For the mathematically minded

[malorum]

http://www.sciencenews.org/articles/20040228/fob2.asp

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Their preliminary data suggest that a coin will land the same way it started about 51 percent of the time. It would take about 10,000 tosses before a casual observer would become aware of such a small bias, Diaconis says. "Maybe that's why society hasn't noticed this before," he says.

This slight bias pales when compared with that of spinning a coin on its edge. A spinning penny will land as tails about

80 percent of the time, Diaconis says, because the extra material on the head side shifts the center of mass slightly.


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"none" is absolutley not too strong a term. It is physically impossible for a coin to be precisely fair. Also, atmospheric effects are constantly changing, so even if a coin could somehow be fair on one flip, it would not be fair on the next.

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lol. Your response reminds me of the post asking weather the probability of God existing can change. (of course it can).

Probability and fairness are observer based models. I can decide that the guy who three bet me on the river has a 90% chance of holding QJ to make the nut straight. But that 90% only applies to my POV. from his POV he is 100% certain one way or another.

Fairness on a single flip depending on gusts of wind and random changes in throwing angle etc. are not relevant unless known to the observer in advance. The coin will of course flip one way or the other, having all the data to hand in principle (though not in practice) you could predict the outcome. The real question is wether when you control for (i.e randomise) all the other factors does the coin under a series of flips display any bias.
I suspect factors like throwing technique, throwing height, landing surface all have such a large impact that any inherent bias in the coin would be effectively masked from detection. Also the direction of any bias under specific conditions may well reverse under alternate conditions.

I am willing to accept that the design of a coin (weight distribution of the embossing perhaps) may potentially bias a coin under certain condtions.
But would that make the toss less than fair, given that this is a 'coin toss' and not a disk toss.

In any case to discern any gerneral bias would require a large number of trials say 1000 different people each tossing the coin with gloves on and blindfolded 100 times in different conditions. Even then youd only end up with a probability as to wether or not the observed bias was significant.

More likely IMHO is the observaton of bias with a particular tosser in a specific location with a particular type of coin, irrespective of the actual coin used.

Any additional concern I might express with regard to a large sequence of heads would thus be put down almost exclusively to those factors rather than to some inherent defect in the particular coin.

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You're completely, absolutely right. My previous comment was not well thought-out; yours was.

Still, I believe the probability that any given coin is "fair" (ie, the coin has precisely a 50% chance of coming up heads on a given flip) has to be zero. This stems from the fact that probabilities are on a continuum from 0 to 1, and probability .5 is only a discrete point on that continuum.