Just to be very clear on this, and although I consider everything in this post as plenty obvious, please read
<ul type="square">...Clearly, if we want to be practical, getting pocket Aces 4 times in a row should be considered as something we want, rather than a Failure!
Same thing when getting more than 1 streak of 3 Aces in a row, once more NOT a Failure!..
So, the question becomes
"What is the probability of getting at least 1 streak of at least 3 times of pocket Aces in a row in the next n hands?"
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Also
<ul type="square">...If we had only n=5 hands to examine, for example, we would calculate
through the above-mentioned formula the probability of getting pocket Aces
P(3)=
exactly 3 times in a row
in the next 5 hands
P(4)=
exactly 4 times in a row
in the next 5 hands
P(5)=
exactly 5 times in a row
in the next 5 hands
and then we would add up those probabilities.
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