TITLE: How to assign 3 rooms to 3 people with 1 coin randomly?
QUESTION [8 upvotes]: We are 3 friends; just checked into an airbnb flat with 3 rooms. And to make things truly random we decided to use 1 coin to assign each person a room. What's the best way to do this?
(Assuming coin flip is truly random.) (One way to define 'best' is minimum number of flips)

REPLY [11 votes]: Since there are six possible outcomes with equal probability, you'd b bettre off with a die, and unfortunately, the number of coin tosses cannot be bounded: With at most $k$ tosses, you can only define probabilities of the form $\frac m{2^k}$.
However, there is a nice(?) method for even more general probabilities: Start an infinite sequence of coin tosses (but don't worry, we will almost surely stop after just a few tosses) and interpret the outcomes as infinite binary number. So e.g. $HHTHHTHHHHTTTTTTHTTH\ldots$ becomes the binary number $.00100100001111110110\ldots$. Already with these 20 tosses, it is clear that our number is approximately $0.1415926\ldots$ in decimal. Now we assign the intervals $[0,\frac16)$, $[\frac16,\frac13)$, $[\frac13,\frac12)$, $[\frac12,\frac23)$, $[\frac23,\frac56)$, $[\frac56,1]$ so that each interval has length $\frac16$ (or whatever probabilty we want); also, it typically does not really matter if we assign the boundary points to the lower or upper interval. As $\frac16$ is $.0010101\ldots$ in binary, it is clear that our generated random number is $\in[0,\frac16)$ and hence we take the first of the six possible outcomes. Actually, we did way too much for the sake of insight into the example: Already after five tosses $HHTHH$, it is clear that our number will end up $\in[0,\frac16)$, hence we could have stopped there (but not earlier).