Science of the coin-toss: Bias in Heads-or-Tails

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Science of the coin-toss: Bias in Heads-or-Tails

Posted by CmdrTaco on Tuesday March 2, 2004 @04:20AM from the didn't-gildenstern-prove-that-already dept.

MrSharkey writes " An interesting article published in Science News puts a new scientific spin on the outcome of the venerable coin-toss. "A new mathematical analysis suggests that coin tossing is inherently biased: A coin is more likely to land on the same face it started out on.""

21 of 559 comments (clear)

well... one way to solve it by UU7 · 2004-03-02 04:21 · Score: 5, Funny

heads they're wrong.
tails they're right.
1. Re:well... one way to solve it by ArmenTanzarian · 2004-03-02 04:22 · Score: 5, Funny
  
  The scientists have asked that you start the coin heads side down.
2. Re:well... one way to solve it by Virtex · 2004-03-02 07:29 · Score: 5, Funny
  
  Someone once told me it was like this:
  
  Heads: Gonna get me some head
  Tails: Gonna get me some tail
  
  So either way you win. I don't get it, though, since everytime I try this, the coin lands on its edge. Seriously, what are the odds of that?
  
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  For every post, there is an equal and opposite re-post.
Oh Darn... by jwthompson2 · 2004-03-02 04:22 · Score: 5, Funny

And the society shaking ramifications of this are what? We will stop tossing coins before football games and instead have a pocket sized random number generator and the teams pick a number?

--
Even if I knew that tomorrow the world would go to pieces, I would still plant my apple tree. -Martin Luther
1. Re:Oh Darn... by Anonymous Coward · 2004-03-02 04:33 · Score: 5, Interesting
  
  In football games they let the coin hit the ground and bounce around before coming to a stop. That introduces complexities that the scientific study did not address.
  
  It may very well turn out that the odds of getting heads/tails after letting the coin fall on the ground are still 50-50.
From the article by Anonymous Coward · 2004-03-02 04:23 · Score: 5, Funny

Their preliminary data suggest that a coin will land the same way it started about 51 percent of the time.

I wonder what their margin of error was.
This is interesting... by WordUpCousin · 2004-03-02 04:25 · Score: 5, Interesting

A coin is more likely to land on the same face it started out on.

If this is true, we would still want to call the opposite face since we after it lands, we always flip it onto the other hand. That is, if we start with heads facing up, and it lands more frequently with heads facing up on our palms, by the time we slap it onto the back of our opposite hands, tails is facing up!
Of course there's a bias by Anonymous Coward · 2004-03-02 04:25 · Score: 5, Funny

Bias:

Heads 49.9%

Tails 49.9%

Coin becomes
Self-aware 00.2%
Re:Let it hit the ground... by Sogol · 2004-03-02 04:26 · Score: 5, Funny

No, the coin always hits the ground beacuse of gravity. Heads I'm right, Tails you're wrong ;)
Re:Thank God we still have by ultrafunkula · 2004-03-02 04:29 · Score: 5, Funny

Good old rock. Nothing beats rock.
NPR by blackmonday · 2004-03-02 04:33 · Score: 5, Informative

Here's the excellent NPR piece, with pics of the gadget they flipped the coins with: NPR.
Re:Thank God we still have by murphyslawyer · 2004-03-02 04:36 · Score: 5, Funny

Poor, predictable ultrafunkula. Always chooses rock.

