Quote:
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Originally Posted by queball
If you get 011111110 then that's three 1111's.
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yeah this is the post that finally got everything to make sense to me.
the issue is overlap. 1111's can overlap 3/4 of the way, 1110s can't overlap at all. so 1111's tend to bunch together; whereever you have one of them, you have on average 2.64 of them overlapping. where ever you have one 1110, you have on average 1 1110 (because they can't overlap at all).
so, running numbers, when you get to a 1111, you've gotten to (on average) 2.64 1111's, but for the methodology described that's no different than getting to one. whereas getting to a 1110 you've gotten to on average 1 1110.
so here's the options:
1) it takes 2.64 times as long (on average) to get to a 1111
2) there are 2.64 times as many 1111s (not the case)
3) combination of 1 and 2 (not the case)
from overlap, everything is pretty easy to figger out:
1110s and 1100s show up quickest (can't overlap at all)
1101s 1011s show up pretty quick (don't overlap much)
1010s take a while (can overlap pretty well, 101010)
1111s take forever (as queball says, 111111 is three of them)
it's rather a non-intuitive result.
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