How to Simulate a Biased Coin Toss With a Fair Coin
We often use a coin toss to choose from two equally preferable outcomes, but can also use one to break a three way tie, or in other situations where you want a probablity distrubition other than 50-50.
[edit] Steps
- Decide what probability you want for each outcome, and make sure they add up to 1.
- Assign each outcome the appropriate length of the interval [0,1]. That is, assign [0,p) to the first outcome, [p,p+q) to the second, [p+q,p+q+r) to the third, etc.
- Convert each endpoint to a binary decimal.
- Define heads=0 and tails=1.
- Flip the coin and record each result.
- Convert the sequence of heads and tails to a binary decimal according to step 4. (Convert HHHTTHHHTT to 0.0001100011)
- Stop flipping when you have enough precision to determine which of the intervals from step 2 your number falls within. and pick the outcome that was assigned that interval.
[edit] Things You'll Need
- A fair coin. If you only have a biased coin, or if you aren't sure if your coin is biased, use Simulate a Fair Coin Toss With a Biased Coin first.
