Puzzle about technique of fair using of unfair coin There is an unfair coin. It tends to land on one side more than on the other. It is unknown which side is it.

There is Mr. A and Mr. B. They argue about something and they want to use that coin to decide who is right.

Is there any technique of using that unfair coin to get fair result?

My solution:
I can think of only that there is going to be 2 rounds. First time Mr. A chooses HEAD, than Mr. B chooses HEAD if any of them wins twice they win.
I think you need an unbounded number of coin tosses, however the expected number of tosses to settle the issue will be finite: Toss twice. If it comes up heads, then tails, A wins. If it comes up tails, then heads, B wins. If the two tosses come up the same, start over. If the coin is extremely unfair, this will probably take a long time, but if it is only a little unfair, you should be settled soon enough.
There's a difference here between randomness and predictability.  If the coin is only tossed one time, the answer is unpredictable, even though the result is biased.  Ask one of them to pick heads or tails, and toss the coin.

The more often you toss, the more the bias will become evident, and predictability becomes an issue.  Fairness is based on unpredictability, not randomness.