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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.""
If you've ever watched a football game, you'll notice that the coin always hits the ground. This is done for at least one reason, to prevent tampering by the tosser.
It seems that it would also be good given the results of this study, as it could add more randomness (through the act of hitting the ground), thereby countering the "same side down" effect.
libertarianswag.com
"didn't-gildenstern-prove-that-already dept"
Wow, Taco, about 7 Slashdot readers will even get that. +1, Obscure!
That was a pretty funny book, actually.
I want to delete my account but Slashdot doesn't allow it.
Here's the excellent NPR piece, with pics of the gadget they flipped the coins with: NPR.
or, failing that, we have rock-paper-scissors-spock-lizard
"I would say that 99 per cent of what my father has written about his own life is false." - L. Ron Hubbard Jr.
If you start 50% of the tosses on heads and 50% of them on tails, that will remove the bias. The fact that you would like do so without even thinking about it, explains why the bias isn't normally seen (that and it is a small bias).
You would only add memory to the system if you always started a flip on the side that it last landed on (or always on the opposite side). If you always start on a predetermined side regardless of how the coin landed last, the outcome would in no way be dependent on the previous outcome (although depending on how you predetermined the side, and how you are using the data you may have to adjust for the bias).
Analyzing the motion of a disc which rotates about both an axis through the side (flipping) and an axis through the face simultaneously is a straightforward physics problem that decades of physics undergrads and grad students have had to solve as part of classical mechanics classes. The problems are typically phrased in "relevant to coin-tossing" form, as well. In my mechanics class, the problem was phrased something like "what ratio of angular velocities (around the two rotational axes) is necessary to have the coin have a 2/3 chance of landing with the same side facing up as that which started?"
New scientific spin?
When you catch the coin, feel it with your finger. If it is right-side-up, just open your hand. Otherwise, slam it down on your opposite wrist, which flips it over. Takes some practice to become smooth at it, but it works very well, especially if you can keep your audience's attention on your face while you're doing it.
You'll get 7 or better out of 10 correct about 17.2% of the time just by chance if there's no bias at all...
No, it has nothing to do with weight or center of gravity due to the bread. You can repeat the experiment by marking one side of the bread with a magic marker.
The reason bread usually lands butter side down has to do with how it falls off a counter. People don't drop bread, it slides off the counter (or plate, or what have you) and people usually have their bread butter side up on the countertop. As it slides off, it rotates, as half of the slice doesn't have a countertop holding it up. Given standard countertop heights and standard bread thickness, the bread has time to rotate 1/2 turn before it hits the ground. Raise or lower the countertop (below about 1' it won't even make 1/2 rotation or above about 10' it'll do a whole rotation) or get thiner or thicker bread (really thin bread, like extra thin rye, or super thick bread, like about a whole loaf).
--Xandu
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.
Um, no. If you want to use von Neumann's procedure, you should flip it twice under the same conditions. Your suggestion would bias the sequence towards TH, which counts as tails.
from my understanding (which could be wrong) in all instances of a 'random generator', the numbers will never be random, as proven in programming.
True, a finite state machine with no continuous input can generate only repeating sequences. However, there do exist sources of entropy; the most common is the least significant bits of an ADC wired to a reasonably unpredictable analog process, such as an FM receiver, a microphone, or even a moving trackball. If your random number generator is based on hashing an entropy source, then the numbers will not follow a repeating sequence. And even in mobile devices that don't have an analog input, it's possible to use a long-period PRNG such as Mersenne Twister and re-seed it with entropy whenever you dock it.
>> And at least Bill never sent a troop into battle who didn't come home to his or her family.
> Is that true?
It is. There were a number of casualties in Somalia. But remember, Bush Sr. sent those troops in, not Bill Clinton.
25% Funny, 25% Insightful, 25% Informative, 25% Troll
Deficit is not the same as debt. Debt is how much you're in the hole. Deficit is the rate at which you're going deeper into the hole.
Carpe Cerevisi - Seize the Beer
Even a study of 100,000 flips. It will not come out 50/50 of course. Some people...... Anyone agree with me here?
Nope. You missed two points, one made in the article, another about statistics.
1) Their argument is not about differential face/tail weight. Their argument is about the likelihood of the coin to flip at all. They make the point that over a surprisingly large RANGE of initial flipping forces, the coin fails to flip...even though it appears to flip in the air to the casual observer. It's actually precessing. This means that, given a flip force chosen randomly from the set of flip forces a person can apply, there's a slight bias that the coin will not actually flip.
2) It doesn't matter that even over many, many trials the count is not exactly 50-50. As you point out, you don't actually expect that even with a fair a coin you will get exactly 50-50 results on a single run. However, you do expect that the variance from 50-50 is normal and unbiased, and dependent on the number of trials you have. You can use inferential statistics to determine if the distribution of non-50/50 results you get after repeated experiments is more or less than the variance predicted by chance. I won't get into how, but apparently their measured bias is reliable.