--
I ain't evil, I'm just good looking.
Law School by Prince+Vegeta+SSJ4 · 2004-03-02 04:41 · Score: 5, Funny

This sort of reminds me of law school (shudders), where I had a Torts prof who was using a probability (trying to) example. Anyhow, she was explaining that everytime you flip a coin you had a 50/50 chance of heads/tails. She then explained that even so you can still get heads numerous times in a row, proceeded to flip 9 heads in a row. The class was amazed (mostly poly-sci and english majors).
I thought about it for a second, and given the odds of throwing 9 heads in a row AND doing it right as you were using it as an example were astronomically high - stood up and said 'that's a two headed coin'
Teacher smiled and proceeded to show the class the two headed quarter
Re:Tax dollars at work, one coin at a time by Anonymous Coward · 2004-03-02 04:52 · Score: 5, Funny

Seeing as it's the way Bush determines his foreign policy choices, I think it's very important to study the coin toss.
Avoiding bias by geophile · 2004-03-02 04:56 · Score: 5, Interesting

There is a neat trick for dealing with a biased coin in a coin toss:

- Flip twice.
- Discard the pair of throws if it's both heads (HH) or both tails (TT).
- Count HT as heads, and TH as tails.

(I think this idea was from John von Neumann.)

Applied to the current situation: Flip twice, once starting H down, once with T down.
Re:Tax dollars at work, one coin at a time by FauxPasIII · 2004-03-02 04:58 · Score: 5, Funny

> Seeing as it's the way Bush determines his foreign policy choices,
> I think it's very important to study the coin toss.

Eek ! Somebody please hand him the coin with the "don't bomb" face showing next time !

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25% Funny, 25% Insightful, 25% Informative, 25% Troll
Re:Tax dollars at work, one coin at a time by Anonymous Coward · 2004-03-02 05:05 · Score: 5, Funny

Somehow I doubt this was the most expensive experiment ever...

Research materials budget - 0.01 $
Re:Butter-side down by mcmonkey · 2004-03-02 05:58 · Score: 5, Interesting

The reason bread usually lands butter side down has to do with how it falls off a counter.
Scientific American actually crunched the numbers on this issue a couple years ago for a piece on Murphy's Law. Turns out the universe is out to get you.
Considering the case of a slice of bread slipping off the counter top, it will begin to rotate at that point the center of gravity is off of the counter. Presuming a fall from rest and you're not spiking your bread, the rate of fall and rotation are determined by gravity.
Your main variable is this case is the height of the counter top. Although it turns out this height is constrained to a narrow range of comfort determined by human physiology.
Now take this argument to the general case of an arbitrary bipedal on an arbitrary planet. The most probable height of humanoid-type life is a function of gravity on the home world. Planets with weaker gravity make it easier to grow taller people; conversely planets with stronger gravity will tend to produce shorter people.
The taller beings have higher counter tops, but the weaker gravity will cause their bread to rotate slower than our earth-bound bread. Turns out their counter tops will also be at a height destined to produce butter-down drops.
Same for the munchkins on the planet with stronger than earth gravity. Their bread will rotate fast enough to make it around to butter-side-down when falling from their munchkin-height counter tops.
So yes, the fundamental laws governing the universe are designed to ruin your breakfast. Look on the bright side, it's not just you--the universe is out to get everyone.
Re:Tax dollars at work, one coin at a time by InfiniteWisdom · 2004-03-02 06:01 · Score: 5, Funny

Eek ! Somebody please hand him the coin with the "don't bomb" face showing next time !

Thats not how it works in this white house. His coin says "Bomb Iraq" and "Bomb Syria"
Re:Tax dollars at work, one coin at a time by Rhubarb+Crumble · 2004-03-02 06:07 · Score: 5, Funny

So we need to stop spending money on everything until the deficit is 0? Equivalently, if you've got a mortgage on your house, then you need to stop spending money on all non-essentials like eating out, owning a car, having more than seven sets of clothes (laundry once a week), computers, eating dessert, ...
If you have a mortgage, but your salary more than covers your mortgage payments, you do not have a deficit.
However, if you already can't pay your mortgage and your solution is to move to a bigger house in the hope that by stimulating the housing market it might get you a better-paying job, the US goverment would probably like to hire you as a financial adviser.
Re:Tax dollars at work, one coin at a time by FauxPasIII · 2004-03-02 06:17 · Score: 5, Funny

> Ever seen the movie "Black Hawk Down"? Bill did that.

Bill produces movies ?

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