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Originally Posted by W
Random.
Random.
Pure coincidence.
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well, of course it is random.
but just thinking about what you would logically expect to see.
it should take, on average, about as long to get to your first 111 series as your first 010, right?
here's the point:
comparing 1110 to 0101,
every 111 is guaranteed to terminate in a 1110 string. so whenever you see '111', 1110 isn't far behind.
every 010 only has a 50% chance of terminating in an 0101 string, and if it doesn't you start over from scratch.
so one could expect 1110 strings to appear, on average, sooner than 0101.
but there are obvious points of weakness in this argument (notably, how do you know that 111 shows up as quickly as 010?), so actually testing it out is always better form.
i get 1110 showing up 12-13 in,
and 0101 showing up 18-20 in.
i would love for someone to prove me wrong.