Something I have always wondered about Pocket Pairs

Ever since I started playing poker online I noticed that when you hold a pocket pair, most of the time other people at the table will be holding pocket pairs as well, sometimes up to 3 or 4 people on fr, at first it made me wonder was it just online this happened, but then I see it in live poker a lot as well, is there an explanation for this or not lol?

The chance of being dealt a pair in Hold'em is exactly 1/17.

At a FR game, there are 9 players. On average, you would expect to see 1 PP every other deal. 2 deals means that 18 people received cards (well, 9 people twice).

Since you expect to see 1 person out of 17 to be dealt a pair, then every 2 deals at a FR table, you'd expect to see 1 PP. Actually a bit more than that, since we're multiplying 1/17 by 18, we get 18/17 = 1 1/17... more than 1.

***
The event (of drawing a pair) is random, so sometimes there might pass a few deals where no one gets dealt a pair, then later there may be a deal where more than 1 person is dealt a pair.

Ultimately, it's all going to even out to ~1 PP every 2 deals at FR games.

***
Realistically, the odds for being dealt a pair will be different for an incomplete deck.
I mean, when the cards are dealt, they are dealt without replacement.
If we had knowledge of the specific cards as they are dealt, we could refine the estimate of 1/17 for each player, but it would not change the basic fact that everyone at the table expects to be dealt a pair 1/17 of the time, over the long term.

In poker your eyes will lie to you. That is why losing players think the game is rigged. It's the black swan all over again

http://en.wikipedia.org/wiki/The_Bla...282007_book%29

Originally Posted by jyms

In poker your eyes will lie to you. That is why losing players think the game is rigged. It's the black swan all over again

http://en.wikipedia.org/wiki/The_Bla...282007_book%29

It's not your eyes. It's the fallible human brain's capacity to ignore successes and focus on failures... for whatever reason.

Humans are notoriously horrible at recognizing whether or not something is random. Humans love to invent patterns where none exist.

Here's a chart which summarizes a geometric distribution for drawing a PP. This shows how many non-PP hands a player will expect to be dealt between PP hands.



25% of the time, you will draw a PP after 5 or fewer non-PP hands.
25% of the time, you will draw a PP after 5 - 12 non-PP hands.
25% of the time, you will draw a PP after 12 - 23 non-PP hands.
20% of the time, you will draw a PP after 23 - 50 non-PP hands.
4% of the time, you will draw a PP after 50 - 76 non-PP hands.
1% of the time, it will be more than 76 hands between being dealt a PP.

Many people seeing that kind of spread will call cheating right away. However, this is the predicted value for an event with a 1/17 chance of occurring.

I play the pocket pairs with some caution. Heads up it's an OK hand at best. Only thing I recommend is to try not to over play them.

Originally Posted by PJfan10

I play the pocket pairs with some caution. Heads up it's an OK hand at best. Only thing I recommend is to try not to over play them.

Ya because that is what we were talking about. And you couldn't be more wrong.

MMM? Was that not kind of the same thing? I haven't had the chance to read the book yet but I am sure it's the same concept. Isn't everything we see with our eyes actually our brains focus

Originally Posted by jyms

Ya because that is what we were talking about.

MMM? Was that not kind of the same thing? I haven't had the chance to read the book yet but I am sure it's the same concept. Isn't everything we see with our eyes actually our brains focus

Fair point.

I wasn't really trying to pick a nit, but I guess I was.

It's FTR. This is where we train to pick

Here's a nit to pick:

Have you ever seen a box-and-whisker applied to a geometric distribution before?
It strikes me as a bit scandalous to use a B&W on an open data set.

Originally Posted by MadMojoMonkey

Here's a nit to pick:

Have you ever seen a box-and-whisker applied to a geometric distribution before?
It strikes me as a bit scandalous to use a B&W on an open data set.

I can't tell if this is science or british. I am guessing it's science based on your post earlier about PP's

The is actually a slight effect of you having a PP making it more likely that other people will too (because they can't draw your value of card as easily) but the effect is absolutely miniscule.

PPs are hands that are relatively like to get played though and you're probably forgetting most of the PPs you've not had showdowns with. The chances of someone else having a PP at showdown are much higher than the chances of one being dealt.



Not clear to me how the black swan is relevant (I've read the book) as these events are highly predictable (statistically): the Black Swan is about events that are utterly outside the range of expectation (like discovering an entire population of Australian black swans when you 'know' that all swans are white and it's never even occurred to you that non-white swans might exist).

Originally Posted by jyms

I can't tell if this is science or british. I am guessing it's science based on your post earlier about PP's

I have no idea what this means.
science or british?
You know I'm not British, right?

Has anyone checked to see if jyms bumped his head?

I didn't say you were british, just sounded like it. I did have laser eye surgery on Thursday. Maybe they went a little too deep

I think he means English haha

possibly

some interesting answers thanks for the time and effort of tryin to answer my question!

Oh... That chart I posted is called a box-and-whisker chart.
It's used to show how data is grouped in a set.

I abbreviated it as B&W.

Sorry, I thought I had called it a box-and-whisker chart when I posted it.

Originally Posted by MrFerguson91

Ever since I started playing poker online I noticed that when you hold a pocket pair, most of the time other people at the table will be holding pocket pairs as well, sometimes up to 3 or 4 people on fr, at first it made me wonder was it just online this happened, but then I see it in live poker a lot as well, is there an explanation for this or not lol?

Come on, playing pocket pairs is easy, especially pocket hooks!

Originally Posted by Springbok

especially pocket hooks!

Please don't do this if you want to considered a poker player, or an FTR'r

Originally Posted by jyms

Please don't do this if you want to considered a poker player, or an FTR'r

Bahahaha I love that video!!!!

Say you have a hand where two players see the flop, and they start with the top 25% of hands:

22+ AT+ KT+ QT+ JT+ 54s+ 86s+ Q9s+ K6s+ A2s+

This is 330 combinations out of 1326 possible. Each pocket pair is dealt in six combinations (2c2h 2c2s 2c2d 2h2s 2h2d 2s2d) and there are 13 pairs, so thats a total of 78/330. So each player has a pocket pair 23.6% when they see the flop.

If one of the players has AcTd, the known cards reduces the other player's range to 283 total combos. Of the 78 pocket pair combos from before, TdTc TdTh TdTs AcAs AcAd AcAh are removed, bringing it down to 72 combos. So the other player will have a pocket pair 72/283 or 25.4%.

If one of the players has 5c5d, the known cards reduces the other player's range to 319 combos, 73 of which are pairs, so that's 22.8%.

If one has AcAd, then the other player's range is 277, 73 of which are pairs, so 26.3%.


Long story short, people are more likely to have pocket pairs when you hold big cards, especially aces and kings, because they block more of the non-pp hands than the pp hands.

Well that's a bigger effect than I thought and it looks like it would be stronger on a tighter range still including 22+ for set-mining.
And you also have the selection from the hands reaching showdown

That might actually make it big enough to notice from play without selection bias.