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You're mixing theoretical odds and practical odds, which might be considered sloppy. Additionally, unfair coins can trivially be used as fair coins, but unbala
by req2 17y ago
You're mixing theoretical odds and practical odds, which might be considered sloppy.
Additionally, unfair coins can trivially be used as fair coins, but unbalanced roulette wheels cannot easily be used as fair roulette wheels.
- splat 17y agoA 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."
- req2 17y agoA 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.