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However, this outcome is exactly as likely as tails tails heads heads, and hence we may as well call the first one HEAD and the second TAIL.
Further, it is clear we can extend this, so that 4 heads followed by 4 tails is called.
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Here we give new algorithms for simulating a flip of an unbiased coin by flipping a coin of unknown bias.
Can one be more efficient, i.e., not flip the coin as often on average?
Von Neumann gave a simple solution: flip the coin twice.
We also prove a conjecture of Hoeffding and Simons that there is no optimal algorithm, i.e., there is no algorithm that is best project for all possible values of the bias.
Tree Algorithms for Unbiased Coin Tossing with a Biased Coin.
We do this in a very strong sense by giving a specific tree T such that if T' is the same tree with the roles of heads and tails reversed, then there is a bias probability p such that for any algorithm A for unbiasing coins, the expected number of flips required by A is.
Abstract m/abstract2525545 City University London - Sir John Cass Business School.
We are interested in efficient algorithms, where the expected number of flips (as a function of the bias) is our measure of efficiency.
HEAD and 4 tails followed by 4 heads is called TAIL, and so on.
If it comes up heads followed by tails, then call the outcome HEAD.
City University London - Sir John Cass Business School.
I.e., one can do a bit better, and in fact would need more than 4 flips only if they were all heads or stories all tails.
This algorithm is quite easy to implement.
It was digitized and placed on JSTOR.
Other authors have represented algorithms as lattices, but by representing them instead as trees we are able to produce an algorithm more efficient than any previously appearing.
Otherwise (i.e., two heads or two tails occured) repeat the process.
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