poker hands =

I hope that it evens out - thanks for the stats

[AlamedaMike]

[maxp]

I'm afraid - because I always fail to grasp it too- that there doesn't seem to be such a thing as "evening out" in the world of gambling.

I think Mike Caro said that you're not due for something, you're already even. All the odds are just saying that in the long run (with "long run" possibly very long) you should get so and so with such probability, but if you don't, you're not "due", just one (un)lucky sucker.

The chances to get rockets dealt are always 1:220, the cards couldn't care less if you think you're dealt less rockets than the odds say.

[the_hawk]

[AlamedaMike]

I understand that random really means random - I have missed up to 6 flush draws in a row - no big deal - then hit 3 in a row.

I also know that the random card shuffle that Poker Stars uses might not be the state of the art and then again it might be.

I have noticed that when I played on Party Poker I saw many more strange hands that I did on Poker Stars. But, again its random so we will never know.

One reason that I posted this is to show just how random it really is. The human mind picks up patterns when there sometimes are none. The brain is so very good at pattern recognition.

Mostly the patterns surrounding cards is just not a real pattern. Like getting the same 2 cards back to back in a live game - many player will play any two cards when this happens the second time.

BTW I got AA one more time - 1600.

Also, in a live game I got AA 5 times in 2 hours - each one lost - what is strange is getting them 5 times - not losing each.

But, to the point - so many gamblers think that they are due because of the odds. You have to love them. They will make an unprofitable call because they think they are due. But, we know better don't we.

The only thing that I think the probabilities are good for is to calculate pot odds.

I would expect that the probability of getting 2 cards would even out after a few million trials - when I took my stats course in college there was a way to determine the confidence level - also to do with sampling. e.g. How many samples (2 cards dealt) do I need before I can trust the results.

BTW, I love stats. Just that I fogot most of it.