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Given a biased 6-sided die of unknown bias, can we simulate a fair coin toss?

user230417
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1 Answers1

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Call a roll of 1-3 "A", and a roll of 4-6 "B". Roll the die twice. If you get AB, call it "Heads" and stop. If you get BA, call it "Tails" and stop. If you get AA or BB then roll the die twice more (i.e. repeat)

This will terminate with probability 1 so long as both A and B have nonzero probability.

vadim123
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  • That is assuming that the bias remains constant which it may not be. The answer to the question is yes it is possible, but cannot be stated for certain because we don't know if the bias is constant or not. For example, the die could me magnetized and the bias could be dynamic on a per roll basis. – David Apr 11 '15 at 01:59
  • That is not what is normally called "bias", which is used to denote constant but non-equal probabilities for the various outcomes of a die or coin. – vadim123 Apr 11 '15 at 02:05
  • I would call that a constant bias and interpret bias to mean anything except the expected value (in this case 1/6 for each side appearing on average). Where in mathematics does it say that a bias has to be constant? – David Apr 11 '15 at 02:14
  • See the second sentence. – vadim123 Apr 11 '15 at 02:39
  • Any deviation from the expected value is referred to as a bias. Any in this context means it could be a constant or variable deviation as long as it is not the expected value. For example, if I had a special coin that would alternate 45% chance of heads then 60% chance of heads... is a biased coin. Nowhere in the definition of biased does it state it has to maintain the same deviation from the expected value such as 60% heads all the time. It just states it has to be something different than the expected value. – David Apr 11 '15 at 02:52
  • @David, I would say that only OP can tell us what he or she had in mind when using the term "bias". My guess is that vadim's interpretation is what was intended (but, of course, I might be biased...). – Gerry Myerson Apr 11 '15 at 03:12