That Random Coin Toss? Not So Random Afterall...
from the a-weaker-man-might-be-moved-to-reexamine-his-faith dept
One of my all-time favorite scenes in a play and movie, is the scene in Tom Stoppard's Rosencrantz & Guildenstern Are Dead where every coin toss comes up heads, leading to a bit of a philosophical discussion on probability. Of course, the randomness of the coin toss is the quintessential example of a random event and is used regularly for a variety of situations in which randomness is required, let alone expected. Except... it turns out the common wisdom may be wrong. Paul Kedrosky has the news of a test that showed that if you ask people to try flip a coin and get more heads than tails, they will, and not by a small margin either. In the test, 13 people were asked to flip a coin 300 times, trying to get as many heads as possible. All 13 participants got more heads than tails. Seven out of the thirteen had statistically significant margins of heads over tails (meaning almost certainly not a matter of chance). The highest was one individual had 68% of the coin flips land heads. In other words, a coin toss isn't particularly random.
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Ok this is weird, but
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Re: Ok this is weird, but
Also, I seem to remember a study where one side just came up slightly more. Might have been heads.
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Re: Ok this is weird, but
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Ok this is weird, but 2
But that doesnt matter if you see what it was face-up before it was flipped. It still applies, though again, if someone else is doing the flipping, your odds arent as good. Still, I always call it opposite when its flipped, and am right more than wrong.
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Re: Ok this is weird, but 2
You call it in the air to prevent the way the flip is performed. If you call it while it's on the thumb, then the flipper can aim for 3 flips versus 4 flips. 3 would produce the same side (provided you "flip-catch-smack") while 4 would produce the opposite. If you "call it in the air" the flip has been performed and the flipper can no longer influence the result. (Actually the advantage would go the "caller" as he now has a split second to determine height and flip speed.)
-CF
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Don't let them see the results, and I suspect they would end up pretty much 50/50 again.
This is "tech" how, anyway? Perhaps this is just a stupid friday blog post that we all have to look at until Monday because Mike hasn't figured out how to release posts over the weekend. The internet is a 5 day a week business!
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Old news
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Methodology
In my opinion a coin toss is random if the coin falls to the ground and bounces because it is possible to know the rate of spin and time your catch to always get heads. I would be very difficult to get that every time, but 300 tosses is plenty of time to practice.
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http://comptop.stanford.edu/preprints/heads.pdf
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I can imagine...
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Re: I can imagine...
Really? There seems to be a lot more detail on tails, seems like it would be tails heavy.
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This is not a shuttlecock with a feathered tail and one end highly weighted far away from the tail. The embossed characters on either side are opposed only on the shortest axis if a basically flat object. The torque a heavier side would exert on the flipping coin is trivial.
The bias thus introduced would probably be less than the confidence interval of the statistical analysis.
I would guess that a more important weight consideration would be "top heavy" or "bottom heavy" (like heavy near the top of the head), but that probably is insignificant, too.
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Re:
This is why in statistics they always say, "if you flipped an unbiased coin" or "if you rolled an unbiased die" they have to add that word unbiased.
In fact, I knew people that used to be able to manipulate how the dice rolled and they seemed very good at getting it to roll however they wanted. They made money just making bets with others on how the dice will land as well. Of course no one would ever admit that they were manipulating the dice but these people were very coordinated and after watching them for a while it becomes somewhat obvious. Then again, they only played for a few dollars, it wasn't worth making an issue about.
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Really?
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Re: Really?
Hey Aaron. How about next time, you don't be a d-bag, and just say, "I thought it was well known heads is heavier."
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Re: Really?
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Ok this is weird, but 3
With the method I described above, I have never even attempted to "time" the flip. It doesnt matter. This is for the flip-catch-slap method. Fall to the ground, and I think its a lot more random.
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Idealized coin flip.
Probability doesn't really care about that, since we use a "idealized coin toss" in all discussions on the topic. Pr{H}=Pr{T}=0.5
Those are even odds.
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call in the air, and let it fall
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1. The one who tosses is not the one who is calling.
2. The caller calls after the coin is flipped. (as a lot of folks have pointed out.)
Give any bloke a coin for a month to practice he can obviously get hold of how to get a head more number of times.
C'mon Mike, is it a slow news day or what?
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Re:
You're just jealous because you don't have a successful blog and nobody listens to you. Poor industry shill.
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he tosses a coin 10 times and gets 10 heads, he went and flipped a coin for 8 hours and eventually gets 10 heads, because of the random nature it's quet unlikely to get 50/50 ratio every ratio has some possebilety and a sample of 13 where only slightly over 50% had more heads then tails is not a very good basis
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Re:
I just flipped a coin a few times to further investigate my trends and I got all heads. I honestly cannot remember the last time a coin I flipped was tails. At least not a quarter. I think I flipped a penny a little over a year ago that was tails, it was a shock at the time, but it was probably some demonic penny mischief.
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If a human flips a coin starting on heads, it tends to come up heads.
http://www.cbc.ca/technology/story/2009/12/07/tech-coin-toss.html
A key fact that is left out of the TechDirt post is that the UBC researchers instructed participants on how to manipulate the toss. Therefore, it is misleading to simply say, "if you ask people to try flip a coin and get more heads than tails, they will." Simply "trying" is not enough.
http://robert.accettura.com/blog/2009/08/24/coin-tosses-not-totally-random/
Finally, coins themselves are not inherently fair.
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Did anyone think....
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But imagine a jar full of pennies
"The creationist/IDers (Intelligent Design advocates) love to say “Life is too complex to have been created by chance”. The problem is that they are looking at the end results and then computing the probability that it got there - rather than computing the probability for any life.
