Bad Beats
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Something has seemed out of whack for a while. I have played well over 1 million hands, but rather than complain about a "feeling", I wanted to look at hard numbers and data. There are many things I could look at to see if different probabilities are out of whack with expectation. The very first thing I decided to look at, using my db with 236,317 tournament hands (a significant sample size), was the distribution of how many times I got dealt pocket pairs, particularlly premium pocket pairs. A pretty simple thing to analyze.
At first, I looked at the breakdown by blind-level and was a bit concerned to find that at level after level, I got dealt fewer AA and KK than any other pocket pairs. For example at the 50/100 blind level, the sample was 73,926, from which I could expect to be dealt a particular pocket pair, like AA, on average apx 336 times. The two that were farthest below expectation were AA (-16) and KK (-21). This repeated at each blind level I looked at.
So next, I aggregated and looked at all 236,317 hands together, regarless of blind level. What I found furthered my concern. Again, the least dealt pocket pair was AA (1010), followed by KK (1040), furthing the suspicion. So I ran some hard statistical analysis on this and found that on average for that sample, there is only a 2.5% chance of being dealt fewer than 1010 AA (and 97.5% chance of being dealt more). Note that this doesnt give any weight to the value of AA vs other lower pairs. The fact that this repeats itself with the other monster pair, KK, is again concerning.
I'll give a quick summary of the mathematical reasoning and tools used for review.
If we think of this as a binomial distribution problem, where success (=1) is being dealt an AA, and failure (=0) is not, we know that we have an expected probability of success in a single trial of 1/220, or .00454545..., the odds of being dealt a pocket pair. From my data, we know we had 1010 successes in 236,317 trials. After working the math on my own, I also found a caclulator online you can use by plugging in these variables: http://stattrek.com/Tables/Binomial.aspx You can see the conclusion is that for this sample, we would expect more AAs 97.4% of the time. I would also expect to see KK significantly more than I did. When you look at both together (use values of .009090909090909090909, 2050, and 236,317 in the online calculator), we see my distribution become even more unlikely (98.3%).
What is more concerning yet is that when I look only at the most recent 100,000 hands, the pattern exacerbates itself more dramatically.
Note that if there is rigging that damps the number of premium hands, it would be foolish to damp them to fall much more than 1 or 2 standard deviations away from the norm. So the 98.3% number I see above would be the maximum one could reasonably expect under that scenario. In other words, its the max range that remains "unprovable" due to variance.
More to come.... note that this is the very first thing I have looked at after suspecting suspicious activity. I am starting to look at other aspects that are looking troubling as well, but will post only after I work out numbers. I would like to keep this an ongoing discussion, and invite others to use their db to plug numbers into the calculator I linked to.
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tin foil hat time
so basically youre saying that according to your data youre seeing AA/KK less and less with each passing blind level? Does it decrease accross every single blind level?
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Also, if anyone has writen any code that parses hand histories and does statistical analysis on the results that wouldnt be easy to see using pokerTracker, please post a link to the code. For example, looking at hand results for how much your pre-flop expectation when HU differs from actual results of the hands, etc, etc. For example, I'd like to be able to run HH through some code that analyzes expected EV vs actual results, or that analyzes the probability of the river hitting opponent vs actual results, etc, etc. I have been working on some Perl code to start doing some of this, but time is tight... so if anyone has anything I could add to, that'd be great.
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no, what I'm saying is that I see fewer AA and KK than any other pocket pair at EVERY blind level, and all together, and that its is statistically significant. Over the quarter million hands I looked at, I saw fewer AA than any other PP. The PP I saw second fewest of was.... take a guess.... yep: KK. And the differences in the number seen vs the number expected for such a large sample is very unlikely. And that doesnt even account for the fact that AA is any better or worse than, say, 22. If you were to weigh the hands by value, with AA and KK being more valuable than other PPs, which they are, the results would be alarming.
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Of course they can't deal AA and KK according to odds...nobody would chase the flushes if they didn't have that suited A or K in their hands.
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Next I'd like to see the amount of times you lose with a better hand (getting it all in preflop) to a larger stack... Seems to happen to happen all to often.
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Looking through my HEM database now and the numbers look pretty normal to me...These are hands for cash games by the way, my mtt database doesn't have nearly enough hands to make any conclusion. Here are my pocket pair frequencies according to HEM over 370k hands ranging from 2nl to 200nl.
AA - 0.47%
KK - 0.44%
QQ - 0.45%
JJ - 0.42%
TT - 0.44%
99 - 0.44%
88 - 0.47%
77 - 0.46%
66 - 0.43%
55 - 0.45%
44 - 0.47%
33 - 0.45%
22 - 0.47%
Nothing that really looks out of balance to me, everything +/- .02%. I do feel that there may be some irregularities due to rng's not really being perfectly random but it doesn't look like any "rigging", at least for mine. Not to dispute your data, definitely seems like something is there. Would be interested to see some others data, tourney and cash. Also for a EV calculator, look in the software section of 2p2, there should be some. Btw a quick look at my mtt database and I was dealt AA .42% and KK .50%, all pairs in that range in no easily recognizable pattern.
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Update: it gets worse. I just looked at the other monster hand, AK (any suit). I had 2767 occurrances in 236,317 sample. It should occur on average 1 in 82 hands. Get this... my results show it is almost *exactly* as out of whack as AA and KK. 98.4% probability that a random sample would have more occurrances of AK. By itself, its a enough to perk up, but in combination with the AA and KK stats all being around 98.4% ALSO, its alarming. All three of the top 3 hands are way out of whack. By my calculations, the odds of this are 2.744 out of 1 million, though I would welcome others showing their calculation methods. With each new item I look at and run numbers for, it becomes farther and farther away from random probability and looks more and more strongly to be rigged. It is very concerning. And I have only begun looking at the more complex, multi-variable scenarios. But so far, a 99.99973%chance that its not random is pretty strong and disturbing.
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In before someone posts sick brag about knowing math.....
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you run good are all these hands from one site or is it multiple sites?
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super system says you should be dealt AK 1 in 110 hands...not sure where youre geting 1 in 82 and claims a pair to be 1 in 220...maybe im reading it wrong?
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i was playing a ring game last weekend, and it took more than 470 hands before i got AA. i dont think its rigged, but just chimen in
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 MarkFSU1: | |
super system says you should be dealt AK 1 in 110 hands...not sure where youre geting 1 in 82 and claims a pair to be 1 in 220...
Such is where Doyle makes his monies...
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