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>If Alice tosses a coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two heads in a row, then on average, Alice will require fo
by hellofunk 11y ago
>If Alice tosses a coin until she sees a head followed by a tail, and Bob tosses a coin until he sees two heads in a row, then on average, Alice will require four tosses while Bob will require six tosses (try this at home!), even though head-tail and head-head have an equal chance of appearing after two coin tosses.
Now that is particularly interesting to think about.
- dhbradshaw 11y agoThat's really cool. An easy way to understand it is by thinking about bunching. Since you're only flipping until you hit the first matching sequence, on average you'll hit the more evenly distributed sequence more quickly than the bunched sequence. Multiple heads in a row are more bunched than transition sequences because, for example, a sequence of three heads in a row will include two sequences with two heads in a row. You can't do that with a transition sequence--it takes at least four tosses to get two identical transition sequences.
- deleted 11y ago[deleted]