Math Help (No-Limit)

No-Limit Hold'em,


A guy I played with for the first time a few months ago limped under-the-gun with pocket aces and knocked me out of a daily tournament. Well I had the same guy again at my table a few nights ago and when he limped UTG I thought "Uh Oh."


It turned out that he had limped with K-2 suited, so I was wondering if you can you approximately determine the chances of this guy actually having pocket aces when he limps UTG with those range of hands? [He also limps with J-6 offsuit on the button]


Thanks

Maybe he's just a calling station. I've seen a lot of players that always limp and never raise. Therefore you have no clue, but they might have. You do know that their money will eventually end up in your hands:) GL


Sheck

Martin,


I have a few things to say that you may want to think about. First, your odds for being dealt pocket aces are 220-to-1. So, if you are playing at a ten handed table you should see pocket aces once every 22 deals.


Something that I have noticed, is if he had them once under the gun, and he limps in under the gun the next round, he will not likely have them, because the odds of being dealt a 220-to-1 hand in the exact same position, I believe would be 2200-to-1(someone correct my math here if I'm wrong). I think this is interesting. This is why I like my opponents to show their hands when they win.


When someone limps in with aces its for one of the following reasons:


1) The action is aggressive and he expects to be raised. He will either call the raiser or reraise depending on the situation.


2) He's been playing very tight and expects his raise to just steal the blinds, so he limps to get action.


3) The table has been very tight and players have been folding to raises.


4) Usually, in the latter stages of the tournament most players will raise with this hand, because others will look at this raise as a sign of weakness, especially if his image is aggressive or if he has a smaller stack and he is looking to play a heads up hand.


Good Luck


Mark

getting it the second time would still be 220 to one.

Martin,


We have about 0.1% of the information we need to give a precise mathematical answer :-).


It would be better to explain how this works so you can do your own calculations. What you need to do is count card combinations. For example, if someone reraises you and you know he will only reraise with AA, KK, QQ or AK then what is the probability that he has AA ? There are 6 AA hands he can have - AsAh, AsAc, AsAd, AhAd, AhAc, AcAd. Likewise 6 KK and 6 QQ, and 16 AK (many more because now the suits can be duplicated, plus AsKc is not the same hand as KsAc). So there are 34 hands he can have, 6 of them are AA and the probability of his having Aces is 6/34 = about 18%. But this is only as accurate as your "knowledge" of his re-raising hands.


Now, that is if you have say JJ. What if you have AK ? Now you remove the combinations which are blocked by your cards, there are 3 AA hands he could have, 3 KK, 6 QQ and 9 AK (check those numbers yourself !). Now the probability of AA is 3/21 = about 14%.


So what you have to do is perform this kind of calculation over the whole range of limping hands he could have, and this range is the necessary information which is missing for us to give you an answer. If he limps with any 2 cards, there are 1326 hands (52 x 51 / 2) he could have and so the probability of Aces is 6/1326 = about 1/220 which is where the figure quoted above comes from.


Hope this helps,


Andy.

Ray,


Thanks for the correction. But, it does appear to be not likely. In my gambling endevors I've noticed some strange things happen. I'm not refering to probabilities here, but the behavior of random events.


For example, I'll observer a player gets a pair of aces once during a tournament and never again. Then I'll see someone get them back-to-back and then not get a decent hand for over an hour.


What's the answer to this question. If UTG gets a pair of aces and then gets them again UTG what are the odds of that event occuring within 10 hands dealt? I know proability says it is a 220 to 1 shot to get a pair of aces.


Last question, what are the odds of being dealt a pair of aces back-to-back?


Help me! I need to figure out why these things occur.

lots of math going on here---but I can tell you an absolute way to have him show up with AA again...just put me in the game with KK ! ! ! !

Mark,


Your questions aren't really specific enough. Let me give you a few examples and you might see why these things do indeed happen :


The odds against you being dealt Aces in both the next two hands are around 50,000-1 (whoah ! How do these things happen !!)


The odds against you being dealt Aces back-to-back at some point during the tournament (assuming 100 hands played) are around 500-1.


The odds against anyone at your table being dealt Aces back-to-back at some point during the tournament are around 50-1.


The odds against anyone in the tournament being dealt Aces back-to-back at some point are around 10 or 20-1 I suppose depending on how many tables there are.


If you, sitting at a full table, say "wow, I'd sure love to get Aces back to back", the odds against someone saying "yeah, I saw a guy do that last week" are really quite low indeed.


