Statistical Anomaly?

Playing $6-12 in LA on Saturday....had AK, both suited and unsuited 8 different times(suited 2 times, I believe) and not even ONCE did I pair the entire BOARD or make any type of hand other than what the board showed(no straights or flushes.....I even called to the river once just because a J-10 flopped because I thought it was incredible.....just wanted to share this statistical anomaly and wondering if anyone knows what the odds of this happening are(not just not hitting the AK but not hitting a straight or flush as well).....


I did manage to pick up one pot just by betting the whole way, but mostly just folded on the flop or a couple times on the turn after I figured that I wouldnt be able to buy it....I even stopped raising from early position with it after the 4th time....

Speaking only of the flop, if the chances of flopping a pair were one in nine, you'd think nothing of missing eight times in a row, right? The real chances are 1 in 3, so missing eight times in a row doesn't strike me as an anomaly. It's about like flipping heads three times in a row, right?


Tommy

Heh, Tommy, I think you better stick to the non-math related posts. This was a spectacular whiff.


Tom Weideman

how many ak were on button...otherwise shoulda been mucked fast...gl

I get the chance of AK not improving the board, nine times in a row, at somewhere between 8 and 20 per ten thousand.


--------


So the largest term in the expansion is the chance of the board having five cards that don't include an ace or king.


C(44,5) / C(50,5) = 0.5126


The biggest things to subtract off are


- boards where there is a Q, J, and T. (This will double-count boards with a QJT and one or two more cards from that set, but so be it, I'm too lazy to add them back in.)


- boards where there is a four- or five-flush of one of your suits (I'll compute this as if you were offsuit, which will slightly overcount), or when you are suited (1/4 of the time) and there is a three-flush of your suit.


There are some other weird boards to add back in or subtract out (the board is a small straight, or ace and quads, or QJT and also makes your flush, etc.) but each of these is probably down in the third decimal place, so I'll ignore them too, since I'm just looking for an answer within shouting distance.


So no pair, minus the straights, minus the five-flushes, minus the four-flushes, minus one-fourth of the three-flushes, is


[ C(44,5) - 4^3*C(32,2) - 2*C(12,5) - 2*C(12,4)*38 - ...

1/4*C(10,3)*C(39,2) ] / C(50,5) = a little less than 47%


So I'm guessing that the real answer is somewhere between 45% and 50%.


That puts the chance of this happening nine times in a row at somewhere between 8 and 20 per ten thousand.


But that's if you start right now and see whether your NEXT nine AK improve the board. Looking backwards, you're always going to be able to find something about the day's poker that looks really unlikely. If it wasn't AK missing the board, it would be something about flush draws, or flopping sets, or getting big pocket pairs cracked, or flopping two pair out of the big blind, or SOMETHING.


--JMike

p.s. Tom, if you're going to say I whiffed, how 'bout a hundred characters of factorials and combinations to demonstrate my error /images/smile.gif

Tom: "Heh, Tommy, I think you better stick to the non-math related posts. This was a spectacular whiff."


Tom,


You just gave me a spectacular case of the giggles. It won't stop! Make it stop!!


Whew. Okay. :::catching breath:::


You are so right. I've been shopping around for a keyboard with no number pad on it. Much safer that way. Heck, the mere name of this place was enough to intimidate into not joining in for a year.


Tommy

Aces,


During one Vegas trip last year I was 1 for 17 with AK. I only hit a pair one time and it got me half a pot. Figures the other player had AK too. Don't know about the odds but it does test ones patience. Hang tough.


KJS

If you only took those 16 missed hands to the flop, then

the chances of only hitting one of seventeen hands -- where

"hitting" is defined as an ace, king, QJT, or assuming you're

suited and flopping a flush (and then multiplying the flush

flops by 1/4), the chance of missing the flop is


C(44,3) - 4^3 - 1/4*(11,3)


--------------------------


C(50,3)


or 0.6703. Set p=0.6703. Then the probability of hitting zero or one hands out of seventeen is


p^17 + 17*p^16*(1-p) = 0.0104.


