An uneven coin

Two groups want to break a tied vote using a simple coin flip, however the only coin they have available is a biased coin (ie. one side will come up more often than the other). To make matters worse nobody in the room knows (or is willing to admit) precisely how the coin is biased.
Assuming that the coin has two distinct sides design a method for using only this coin to determine a fair outcome between the two parties

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Originally Posted by b0mb3rz

Two groups want to break a tied vote using a simple coin flip, however the only coin they have available is a biased coin (ie. one side will come up more often than the other). To make matters worse nobody in the room knows (or is willing to admit) precisely how the coin is biased.
Assuming that the coin has two distinct sides design a method for using only this coin to determine a fair outcome between the two parties

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Toss the coin twice if HT comes up group 1 wins, if TH group 2 wins, any other outcome repeat until HT or TH occurs.

(Of course if nobody knew how the coin was biased a single toss would suffice)

CB