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AA, where are you?

Monday, April 27th, 2009 | admin | Poker Articles, Poker Mathematics

Submitted by Mctap, this article belongs to the Poker Mathematics series.

This blog consists of 3 separate posts on my site that I have consolidated into 1 longer, more detailed post here.

About a month and a half ago I decided to check out my Poker Tracker stats for Poker Stars and noticed something interesting. At that point in time I had only played about 656 tournament hands and still hadn’t seen AA. No big deal as I was still up a few bucks since I started. I just found it interesting that with the probability of AA coming up being 1 in every 221 hands, I should have seen them almost 3 times by then. What did this mean, well, since the cards are generated through a Random Number Generator (RNG) program and many people complain that online poker is fixed, I *should* eventually hit a stretch of hands where I get AA more times than expected. Now keep in mind, I don’t think that online poker is fixed/rigged in any way, shape, or form, but if you spend time reading forums/blogs, you may get the impression that with so many bad beats given out, something fishy could be awry.

Several weeks went by before I looked at my Poker Stars tournament numbers again on Poker Tracker and discovered that I had played another 500+ hands (I know, I was just tearing through those hands) and during that time, I managed to see AA 3 more times. Much better, as this worked out to be 1 in approximately every 166 hands, which is more than the probability of getting a pocket pair (1:221). During those 3 times I had AA, I managed to take down all the pots! Another positive. What made all of this interesting, to me at least, is that over 1100+ hands I had seen AA 3 times and won with them each time (everybody expects to win with AA, but that does not always happen). So even though their frequency was worse (1:366) than their probability (1:221), their win rate was better (100%) than expected (~80%).

At this point I really started to expect that, according to odds and statistics, I *could* see them again soon. This time, I *could* also expect to possibly lose with them in order to balance out the numbers. Now some may say that this is Gambler’s Fallacy. For those who don’t exactly know what Gambler’s Fallacy is, it is to assume that one random event is somehow connected to another random event. Wikipedia has a great write up on Gambler’s Fallacy if you want to know more. Keep in mind, that when I say I *could* expect to see AA again, doesn’t mean I will to see them again. I am a numbers person and fully understand that each and every hand is randomly generated and has no correlation to any other hand played or to be played. Anyway I look at it, the odds of getting a pocket pair (in this case AA) is always 1:221, for each and every hand played, and it is very possible that I get the same exact hand dealt to me multiple times in a row. Although with a good RNG, the odds of this happening is quick small. Bottom line is that with the presumptions that I *could* lose with them, or that I may get AA more often, my thoughts are to play them strong and IF I lose, that is the nature of the game and really can’t complain about it (no matter how much it hurts to get your Aces Cracked).

Finally after playing another 1000 hands over the next 3 weeks (I’m just a machine, lol), my numbers stated that I was lucky enough to get AA only once more. Although that doesn’t fall within the realms of probability, it does show that the RNG is exactly that, random. Also, I did manage to win with them, which demonstrates that AA is a dominant hand against most random hands. So much for the Gambler’s fallacy.

Now to this point on Poker Stars, I’ve played a little over 2000 hands and have seen AA 4 times in my hand. That is roughly once every 500 hands. Nowhere near the 1:221 probability of getting a PP, but I have managed to make the most chips with them while playing (according to PT3). Again, at some point I *should* expect to start seeing AA more often and *might* lose with them (no hand can run 100% forever). Even if this becomes true, I will still play them aggressively to maximize my chip return.

Another interesting point is that during this stretch of hands on Poker Stars I did managed to see 77 18 times (1:111), which is much greater than the probability of seeing a pocket pair (1:221), but with 7’s I only won 56% of the time and actually was down chips overall. If you are confused, I won 10 out of 18 pots, but the total amount of chips won is less than the chips I lost during the other 8 times I had 77.

Bottom line is that I’m not complaining about not getting AA, nor any other pocket pair, I’m just monitoring this trend to see how it plays out for me. Always try to remember, that just because someone was lucky enough to get AA, or any PP for that matter, doesn’t mean they can’t get it again the very next hand.

See you on the felt.

McTap03

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