(OT) mathematicians-discover-prime-conspiracy

[Viktor Dick]

On 2016-03-18 13:18, Peter Lebbing wrote:
> Can someone point me in the direction of the solution to this
> counterintuitive probability theory result? Any of a common name for the
> property, a mathematical explanation or an intuitive explanation are
> much appreciated!

Any match of a pattern (HH or HT) to a sequence of coin tosses can be
either align (i.e., starting at the first/third/fifth etc. toss) or
misaligned (second/fourth etc.). If you count the number of aligned
matches in a sequence of a given length, you will get the same
probability regardless of the pattern. The same with the misaligned
matches. However, the number of aligned and misaligned matches is not
independent. For HH, they are correlated (if one pair of tosses is a
match, the two overlapping ones are each matches with probability 0.5
instead of 0.25) while for HT they are anticorrelated (if one pair is a
match, the overlapping ones can't be matches). Therefore, you will find
more matches for HH than for HT. If you toss until you get a result,
with HH you will get it quicker on average.

Regards,
Viktor

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