How to Simulate a Fair Coin Toss With a Biased Coin

One Methods:Example

Coin tosses are a popular way of picking a random winner. Usually it suffices to simply nominate one outcome heads, the other tails, and flip the coin to decide, but what if one party to the dispute thinks that the coin is unevenly weighted and has a 51% chance of landing on heads. This method takes any coin, and by making a sequence of tosses, allows you to choose one outcome with exactly 50%.

Steps

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    Find any coin.
  2. Image titled Simulate a Fair Coin Toss With a Biased Coin Step 2
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    Designate one outcome heads. (This outcome occurs with probability p.)
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    Designate another outcome tails. (This outcome occurs with probability q).
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    Flip the coin twice.
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    If both tosses gave the same outcome, or if either toss landed on its edge or did something else not accounted for in steps 2 and 3, don't count either toss and redo step 4.
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    If you got heads before tails, count it as heads. If you got tails before heads, count it as tails. Since these two outcomes for a pair of tosses each have probability p*q, you have a fair coin toss.

Example

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    A biased coin might give a sequence like HHTHTHHHHHHSHHTTHTHTHHHH (generated on the assumption that heads are twice a probably as tails)
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    Split this into pairs HH TH TH HH HH HS HH TT HT HT HH HH.
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    Void anything other than HT or TH leaving only TH TH HT HT.
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    Pick the first of each pair, for TTHH.

Things You'll Need

  • Any coin, die, or other random device with at least two outcomes. It is not necessary to know the probability of these outcomes.

Article Info

Categories: Games of Chance