AA and KK statistics

I suppose this is kind of a rant, but I'll share anyway.

I've been dealt AA or KK only 5 times the last 2100 hands. Since the odds of this happening are 110:1, that means that on average I should have had this happen 19 times during this run.

To make it worse, I've only broke even on the 5 I was dealt! Obviously if you play aces enough, someones going to flop a set on you. But given my bad luck already the past few weeks, this is getting a little ridiculous.

Clearly 2100 hands isn't a huge amount of play, but its not small either. I've been very patient just waiting for some cards to come my way, but its tough when the game becomes a folding marathon.

Anyone else had bad runs like this? I guess the poker gods just don't like me right now.

many players would consider 10k hands small. 2100 isn't nearly enough to tell you anything about your game. about the only thing it's useful for is get a general idea of where you're headed. if you use pokertracker you can see how much you limp in, how much you raise, etc. and with 2100 hands you can kinda see which direction you're headed, but it's just a prediction. you need around 20k hands before the stats start to converge.

FYI AA and KK only win about 50% if you're up against 5 opponents. so either bet them out of the hand or take your chances.

I thought it was 1:220...

Originally Posted by mike4066

I thought it was 1:220...

that is correct. littletrogdor where did you get that 110:1 figure?

Your right, the odds of getting any pocket pair are 220:1.

But I'm looking at the chance of getting dealt AA or KK, which drops it by half since both are 220:1.

I always raise big with these hands, so normally im heads up or against 2 people. I'm not worried too much about losing with aces or kings, it happens. But its frustrating when I simply don't get them.

hyper: How many hands do you usually play a week? I think I do around 1000, so maybe it seems like a lot to me since this is over a relatively long period of time.

I think I'd go mad if this kind of statistical anomaly continued for another 10k hands.

Just for fun, P(KK or AA) = 1/110 = .009

P(5 AA/KK or fewer in 2100 hands) = P(5) + P(4) + P(3) + P(2) + P(1)

Hey, this is easy in Excel... 1 in 100,000. Ouch.

Originally Posted by littletrogdor

Your right, the odds of getting any pocket pair are 220:1.

But I'm looking at the chance of getting dealt AA or KK, which drops it by half since both are 220:1.

I always raise big with these hands, so normally im heads up or against 2 people. I'm not worried too much about losing with aces or kings, it happens. But its frustrating when I simply don't get them.

hyper: How many hands do you usually play a week? I think I do around 1000, so maybe it seems like a lot to me since this is over a relatively long period of time.

I think I'd go mad if this kind of statistical anomaly continued for another 10k hands.

lately i haven't been playing much because of school. in fact these next 2 weeks i'll be playing next to nothing cuz of finals

i'm not good enough to quad table. the most i'll do is double table, so a little under 200 hands an hour (i play 6 max). when i had time i would play at least an hour a day....more on the weekends. so i guess 10 hours a week would be 2000 hands.

don't worry about the swings, it's all short term. some dude at 2+2 posted a 15BB/100 win rate over 12000 hands...at the 10/20 limits!! i think it was like 33 grand in profits.

just look over hands you've won and lost in and see if you made the right plays. the money will follow the expectation.

2k hand is not even close

you can talk card-dead after you get dealt 10 k hands

For the sake of accuracy,

The chances of getting pocket A's or Ks is 2/221, which is equal to 220:2 or 110.5:1

Simply dividing by 2 is close enough but you do lose some precision.

Sorry, 220:2 or 109.5:1

quote:
Clearly 2100 hands isn't a huge amount of play, but its not small either. I've been very patient just waiting for some cards to come my way, but its tough when the game becomes a folding marathon.

Anyone else had bad runs like this? I guess the poker gods just don't like me right now.

