How to use a bent coin

You play football on a deserted island and you want to flip a coin to decide which team will get the ball. The only coin you have is bent and therefore introduces a clear distortion in the result when tossing. How can you still use such a coin to make a fair decision?

Actually, there are two solution options for this challenge.

The first solution is to flip a coin multiple times to discover the percentage of heads and tails. Once you know that there are 54.7% of heads events (with an identified error limit), you use this fact to think of a bet with many tosses, when the chances of getting a result will be close to what you want.

The second solution option is much easier: flip a coin twice. Four outcomes are possible: HH, HT, TH, and TT (Heads – tails, T – tails). Since the coin is “favourable” to one side, the chances of a TH drop are not equivalent to the odds of the TT. On the flip side, the chances of dropping the HT and the TH should be the same, regardless of the coin’s “favour”. Thus, the first team puts a stake in the HT, the second in the TH. In case you see HH or TT, you should ignore these events and throw a couple more times.

Additionally, the second solution is both easier and undoubtedly fair. The first solution option only tends to 50/50 if we talk about accuracy.