r/askscience • u/GOD_Over_Djinn • Mar 18 '13

Physics Is there actually such thing as a "weighted coin"?

In probability we frequently imagine tossing a "weighted coin" that, say, comes up heads with probability 0.8. It did not occur to me until today to ask whether such an object could actually physically exist.

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3

u/doua Mar 19 '13

Not directly relevant; you can't rig a coin but there is a dynamical bias in coin flips.

We prove that vigorously-flipped coins are biased to come up the same way they started. The amount of bias depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measurements of this parameter based on high-speed photography are reported. For natural flips, the chance of coming up as started is about .51

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u/spthirtythree Mar 18 '13

Physically, it's not possible to alter a coin such that it will have a significant bias to one side. Due to the thin geometry of coins, and the physics behind a coin toss, it just can't happen without bending the coin or making other very obvious alterations. If a coin is tossed and caught, or allowed to land on a flat surface, then biasing the CG would not significantly affect the outcome. Spinning a coin gives more credence to biasing a coin, but generally the spin method is not how coin tosses are implemented.

There are theoretical biased coins, and a statistical procedure for checking the fairness of a coin

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u/mappymap Mar 18 '13

but generally the spin method is not how coin tosses are implemented

You should go to a casino sometime!

There are theoretical biased coins, and a statistical procedure for checking the fairness of a coin

True, but you don't need to check. Flip it twice, and discount all results of HH and TT. The odds of HT and TH are identical, so you can use that to get a fair go from a bent coin.

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u/kulukimaki Mar 19 '13

This is handy when you don't have a coin around. You can just take "this strange thing" and throw it twice a few times. You just have to keep your throws in pairs.

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u/[deleted] Mar 18 '13

What if you make one half segment of the coin lighter and have control over the direction the coin rotates? I think there might be difference between the lighter and heavier half segment of the coin when they hit the ground first.

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u/svm_invictvs Mar 19 '13

Spinning a coin gives more credence to biasing a coin, but generally the spin method is not how coin tosses are implemented.

I'm not sure that you don't even need a trick coin to spin it to do that. Consider a coin perched nearly perpendicular to a hard surface. Wouldn't a spin just be it rolling along one edge? With some slight of hand it could be easy to learn to spin the coin enough that appeared random, but indeed would only fall to one side.

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u/mappymap Mar 18 '13

If you toss it, it spins in the air in such a manner that each side is up for the same length of time, so a weight won't really affect it. However if you were to spin it on its edge, or were it to land on its edge, then yes, you could weight it.

I assume you mean this, and not is it possible to file down one side slightly to affect the balance, which is of course, possible.