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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1Find any coin.Ad
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2Designate one outcome heads. (This outcome occurs with probability p.)
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3Designate another outcome tails. (This outcome occurs with probability q).
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4Flip the coin twice.
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5If 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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6If 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.Ad
Example
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1A biased coin might give a sequence like HHTHTHHHHHHSHHTTHTHTHHHH (generated on the assumption that heads are twice a probably as tails)
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2Split this into pairs HH TH TH HH HH HS HH TT HT HT HH HH.
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3Void anything other than HT or TH leaving only TH TH HT HT.
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4Pick the first of each pair, for TTHH.Ad
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
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