Tossing old gold coin puzzle
Two men find an old gold coin and want to have a coin toss with it to decide who gets it. The only problem is the coin is heavier on one side so it comes up heads more than tails.
What is a fair way for the men to toss the coin and decide who gets the coin?
A competition of two rounds, they can make a deal for both of them to choose one same face then one of them toss as a first round then the second round for the other man,
If the result of the rounds are the same face the competition should be repeated till the result of rounds are different and the winner is the one who had the chosen face
Lets assume probability of H is x and that of tail is 1-x. We can see that the probability of coming HT and TH is same which is x(1-x).
So The two guys can chose one of the two cases(HT or TH) for each of them. And start flipping the coin:
if HH came then the cycle restarts.. and same for TT.
Hence HT and TH can be obtained equiprobably.
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