Re:The math of gambling
by splat on Tuesday August 11, 2009 @05:33PM
(#756487)
A fair coin has a roughly 51% chance of landing with the same side up as it started with. See the paper by Diaconis et al. "Dynamical Bias in the Coin Toss."
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A fair coin is one on which p = 0.5.
A coin that has a 51% chance is clearly not a fair coin.
This isn't even what I was talking about, but is still equally easy to turn into a fair coin.
In this case, caller calls in the air after flipper hides the side that starts up. 0.5 * 0.51 + 0.5 * 0.49 = 0.5
For any other case, flip a coin twice. Assign one person HT and the other person TH, reflipping TT and HH. Since p * (1 - p) = (1 - p) * p, the dual flip is a fair flip.
Please don't mention the possibility of sleight of hand next.