One-percent shots happen all the time /images/smile.gif

>> Tom, if you're going to say I whiffed, how 'bout a hundred characters of factorials <<


I don't make posts that include factorials!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


Tom Weideman


P.S. I'm glad Tommy took my post in the light-hearted vein it was intended.

Counting the times you fold on the flop or the turn, you can expect to make a pair about half the time. So missing 8 times in a row would be .5**8 or 1/256 or .0038 or 255:1 against. This means that the NEXT time (and actually EACH time) you get AK you have a 1 in 256 chance of starting a 8 hand missing streak. Since you have surely had AK at least 256 times in your career, I'd say its no big deal.


What gets me about this is [1] your counting you bad steaks, and [2] you got demorilized after on 4 misses.


- Louie

Stop me if you've heard this one.


There was this little Jewish kid, Stanley, who was having a horrible time in math. His parents tried everything, tutors, special programs, learning aids, nothing helped.


One day a friend of theirs told them about a school across town that had done wonders with poor math students. The only problem was it was a Catholic School.


The parents felt if this was what was necessary for their child to have a shot at a decent life then Catholic School it was.


After the first day Stanley got home from school and ran right upstairs to do his math homework. When he didn't come down for dinner his parents got worried. "Sidney, aren't you going to eat?" "No time, Mom. Got to study!"


This went on for weeks. Them one day Stanley came home, dropped his report card on the table and ran upstairs to study. His parents looked at his report card and were very pleased to see an "A" next to Math. They called him down. "But, Mom, I have to study." "Stanley, you got an "A" in math you can take a break from your studying, now come down we want to talk to you."


Stanley came into the kitchen and his father said, "Stanley, this school has done wonders for you. How did they do it? Was it something the Priest said?" Stanley shook his head. "Well, was it one of the nuns or one of your teachers?' Stanley still shook his head. "So, tell me why have you been doing so well?"


"Well, when I went in on my first day and I saw that guy nailed to the plus sign I figured they were really serious about math in this school!"

Hey Tom, I'm just curious but do you know how to prove that O! = 1?

Why do I feel like the guy who's making a crank phone call and the people on the other end are trying to keep me on long enough for the police to get a trace?


The answer is that you can't "prove" 0! = 1. This is a DEFINITION that is convenient for cases where factorials are used. It's fairly simple to demonstrate why this definition is convenient (eg. the binomial expansion).


This convenience is also confirmed by something called the "gamma function", which is an analytic continuation of the factorial operation (which acts only on non-negative integers) into a function that is defined over all positive real numbers. Basically this is a smooth function that passes through the factorial values and is well-defined for numbers that are not integers. If you follow this function to the point where the equivalent factorial would be that of 0, you get that the function's value is 1.


That concludes today's off-topic math lesson. I'm hanging up before you get a trace.


Tom Weideman

You have the answer above. You use the gamma function.


By the way, I don't remember anything else from my probability courses so there will be no more questions.


Best wishes,

Mason

Aces Full,


Assuming you are telling the truth aren't the chances that this happened 100%? Weird things happen in retrospect :-).


Regards,


Rick

That's a relief. I've never actually taken a course in probability (or statistics).


Tom Weideman

My buddy Chad had a way of coming up with the profoundest sounding things. Such is the way of understatement. Here's one of my favorites from him:


You never know when the inevitable is about to happen.


Tommy

I'm not counting my bad streaks, just thought it was pretty amazing....the reason I stopped raising with it was because I also found that raising with it didnt cause anyone to fold pre-flop anyways, i didnt get "demoralized".....in fact, i thought it was pretty funny....

...if someone bashed you over the head with it.

A classic from Yogi Berra, which is strangely applicable now:


"The future ain't what it used to be."