Should you catch a tossed coin? - Numberphile

Randomness expert (and former magician) Persi Diaconis on whether it is best to catch a coin or let it fall to the ground.
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NUMBERPHILE

Videos by Brady Haran

[ShiroKage]

The sound of a coin hitting the floor in slow motion is magical.

[winmine]

That's a 1964 kennedy coin, the last year that had 90% silver coins. 

[MitchBurns]

That makes sense about the edge bias when letting them land on a table. However, there are ways to cheat when catching it in your hand. If you practice enough you can feel the difference between heads and tails on your skin, and know the result before you see the coin, because you already felt the result. Also, some people after catching simply open their hand, while other times they flip the coin over and set it on the palm of their other hand, changing the result. With enough skill you could do this to make sure you always win, even while letting the other person call heads or tails. It may lessen the bias of the coin, but it certainly makes it possible to cheat the toss by catching it.

[AlanKey]

I saw an interesting physics puzzle once which asked
_How thick would a coin need to be such that there was a 1/3 chance of heads, 1/3 chance of tails and 1/3 chance of it landing on its edge?_



One answer is the thickness (t) has to be about 0.5774 times the diameter (d)

*Reasoning*
The coin can spin through 360 degrees. Dividing this full rotation into thirds means that 1/3 of the available rotation must result in heads, 1/3 tails and 1/3 edge.
Viewing the coin from the side (imagine slicing it through it's diameter and looking edge on) the angle subtended by the heads face (length d) and the centre of mass must be 120 degrees. The angle subtended by the edge and centre of mass (length t) must be 60 degrees.

t/d = tan(30)
t = ~0.5774d

[Sensenwerk]

Randomness expert AND FORMER MAGICIAN! I love both subjects - I want to see an entire channel featuring Persi Diaconis!

[trucid]

Yet another video that's 3 minutes and 14 seconds long. I see a trend here...

[jberni]

That means I could select or prepare a coin, so that it comes out in my favor. Great Explanation by the way!

[darcipeeps]

I love all the videos from this professor

[thehitcher]

Hey Brady, I'm a second year uni maths student and just started a module on Bayesian Statistics. I was wondering if you could do a video, similar to the Tau vs Pi one, where you have a Bayesian statistician and a classical/ frequentist statistician go against each other explaining why they prefer their type of stats. Thanks. Love the videos by the way!

[mexicanreformist]

Thanks for creating amazing and entertaining content numberphile! :D

[xDMrGarrison]

Dear Brady, as much as I love your videos from sixty symbols and numberphile and ofcourse objectivity, this might be the most interesting one yet!

[hiworld]

Love this! Never thought about it in my life

[ShaunDreclin]

What if you toss it and it lands on carpet or dirt? Those wouldnt let the coin bounce and spin so theyd be fairer right?

[Ottuln]

Awesome video. I really liked the slow motion of the coins.

[MOSSO]

I'd like to know if the composition of the coin can make a difference, even slightly. The 1964 Kennedy half dollar as shown at 2:38 is made of 90% silver and was the only year it was made of 90% silver.

[JordanMetroidManiac]

Letting a coin land on the ground allows more parameters to affect the outcome. Parameters such as ground restitution/bounciness, height at which the coin is tossed, ground friction, bumpiness/protrusion and sloping of the ground, et cetera.

[therealzilch]

Counterintuitive but true, and convincingly explained.  Thanks.

[Regtic]

But whether or not the coin is biased if you have no idea what the bias is, it's still "fair" in the sense that you have an equal chance of winning the toss up based on the information you have. 

[jacketsj]

So then if you add in the possibility of the catcher cheating, the fairest way would be to make it land on a bed? (That is assuming it won't spin on the bed, I haven't tried it out)

[bele]

Interesting videos with the superbowl comming up.