KK ran into AA 4 times in a row - NOT a bad beat post

[BruceZ]

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In the last 5 days I have been dealt KK 4 times. Each time I have ran into AA. Now I've been playing long enough not to be worried about this sort of thing (anyway, I sucked out the fourth time [img]/images/graemlins/smile.gif[/img]) but it got me thinking about how unlikely it is, and I realised I was not sure how to calculate the probability of this happening.

Is my simple method correct?...

It is approximately 20 to 1 to run into AA when you have KK at a full handed table, so I simply multiplied the 20 to 1s together. So the odds of having KK run into AA the last 4 times I had KK would be (20x20x20x20) to 1. This is 160,000 to 1. Is this the correct method?

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Not quite. If it were 20-to-1, that would be a probability of 1 in 21, and you would multiply 21*21*21*21 to get the probability, and then subtract 1 to get odds, since you multiply probabilities not odds. The actual number for a 10-handed table is 21.8-to-1 as shown here, so you would take 22.8*22.8*22.8*22.8 - 1 =~ 270,233-to-1.


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160,000 to 1 is rather a long shot, and I wouldn't believe anyone who told me it had happened to them, but there you go...

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While this is very unlikely for any 4 specific hands, it is almost guaranteed to happen over enough hands. Remember, extremely rare events happen all the time.