Pocket Pair Spring

vapandrei

vapandrei

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First off, I don't want this to become / sound / insinuate the 'rigged theory'. I'm trying to find out what are the actual odds.. and why it feels strange.

The thing is this. I've played real life poker from when I was a kid. Heads up, 2h, 6h, 10h.. and I've never noticed this. I've also played on PS a lot.. but I recently took up 888. I haven't made a statistic based on hh, but it seems that at least 50% times, when I get a pocket pair, at least 1 other player has a pp too. I say at least, because often, there are 2 or even 3 other guys with pairs in hand.

Is there a mathematical thingy that I'm missing or I'm seeing a pattern which isn't there?

I'm asking because I end up folding high pairs (except AA) right from the flop if some moderately tight player 3x-es me or shoves. And most of the times I'm right.. he's got the set.
 
pr0serbian

pr0serbian

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Mathematical explenation would be that you see more hands par hour online then live,so more hands more chances for cooler situations.This things also happen live but not so often as online.But its not like its every time you have pocket pair somone has too..Our mind is selective and only rembers bad beats for expamle i remamber situation on the bubble qq vs 99 vs aa and situation when i hit big spinandgo and first hand was kk vs aa vs aq..but there was more situations where i was delt qq reised before the flop and everbody folds their trash hands,or where i picked up the pot on the flop cbeting the 88 ..ofc i dont remeber and think of hands like this who happend more often then bad beats becouse they are not painfull,tilting memory like AA crushing my KK
 
Vlad symrak

Vlad symrak

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Much depends on the strength of your pair ...
 
BuzzKillington

BuzzKillington

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Is there a mathematical thingy that I'm missing or I'm seeing a pattern which isn't there?

I'm asking because I end up folding high pairs (except AA) right from the flop if some moderately tight player 3x-es me or shoves. And most of the times I'm right.. he's got the set.
The probability of getting a pocket pair is around 1/17 (or ~5%). The probability of hitting a set with your pocket pair is around ~12%. Therefore, the probability of getting a set is in theory 12% * 5% = 0.6%. Or let's just say 1% for simplicity's sake. So, you would think that 99% of the time, someone doesn't have a set on the flop, which is actually correct.

How can this be correct? Well, what you're missing is a mathematical concept called conditional probability. It is only 99% of the time that someone doesn't have a set if they would play every single hand. In reality, nobody plays every hand -- not even the biggest maniac in the world. So, given that we get to the flop with the villain, we can already drop a significant portion of hands (trash such as unsuited, unconnected, low rank hands). This is the conditional part that you're leaving out.

We also know that most people will play pocket pairs when they get them. So someone might be folding 60 - 70% of their hands, but play all pocket pairs. This increases their chance of hitting a set on the flop significantly (because they won't be seeing the flop if they fold pre-flop with junk). Now, multiply this by the number of villains you're facing. Then consider what players will do when they don't hit a set with a small or medium: they might bet small, check-call, or just check-fold. It is only when they have something big that they are willing to risk it all. And when this happens, you have the conditions sufficiently narrowed down to calculate the conditional probability, which is probably going to be relatively high. It is also possible that they have something else, such as a straight or a flush.

And now consider the fact that you see much more hands online than in real-life. Obviously when someone shoves with a set is an event you are going to remember much better than when everyone folded pre-flop and the button steals the blinds, or when no one has much of anything and the flop/turn/river goes check-check, check-check, and check-check, ending with you or the villain winning just a few chips. Nothing interesting, so easy to forget. Or perhaps you c-bet and the villain, who didn't hit their set, folds to your c-bet. It's easy to forget about all those times.
 
vapandrei

vapandrei

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Thanks. That was a nice read. Here is a statement. Is it true or false?

At a 2h+ table, if one player gets a pocket pair, the mathematical probability of other players at that table to get pocket pair increases significantly.

This was the actual question and not about hitting sets.

And I agree with playing more hands online than live and getting to showdown more when I have a strong-ish hand with pocket pairs. That's why I mentioned about me seeing a pattern where there is none.
 
U

ucdengboss

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The probability of getting a pocket pair is around 1/17 (or ~5%).

This is true for any single player. You have a 5.88% chance of being dealt any pocket pair 22-AA. The question is what are the odds of multiple pocket pairs being dealt in a single hand. So if you have a 9 handed table what are the odds that 3 players get dealt pocket pairs? Now there are 8 others who each have a 5.88% chance to hold a pair. How do we calculate this?
 
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