There are so many hands being played all the time and so many ways for someone to hear about some bizarre hand from a friend of a friend of a guy on the rail that everything comes up sooner or later. It would only be surprising if it didn't.


Andy.

Andy,


I would like to know how you determined those answers. I'm the one that needs the math help.


Anyway, I'm speculating about how random events occur. Forget probabilities, I want to know why someone will get two great hands back-to-back and then get no help at all. Or why you get great hands during a tournament and either get busted or have to lay them down, and then you win with trash in the big blind because no one raised you.


I've noticed patterns occuring in random events. This is what I think is interesting. I'm talking about patterns that occur in relatively short periods of time, not probability, I know most of that.


I guess you could say that I'm looking beyond probabilities. That's why if I see someone win with a pair of aces they usually don't have them again within a short period of time. This may sound crazy, and I can't prove it, but I think that the "luck" factor is a short term pheonemon. During a tournament you go though cycles when you get lucky and when you are not. I've observed these patterns first when I was previously a Crap player.


Good Luck


Mark

Patterns can be found in any discernible past event. However, in cases like cards or dice, those patterns are only present in the past, and can never be extended into the future. Thus, there is no advantage to looking at the past as an aid to predicting the future in poker or dice. The only connection is in how the cards of the past have changed the attitude, demeanor, or style of our opponents (or ourselves).


Later, Greg Raymer (FossilMan)

Mark,


There was an interview with Richard Tatalovich on Poker Pages recently which I was very impressed with. One of his themes was "why ask why ?". I think it applies perfectly here. There are a lot more useful things you can think about. Why do these things happen ? They just do !


One more point to try to make it clear : you say "if I see someone win with a pair of aces they usually don't have them again within a short period of time.". Well, if someone doesn't get Aces on a particular hand, they also usually don't have them again within a short period of time. Just like Greg says, you can observe random patterns in the past, but it doesn't help you predict the future.


Andy.

Greg,


You said,"Patterns can be found in any discernible past event. However, in cases like cards or dice, those patterns are only present in the past, and can never be extended into the future."


Do you have any mathematical or scientific proof that patterns in random events can not be extended into the future?


In the late 80's I worked for a company that sponsored research at the Univerity of Illinois and Pennsylvania. The basis for the research was to be able to predict cardiac arrests in critically ill infants before it happened. It's been a long time since then so I can't give you exact details. But, they were able to do this with very high accuracy. What they looked for were patterns created from plotting a fourier transform based on the respiratory rate/heart rate. With later research at the University of Texas they found that substituting blood pressure was more accurate.


I just wanted to mention this so you understand where I'm coming from and why I am interested in patterns occuring in random events.


Mark

in random events like dice. past results do not affect the future as each event is on its own. with cardiac arrests past events do in fact determine future events. so thats the difference. it may be hard to understand if you look at random events and want to find patterns for the future but they are not there. just like fortune tellers are a hoax.

Ray,


There has been plenty of proof that fortune tellers are a hoax. I will not go into the details, but it is totally off base to even refer to that subject in this context.


What I am interested in talking about is patterns that occur. Many people obverve this phenonemom, but no one here can show me some research to prove otherwise. Furthermore, everyone here refers to probability, but probability only deals with the behavior of long term results.


Most gamblers have observed patterns in even money or close to even money events whether it is dice or coin flips.


Gambling rusults fall into three different categories. At the Craps table players will call it choppy, hot, or cold. The extremes of these patterns is what hooks a gambler on this game. For example, when the table is hot players will make alot of money on all kinds of bets that would be bad. Once, they have made a killing they keep coming back to make that big kill again. The problem with this thinking is that these patterns of events don't occur often enough and are unpredicable when they happen. The phase that most gamblers experience is the choppy phase. This is when the hot and cold streaks are short and the house percentage on the game will assert itself. The choppy streaks usually may run hot or cold for four to six decisions from my observations.


I know you are not interested probably in any of this information. But, I am willing to do some reseach to prove that you can gain a slight edge. When I'm finished I will publish it. Case closed.


Goodbye


Mark

Hell, don't publish it Mark. Keep it to yourself and win a few million first.


Joke :-)


Andy.

Andy,


I'm only going to publish the stuff that has only a small edge, the rest I'll get rich from. Just like Ray Zee. He only tells us a little and keeps the good stuff for himself. Mason told me that he does share his stuff with his best friends, but I can just about bet that he will not write a No-Limit Hold'em or Omaha High book.


Good Luck


Mark