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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.""
Perhaps related, bread more often falls butter-side down because it usually only has time to complete half a rotation in the distance it falls from your countertop.
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!
Yeah, guys, 51% is really biased there... especially when you can completely solve this by the simple expedient of not looking at the coin before you toss it. (or by having one person pass the coin over, and the other person call it)
pb Reply or e-mail; don't vaguely moderate.
An interesting alternative is to flip the coin so that it lands on a smooth floor, spinning on a vertical axis. Then the uneven distribution of mass between the head-side and the tail-side will cause a bias.
It is my experience that dimes and quarters are nearly unbiased for this test, whereas nickels are heavily biased (pun intended) toward tails . [In a past life, I taught a statistics class for which I assigned daily homework, deciding whether or not to take it up on the basis of a coin flip at the end of class. On days for which I really didn't want to spend all evening grading papers, I would use a nickel; I'd use a much-fairer quarter on other days. And none of the class caught on... ]
"My opinions are my own, and I've got *lots* of them!"
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.
This was on NPR the other day. There are a number of issues one of which is that when we flip a coin it actually has a fairly high probability of never actually "flipping" end-over-end. You can test this by attaching a ribbon to the coin and to, say, the table, flipping the coin and then counting the number of twists in the ribbon. It isn't a question of trying to flip it more or less times so much as the physics of the flip. As mentioned in other posts, letting the coin bounce on the ground does make things better since in that case the coin's motion is less predictable.
I'm a magician, and a "mentalist". That means, I pretend to have psychich powers (which I don't, but I don't explain that until after I've convinced the spectator that I have).
One of my tricks is to predict the outcome of a cointoss. I start out with pseudo science explanation, and then, as I continue to be correct, continue on to a supernatural explanation.
The explanation given in this article, as to why a coin is biased, can be boiled down to this (quote from the article): For a wide range of possible spins, the coin never flips at all, the team proved. . That is - the extra bias is towards the side that was up from before the toss, and is a result of the coin not spinning at all. If that's their big scoop, I'm dissapointed, because if the coin doesn't spin, it's not within my definition of a coin toss.
The article actually mentions magicians: Magicians and charlatans may take advantage of this illusion. Keller observes, "Some people can throw the coin up so that it just wobbles but looks to the observer as if it is turning over."
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. The dirty work does not happen in the toss. The coin actually do spin, and the secret move is done at an offbeat moment.
Some level of added insurance would be provided by simply not allowing those selecting a landing side to see the side on which the coin begins. If the flip is being done by a third party, of course, there's the danger that there's collusion between the third party and one of the participants prior to the toss, even for a 1% better chance in the throw, but we still have a better chance of non-tampering and non-bias as a result. And regardless, even in the worst case scenario, where the participants know the side on which the flip is beginning, we only have a 1% statistical advantage to the one side. Furthermore, a non-level, somwhat randomly varied surface onto which the coin is tossed, rather than a plane, will add another randomising factor.
Another case of duh. I observed this in High School in the late 1980s when my friends and I used to play various quarter games for money. It greatly increased my chances when spinning a quarter for money during lunch.
I also used it to increase my chances when playing same/different with another player. Each person spins a quarter, and both players stop their respective quarters wihtout letting the other see the results. The person can look at their own results, and one person guesses whether the quarters are they same or different. If the person guesses correctly, then they take the money. Otherwise, the other person takes the money. Other amounts of money oculd be bet, but only quarters were used to spin in the game. You can really gain a psychological advantage over a person when you win a few without looking at your results and winning each one!
At the next eco-hypocrisy-meeting, count the private jets used to get to the meeting. Should be interesting to see that
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.
I remember my middle school science teacher would have a "coin tossing" lab each year with students, students would keep track and submit the totals. It was all a lesson in probability. He had everyone use pennies dated after 1982 (when they changed the alloy). Heads up was almost 51% of the time. His theory was that heads was "rounder" than tails and that accounted for the difference. Course, 7th grade students don't exactly make the best objective testers