Instead of a folding marathon try switching it up and playing cards that arent usually as worthy of a limp or calling a raise. People love to think they have the upper hand. To me this sounds like a simple stratagy error, if people think you are a rock then odds are they will only play against you when they have a hand that can beat a rock. Another thing is bad runs happen, sometimes the cards are not in your favor, if this is the case stop playing for a little bit, or maybe in your case its the reverse, you might need to play a little more so some of these bad beats are smaller then the amount of hands you win. anyone else think they can add or subtract from this list?

i dont think playing different hands is a good idea, personally. Why call a raise pre-flop with 10Jo/s or somethin like that, your most likely beat, at best he has low pockets and then its fairly even, but your odds of losing the hand (and therefore more money) are still high... dry spells will eventually end, just try to tough it out... just for a change, maybe play lower stakes tables and play aggressive, that way if you lose you dont lose much

i didnt mean to call all ins or any huge bet or raise with a not so good hand. I mean like simple 2xBB hands, it adds to the value of deception. If people watch you like your a fish and you act like a fish, they are going to treat you like a fish and call with less marginal hands. Then when you hit AA, KK BBBAAAMMM!!!! your still a fish to them but all of a sudden your a 3-1 minimum favorite preflop. Dont make stupid calls, just throw out a couple of bucks to later in turn take their whole stack.

Quote:i dont think playing different hands is a good idea, personally. Why call a raise pre-flop with 10Jo/s or somethin like that, your most likely beat.

Thats the point, they will look at you like your an moron learning the game. How i look at it, turn bad cards over cheaply and Strong hands over when there is a large pot.

Someone asked my that I show my work on this.

OK, P(5 KK or AA|2100 hands)

Is mostly P(5) but techncially you want to say "5 KK/AA or _fewer_" so you have to sum P(1)...(2)(3)(4)(5). The are all calcualted the same way, but I will do P(1) (simplest) and P(5) (most germain)

P(1) - what are the odds that you are so pathetic as to get AA or KK exactly ONCE in 2100 hands?

Well, in 1 hand - 1/110 (roughly) (or .00905 exactly, according to excel)

In the first hand, but not the next two: - 1/110 * (1-1/110) = 109/110 * 109/110 = .0088 (a smidge less than 1/110).

Now, in 3 hands - you could get KK on the first, second, or third hand - so there are 3 "combinations" (or permutations... I get them confused), so you have to multiply by 6 = .0267

You can also write this (3 p 1) * P^1 * (1-P)^(2)
or in general
(N p M) * P^M* (1-P)^(N-M)
Where P = the probability of a single event
N = number of trials
M = number of succeses
And (N p M) = N "permute" M, or N!/(M-N)!

Now, some math symbols:
* = "times" but this is the comp sci way of writing it.
X^Y = X to the power Y, i.e, X^2 is X-squared
X! = X "factorial" is X * (X-1) * (X-2)... * 2 * 1

Dang, gotta go. More later... or maybe someone can finish this for me

Where was I?

OK, so what's the chance of getting a single AA or KK in 2100 hands?
Really, really low.

(2100 p 1) * (.00905) * (.99195) ^ 2099

(note that Excel has a BINOMIAL function which does this for you)

P(1) = 9.8 x 10^-08. Or .000000098, ~ 1 in 10 million

Now, P(5 KK or AA)

(2100 p 5) * (.00905)^5 * (.99195) ^ 2095

P(5) = .00011, or 1 in 9085. Which means my original post of 1 in 1 million is way, way, WAY off.

Hmmm... and I did both in excel. I must have entered something wrong.

Well, I either get the above for P(5) directly, and summing P(4,3,2,1) I get P = .00019, which is 1 in 5267

OR if I use the cumulative binomdist function in excel for 5/2100,
I get P = .000146, which is 1 in 6855

I think it's a rounding error, and probably 1/6855 is right. I didn't save my file the first time, but I think it's way wrong.

Conclusion:
1) Always check your work (better yet, have someone else do it)... funny that my P(KK/AA) = 1/110 was challenged by 1/2 a percent,. but no one noticed that my actually calculation was off by a factor of 20 or so.

2) littletrogdor, not as unlucky as we originally thought.

lol, good to know that lady luck isn't as mean to me as it seemed. I actually did the same type of statistics calculations in excel, I'm pretty sure I got something similar (1/8000) for about 3k hands. So its bad, but it could be much worse.

I'll continue to track it for a while just for kicks, we'll see if things get back to normal by 10k hands or so. 8-)

Originally Posted by littletrogdor

Anyone else had bad runs like this? I guess the poker gods just don't like me right now.

For me, the easiest way to beat a bad run is limp wherever you can and deliver a bad beat. It's purely psychological, mind you...but it makes you feel better and lifts you up a bit.

On my last bad run, I went all in with Q9 (4 bucks or something like that) and delivered a straight beat down to pocket kings.