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Flipping a coin may not be an even bet after all

mathematics statistics probability physics

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#1 Hum

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Posted 04 December 2012 - 15:58

YOU don't need to be a mathematician or a Vegas card shark to know that, when all things are equal, the probability of flipping a coin and guessing which side lands up correctly is 50-50.

But what most people seem to forget, or so says Stanford math professor Persi Diaconis, is that things are almost never equal.

In reality, the odds of guessing heads or tails correctly aren't as even as you might think, and the reason has much more to do with physics than probability.

According to Prof Diaconis, a natural bias occurs when coins are flipped, which results in the side that was originally facing up returning to that same position 51 per cent of the time.

This means that if a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times.

Prof Diaconis came to this conclusion after determining that no matter how hard a coin is flipped, the side that started up will spend more time facing up.

One way of thinking about this, as noted in an article from Coding Wheel, is to look at the ratio of even and odd numbers starting from one. What you'll discover is that no matter what number you stop at, there will never be more even numbers than odd numbers in that sequence. The coin flips work in much the same way.

Prof Diaconis first realised that coin flips were not random after he and his colleagues managed to rig a coin-flipping machine to get a coin to land heads every time.

He and his team then asked human subjects do the same thing over and over, recording the results with a high-speed camera. Though the results were a little more random, they still ended up with the 51-49 per cent margin.

Prof Diaconis noted that the randomness is attributed to the fact that when humans flip coins, there are a number of different motions the coin is likely to make.

For instance, he showed how coins don't just move end to end, but also in a circular motion, like a tossed pizza.

He also found that there are ways to flip a coin where it looks like it is tumbling in the air, but in reality, it doesn't move at all.

Prof Diaconis proved this by tying a ribbon to a coin and showing how in four out of 10 times the ribbon would remain flat after the coin was caught.

While the margin is relatively small, it's enough to maybe get you reconsidering using a coin toss to settle your next argument.

In another startling discovery, Prof Diaconis determined that the probability of guessing which side comes up of a spinning copper-plated penny is also skewed more in one direction.

According to Prof Diaconis' research, a spinning penny will land tails side up roughly 80 per cent of the time.

source


#2 Astra.Xtreme

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Posted 04 December 2012 - 16:06

Interesting thoughts and it was somewhat reasonable until the last sentence:

According to Prof Diaconis' research, a spinning penny will land tails side up roughly 80 per cent of the time.


There's no way in hell that's remotely true.

#3 Art3x

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Posted 04 December 2012 - 16:07

I read this a while back, pretty cool.

#4 Nick H.

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Posted 04 December 2012 - 16:08

There's no way in hell that's remotely true.

Why not?

(That's a genuine question, I'm asking if you have the science to back it up or if you just don't believe it to be true).

#5 typu

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Posted 04 December 2012 - 16:10

i tried it one time and it was tails. so 100%. no biggie.

Interesting thoughts and it was somewhat reasonable until the last sentence:



There's no way in hell that's remotely true.



#6 OP Hum

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Posted 04 December 2012 - 16:11

According to Prof Diaconis' research, a spinning penny will land tails side up roughly 80 per cent of the time.

source


Now is that true for all pennies ? Steel, high copper of olden days, and the 95% zinc ones ? :laugh:

Why not?

(That's a genuine question, I'm asking if you have the science to back it up or if you just don't believe it to be true).


You know how it is with the instant experts on Neowin. Seldom do they have reasons. ;)

#7 Astra.Xtreme

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Posted 04 December 2012 - 16:14

Why not?

(That's a genuine question, I'm asking if you have the science to back it up or if you just don't believe it to be true).


Sure, I could test it myself if I wanted. So could you. Even if I flipped a penny 1000 times, I can guarantee it will come nowhere close to 80% in favor of tails. I could maybe believe that a penny might have an uneven weight distribution giving tails an advantage, but thinking it has that huge of an advantage isn't even logical.

#8 Art3x

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Posted 04 December 2012 - 16:20

Sure, I could test it myself if I wanted. So could you. Even if I flipped a penny 1000 times, I can guarantee it will come nowhere close to 80% in favor of tails. I could maybe believe that a penny might have an uneven weight distribution giving tails an advantage, but thinking it has that huge of an advantage isn't even logical.


Spin, not flip.

I imagine it is off center because the head protrudes ever so slightly more than the backside.

#9 Astra.Xtreme

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Posted 04 December 2012 - 16:23

You know how it is with the instant experts on Neowin. Seldom do they have reasons. ;)


Pretty quick to the gun on that assumption, don't you think? Are we not allowed time to back up our stance?

Spin, not flip.

I imagine it is off center because the head protrudes ever so slightly more than the backside.


Ooo, good call. I misread the "spinning" part. I guess in that case, the center of gravity offset would have a greater effect and the environment lesser an effect. Though 80%-20% still seems rather extreme.

#10 Shadrack

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Posted 04 December 2012 - 16:38

This means that if a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times.


Statement is grossly wrong... Such a bad statement it was hard to continue reading the article... The probability of this actually happening (51/100 with those odds) is actually extremely low.

#11 threetonesun

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Posted 04 December 2012 - 16:43

There's a reason why, in sports, they let the coin fall to the ground.

#12 Art3x

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Posted 04 December 2012 - 16:45

There's a reason why, in sports, they let the coin fall to the ground.


I don't follow your logic. Is it to allow the ground to add an extra variable?

#13 Astra.Xtreme

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Posted 04 December 2012 - 16:53

I don't follow your logic. Is it to allow the ground to add an extra variable?


Yep. The more variables, the more random the odds.

#14 Original Poster

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Posted 04 December 2012 - 16:54

well then.... lets throw a bit of schrodinger's cat in to this ... hide the coin before the flip! therefore the coin is both starting on heads and on tails! making it 51% chance it will land on either side ... 102% in total ... mind blown lets go home ..this post was pointless but gives you something to think about!

#15 threetonesun

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Posted 04 December 2012 - 16:56

I don't follow your logic. Is it to allow the ground to add an extra variable?


Yeah, turf bounce. Someone flipping a coin can either flip it a set number of times, making it land in their hand one way or the other (not hard, if you practice, also made easier by those giant novelty coins they often use in sports), or catch it at the correct time to have it land one way (not hard if you have excellent eyesight), or rotate it after catching it (just plain old cheating).

If you toss it into the air and let it hit the ground, though, you can't account for how it will bounce, making it uncontrolled enough.