Bob Dancer is absolutely correct when he wrote "Doing these after-the-fact calculations is
meaningless."
It's what I call 'selective sampling'. If I look at all my plays over a year ( or several years) I can find certain oddities. Of course there are oddities on every hand , as Bob mentioned. There will be 'paying oddities'.
For example, early in my vp careerm back when the LVA used to give you the free roll of coins at 4 Queens, I had a sequence of 3 of a kind, 4 of a kind, 4 of a kind, 3 of a kind.
The odds of that particular sequence ( 10/7 DB) is 1/14 * 1/420 * 1/420 * 1/14 ( approximately) or about 1 in 34.5 Million. To make it a valid statistic, I need to specify what the event is and how many samples I'm going to take. By saying I hit a 1 in 34.5 million shot, I'm being misleading. Also, in the 20 years of video poker since then I have never had that sequence again. Have I play 34.5 million hands ( or 138 million hands, depending on you define the interval)? Probably not but I have played enough to make that occurrence not all that unusual.
I have a theory ( as yet untested) that any sufficiently large sample of hands will produce at least one unexpected occurrence of a hand type. I will define 'large sample' as 5000 hands or more and ' unexpected occurrence ' as a hand type being more than 2 sigma away from the expected value. One of these days I will test that theory.
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