An alternative way to calculate this would be 1-(runouts without an A/K)/(total runouts), or 1-(44 choose 5)/(52 choose 5) = 58%
Quote:
Originally Posted by statmanhal
The observed 64% is a bit surprising simply because if a hand went to completion, there's a pretty good chance that at least one player has an ace or king, making the theoretical probability even smaller than 58%.
The chance of observing an Ace or King 640 or more times in 1000 hands is about 0.011% given we accept the optimistic 58% number. So, we can either suspect rigging or faulty data analysis such as a wrong filter. I strongly go for the latter.
I think a vast majority of these types of situations arise as a result of selection bias. Someone running bad is looking for a reason that the game isn't fair and of course they will find something. If everybody was posting about their experience of seeing too many As/Ks, or getting oversetted too much, or getting AA cracked AIPF too much, it would be suspicious, but instead each individual has distinct types of run-bad most of the time.
Even though the event of getting so many As/Ks on 5-card runouts is pretty low, the pool of events being chosen from was likely enormous. What I mean by that is, if a normal amount of As/Ks appeared, we'd likely instead be asked the probability of not getting AA once in 1000 hands after it happened to the asker