To demonstrate what I mean I would like you to do a little experiment. You will need two things - a jar of pennies (the more pennies the better), and a 5×4 foot (or larger) unobstructed clean flat spot on the floor - preferably with out any carpet - the larger the area the better....."
http://blog.chronofish.com/?p=47
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Mike, wtf mate!?
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coin Tossers
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NONSENSE! One can add BIAS to a coin toss (in fact, a university study showed that if you hold a coin a certain way (with some practice) you can almost guarantee that it will come up heads or tails).
But all that demonstrates is that "figures never lie, but liars figure".
Coin tosses are random, coin tossers are not.
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Re:
"a university study showed that if you hold a coin a certain way (with some practice) you can almost guarantee that it will come up heads or tails"
No matter how I hold the coin I can guarantee that it will come up heads or tails. Since there's only two sides to coins it has to come up heads or tails! :)
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- Engineering Student
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Re:
Also, for the "no such thing as random", the decay of individual radioactive atoms currently does appear to be random (although I know there are arguments that it is merely chaotic, and I guess that there could be further developments that can aid predictions of decay? IANAP ...)
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Reliable
I don't know why I can so consistently flip a coin, I've just always been able to do it.
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True randomness is hard to find
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Defining Randomness
I suggest reading "The Black Swan" by Nassim Nicholas Taleb, or his previous book "Fooled by Randomness" probably the only guy who can explain this idea correctly. In it you'll discover that even gambling in a casino is completely non-random, it's fixed, we all know that. The randomness that effects casino's are truly random events such as entertainers getting mauled by tigers. (The biggest losses in casino history have been true random events, such as being robbed, or the classic Sigfried and Roy tiger mauling at the Mirage, which resulted in huge losses)
So remember - randomness is unpredictable, with an unknown set of possible outcomes. Flipping a coin is almost the opposite of randomness, its the kind of predetermined experiment that you'll rarely find in nature.
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Re: Defining Randomness
A: Past outcomes do nothing to help predict future outcomes.
B: Non compressibility. That is, a file full of random bytes should not compress very much when a compression algorithm is applied to it.
These are also characteristics that people try to make encrypted files exhibit so that they appear random.
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Re: Re: Defining Randomness
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Re: Re: Defining Randomness
This principle is nowhere to be found in the coin toss scenario. This may not sound intuitive, but I can predict with nearly 100% certainty based on past coin flipping data that the coin will land on either heads or tails. (the randomness only comes in, as I explained before, if something else happens, like the coin lands on its side or is hit by a stray bullet and destroyed). A coin toss is almost perfectly predictable.
Something is not random if you can known all the possible outcomes and their chances of occurring. Randomness involves unknown outcomes (or at least unknown probabilities for known outcomes)
The problem is dependent on defining randomness, and sadly the conventional definition of randomness is very based on statistically non-random events such as casino gambling and coin tosses, and not on the kind of randomness thats found in the chaos of nature.
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Re: Re: Defining Randomness
This principle is nowhere to be found in the coin toss scenario. This may not sound intuitive, but I can predict with nearly 100% certainty based on past coin flipping data that the coin will land on either heads or tails. (the randomness only comes in, as I explained before, if something else happens, like the coin lands on its side or is hit by a stray bullet and destroyed). A coin toss is almost perfectly predictable.
Something is not random if you can known all the possible outcomes and their chances of occurring. Randomness involves unknown outcomes (or at least unknown probabilities for known outcomes)
The problem is dependent on defining randomness, and sadly the conventional definition of randomness is very based on statistically non-random events such as casino gambling and coin tosses, and not on the kind of randomness thats found in the chaos of nature.
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Of course!
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Measuring constants to determine probability still moves the goal post only 1 to 2%
http://bayes.wustl.edu/etj/science.and.engineering/lect.19.pdf
There exist coin-toss programs that remains slightly more reliable because they are based on Numismatics which take into consideration variability of a coin's size, distribution of weight, all are factors which can affect the outcome, and are incorporated into the algorithm.
You could get real crazy and incorporate environmental factors such as atmospheric pressure, wind speed and turbulence to further complicate your statistical prediction model, but at this point, you're measuring environmental constants which affect a 1 to 2% variability from say, a 49-51 split. Visual representations of these complex equations can be quite beautiful. Consider the Mandelbrot set.
But why go to all this effort? Besides, you're measuring the probability, it is just that- probability, and not the event's outcome. The full accurateness of such a complex probability equation is truly non-computable until the actual event occurs. But attempting to go to such lengths to measure probability could at one point or another may influence the outcome, and that just ruins the fun.
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coin flipping
costs you £4 and you can never spend it, but it will make it's value back quickly...
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In fact, if you were to know those variables, you could predict the outcome 100% of the time.
1. Coin is on heads
2. Coin flips 4 times in the air.
3. Catch the coin and do the smacking on the back of your hand
4. Result will be tails. Every time.
If the coin only only made 3 flips, it will be heads. If the coin made 5 flips, it will be tails.
To full keep things random, the person flipping the coin must NOT be aware of what position the coin is before flipping, and they must NOT be able to manipulate or predict the number of flips it would make in the air.
A "coin toss" program in a computer will always be fully random because it does not take these variables into account. Since humans can, of course it's not fool proof.
Calling 68% extremely predictable though........ I don't know if I agree with that in any case. Keep in mind that as unlikely as it is that all outcomes will be heads, it's still theoretically possible for it to happen. It may have been just as likely to be 68% tails. Come back to me when it's 90%.
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Then again, from a theological perspective true randomness doesn't really exist. Everything is ultimately the product of divine providence.
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random
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Did they try it the other way around?
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Random vs uncertain
If the outcomes and/or the probabilities cannot be enumerated, the situation involves "uncertainty" rather than randomness: That is, we do not know what we do not know.
The distinction is important.
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