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

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.""

Comments

randomness

[freerecords]

Surely coins randomness in values and the reason they make the best 1 out of 2 decision as it were, is because of these small variables, not many of which are under human control, to bring out a "good" result. This study has also been done by a statistician. Personally, a statistician talking about the requirement of Super-human strength to do a task, does not convince me as much as, say a Biologist. If we wanted to know really, we would need an expert panel from many fields. But then again, who cares?

Re:Mmm-hmm.

[jcrash]

Yeah, whatever. You were lucky. 51% is the stated bias. in 13 tosses, that would possibly bias it one count and even then it is statistically more likely it wouldn't.

The question

[FreemanPatrickHenry]

What does this mean for...any number of things? If the coin toss is no longer a theoretically valid randomizer (or at least a completely unbiased one), what's going to happen to, for instance, the NFL? That whole initial coin toss thing kinda goes out the window, I guess.

But don't ask me, I'm not a football guy.

Crap science

[lukewarmfusion]

First - the experiment they used to "prove" this involves creating a mechanical device that will flip a coin for you. After some tweaking, they got it to flip and land consistently with heads up.

Of course you can flip a coin (or any other object) and get it to land the same way every time. All it means is that you've eliminated the random factors of human interaction, air, friction, etc. There's nothing inherently random about a coin - it's the random factor in the action.

I say bollocks

[(void*)]

Is a coin fair or unfair. So you perform the experiment 10000 times. Does one expect it to be the same 5000 times exactly? No! The fractional devation expects to see is sqrt(1/10000) = 1%. One should expect to see an error of 1% about 2/3 of the time.

So they did the experirment and got 51%. This is wholly compatible with the notion that the coin is random.

And by the way, ONE trial of 10000 does not prove anything. Show me 51% for ALL trials of 10000 and then lets' talk.

Don't know if that actually works though....

[carlmenezes]

Considering a football game and the grass/turf on the ground, the coin doesn't really get much of a chance to add much randomness due to the amount of energy absorbed - in fact, usually, it falls and lies there - hardly any bounce back. A fairer way would be to have the coin fall on a glass plate so it bounces back more, thereby inserting much more randomness into the toss.

While we're still on the subject, what about using a roulette wheel to decide? Pick red or black and let the ball decide. You can have a nice transparent glass ball (so that you can see that there's no metal inside it to bias it in any way) hitting a metal roulette wheel and glass and metal collisions have among the highest bounce co-efficients.

Re:Tax dollars at work, one coin at a time

[Anonymous Coward]

Besides the fact that neither college is government funded in any significant way, the last thing I would think we should cut is education spending to save the deficit.

And I know I shouldn't feed the trolls.

Re:Tax dollars at work, one coin at a time

[Short Circuit]

Actually, I see this as very important.

Everyone I personally know assumes that coin tosses is a fair, random decision. And that's a fairly fundamental assumption.

This shows that you can assume some things, and you can't assume others. And the list of things you can and can't assume is always changing.

And, just to make your head explode, I'll point out that that means that, over the long term, you can't assume anything.

Think of this research as a sort of lesson in appropriate behavior

Re:Comments from someone who's been studying this

[gowen]

He has obviously seen a magician to the same trick I do. Of course I wont reveal the secret, but I can tell you this: he's wrong.

Or, alternatively, he's seen a Magician do a different trick than yours, and he's right.

Re:I don't think that helps

[norton_I]

No, if hitting the ground has a 50% chance of flipping the coin, it will eliminate the bias. It would even eliminate the bias if the coin always hit the ground heads up.

Baloney

[Cryp2Nite]

I don't know wether the article or the researcher is talking nonsense. But this makes no sense.

The article starts out stating:
A new mathematical analysis suggests that coin tossing is inherently biased

And somewhere later it states:
In experiments, the researchers were surprised...

So what is it? Mathematical or experimental proof?

The hand waiving explanation in paragrahs 6 through seven is not very convincing, one could also argue that the tilting of the axis is an inherent part of the randomness of the toss.

