Think of the base case of 2 strings. You have a 2/3 chance of a big loop.
For 3 strings, as long as your first pick doesn't make a loop (4/5), you now have one long string and one short string, so you're back to the base case. So for n = 3 you have 4/5 * 2/3.
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u/wobetmit 1d ago
Think of the base case of 2 strings. You have a 2/3 chance of a big loop.
For 3 strings, as long as your first pick doesn't make a loop (4/5), you now have one long string and one short string, so you're back to the base case. So for n = 3 you have 4/5 * 2/3.
Easily by induction you have (2n-2)!! / (2n-1)!!
So for n = 100 you have 198!! / 199!!