Sunday, March 25, 2012

The Odds in a Coin Flip are not 50/50

To me the idea of "triplethought" (the name of my blog) is exemplified by this study.  It just goes to show you have to really challenge what you think you know as fact.  Do you think the odds of a flipped coin coming up either heads or tails is 50/50? Think again. A Standford study shows the odds in a coin toss odds aren’t 50/50 as almost everyone believes.... but more like 51% versus 49% in favor of the side that starts up when it is initially flipped. It has nothing to do with the weight or imbalance in the coin.  There is a bias towards the side that starts up.  They used a machine to perform a large number of coin tosses and found the following:

  1. If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was launched. (If it starts out as heads, there's a 51% chance it will end as heads).
  2. If the coin is spun, rather than tossed, it can have a much-larger-than-50% chance of ending with the heavier side down. Spun coins can exhibit "huge bias" (some spun coins will fall tails-up 80% of the time).
  3. If the coin is tossed and allowed to clatter to the floor, this probably adds randomness.
  4. If the coin is tossed and allowed to clatter to the floor where it spins, as will sometimes happen, the above spinning bias probably comes into play.
  5. A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity.
  6. The same initial coin-flipping conditions produce the same coin flip result. That is, there's a certain amount of determinism to the coin flip.
  7. A more robust coin toss (more revolutions) decreases the bias.

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