Re:Tax dollars at work, one coin at a time

[chef_raekwon]

that coin tosses is a fair, random decision

if the person who calls the toss never sees the face of the coin upon the toss, and doesn't call it until its in the air, is it not still random, and fair?

Start on the side?

[Jtheletter]

So what happens if I perform a coin toss starting with the coin perpendicular to the ground? This should eliminate the bias.
Of course one could also just flip a coin to see which side to start up before performing a coin toss (begin infinite loop regression)....

Re:Is anything truely random?

[Jonboy X]

Well, it depends on what definition of the word "random" we use. Dictionary.com gives us 3 definions (paraphrased here):

1) No pattern, purpose or objective.
A coin flip is NOT random, modern physics can describe it down to the quantum level.

2) Described by a probability curve.
A coin flip IS random, i.e. 51/49 probability dictribution.

3) All outcomes equally likely.
A coin flip is NOT random, as it's not exactly 50/50

I think that people use the word "random" a lot, when they mean "unpredictable". Specifically, unpredictable with the information that they have. Really, the only source of randomness we have is events that are biased by some quantum factor in a significant way. Everything else is just the product of a bunch of factors that aren't widely known. Not random, just unpredictable. There's a reason they call 'em "pseudo-random" number generators: They appear to be random, unless you know the seed...

Re:Tax dollars at work, one coin at a time

[phliar]

We've got a deficit over a half-trillion and things like this are getting funded. Riiiiight.

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, ...

Thousands of children die every day, yet things like faster semiconductors are getting funded. Riiiiight.

Re:Tax dollars at work, one coin at a time

[RevAaron]

And at least Bill never sent a troop into battle who didn't come home to his or her family.

Is that true?

Or do you include coming home dead as coming home?

I mean, I would take Bill of any Bush any year, but I find it a little unlikely that no soldier died during duty during Clinton's stretch...

Re:A useful skill

[raytracer]

It would very useful to learn how to flip a coin (into the air), but not have it actually flip (end-over-end) as per the article. They implied that if the coin is oscillating or wobbling, people would not notice that it's not actually flipping. This could win me a lot of root beers!

It actually isn't all that hard to teach yourself to flip a coin, catch it after the right number of turns, slap it onto your wrist and make it come out however you like. I achieved about 80% success when I practiced this. I'm not exactly the most adept at leger-de-main: I have little doubt somebody could get to the high 90% with practice.

You could probably even get good enough to allow somebody to call it in the air.

Re:Tax dollars at work, one coin at a time

[Anonymous Coward]

Well. obviously, but only if the caller is just as likely to call heads as tails.

Re:well... one way to solve it

[Open_The_Box]

As far as I could interpret the article, the issue wasn't that the weight of one side made it heavier, but rather that no matter how much force you use to flip the coin you may not actually flip it - or something. That's a bit vague but it seems to be that there are two extremes: perfectly symmetrical flip of the coin around its central axis, and flip where the coin stays flat (ie doesn't flip at all). The first is unbiased and the second is fully biased. The research seems to have shown that any flip where the coin is not flipped perfectly symmetrically is slightly biased - ie any flip where the axis around which the coin is flipped is off centre or that it doesn't actually flip but is precessing around an axis.

I think the idea is that all flips are a combination of these two states. Then the sum over the possibile flips gives a slight bias to the initial state.

I could have read it wrong though. Mind you, I'd guess that for proper research into this they wouldn't have just started with the same side up each time. Instead they'd have to note which way up the coin was before they started to get a random sampling of heads and tails results.

Re:Tax dollars at work, one coin at a time

[dbc001]

IN A BATTLE, PEOPLE DIE.

That's why intelligent people tend to avoid such battles in the first place...

Re:Tax dollars at work, one coin at a time

[JahToasted]

You're right, of course. I think the difference really is that Bill Clinton actually attended the funerals of those who were killed in action. Bush not only doesn't attend, he doesn't even allow the funerals to be mentioned by the media. Oh, and he also cuts the benefits to any soldier that does survive. A true patriot.