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I was thinking about a puzzle, unfortunately I do not remember where I saw it, which asked about

Given a skewed coin where the $p_H \neq p_T$ where $p_H$ and $p_T$ are probability of observing head in one coin flip and probability of observing tail in a single coin flip, respectively. Is it possible to obtain a non-skewed coin by flipping the given skewed coin?

Even keywords for more search are greatly welcomed.

RGS
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Ali Shakiba
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Yes, this is a very famous trick by von Neumann:

Say player I wins if in two consecutive coin tosses we get heads followed by tails. Player II wins if in two consecutive coin tosses we get tails followed by heads.

Toss the coin until one of the players wins - rejecting both tosses every time neither player wins. You can calculate that each player now has a 50% chance of success. However, if the coin is heavily skewed, you may have a very high average waiting time (infinite for a one sided coin) for one player to win.

Stefan Mesken
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    Btw. I think that - at least when two mathematicians decide to rely on a coin toss - this (or an equivalent) approach is the only acceptable option to do it. – Stefan Mesken May 27 '17 at 10:48
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    Also note that the repeating must start afresh, that is if the first two tosses are the same, then we reject both tosses, not just the first one. (If we did not, the final outcome would obviously depend only on the first toss and be biased) – Hagen von Eitzen May 27 '17 at 10:50
  • @HagenvonEitzen Yes, sorry I didn't make that clear. – Stefan Mesken May 27 '17 at 10:51
  • That's interesting. Is there a reference that states this trick is due to von Neumann? – littleO May 27 '17 at 10:57
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    @littleO I was told this by a former professor of mine but the link I provided cites the following reference: Various techniques used in connection with random digits. NIST journal, Applied Math Series, 12:36-38, 1951. This article does not seem to be available online, though it is widely cited. It is reprinted in pages 768-770 of Von Neumann’s collected works, Vol. 5, Pergamon Press 1961 – Stefan Mesken May 27 '17 at 10:58
  • Oh I see, thanks! – littleO May 27 '17 at 11:00
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    @littleO I think it's incredibly likely that he wasn't the first human ever to discover this (given that it's a very natural thing to look at) but he might be the first one to publish his findings in the scientific community. If there is an earlier account of this, I'd be happy to know about it. – Stefan Mesken May 27 '17 at 11:01
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    They should do this in football. – AAM111 May 27 '17 at 12:24
  • Made a Python quick version of this, look at the randomness! http://imgur.com/a/Q980g. Go to https://repl.it/IUS6/1 to try it yourself! – AAM111 May 27 '17 at 12:44
  • @OldBunny2800 Pretty good, huh? ;-) – Stefan Mesken May 27 '17 at 12:48
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    You can reduce the "waiting time" by applying this algorithm recursively, for example Tossing a Biased Coin. – pipe May 27 '17 at 17:40