March 03, 2004
Scientists: Coin tosses are never 50/50
This is weird: the Science News is reporting on a new mathematical analysis showing that coin tosses are inherently biased -- because a coin is more likely to land on the same face it started out on.
Apparently, this new discovery is based on some 1986 work done by the famous mathematician Joseph Keller. He argued that the only fair way to toss a coin is to toss it so vigorously that it spins perfectly around the horizontal axis in the center. Since it's impossible to throw it with such precision, every other toss becomes biased -- because the coin spins around a tilted axis. The end result is a coin will land on the same face it started on 51 per cent of the time. You'd need to flip a coin 10,000 times before you noticed this bias, mind you, so for all human purposes a coin-flip is still 50/50.
Though if anyone ever tries to do a coin-flip by spinning the coin on its edge on a table, watch out:
This slight bias pales when compared with that of spinning a coin on its edge. A spinning penny will land as tails about 80 percent of the time, Diaconis says, because the extra material on the head side shifts the center of mass slightly.
This also makes me wonder: If the problem with a coin-toss is that humans cannot achieve perfect spin, what about robots? Maybe we could make a robot to do perfect coin tosses with genuine 50/50 distribution. Oh, hell -- there's probably already a robot somewhere in Japan designed specifically for that purpose.
Posted by Clive Thompson at March 03, 2004 03:49 PM
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You realize what this means, man? We have a coin-toss distribution GAP!
From now on, I'm never going to use a coin toss to decide anything.
I'm going to carry around a Dell laptop loaded with military-class pseudorandom number generators instead.
Not only we need perfect tosses, we also need perfect coins with accurately even distribution of masses...
...What is fascinating to me is the fact that to decide between two different and apparently equivalent options we have to toss a coin or do something similar. Is human mind incapable of random choices? At least in some circomstances we feel incapable to just pick one without being affected by "impressions" or previous experiences. And that IS funny because often we make important choices based on trivial facts without even noticing.
Does this make any sense to you people out there?
Always remember tho ... we are talking about long-run probabilities. Unless you keep doing heads vs. tails flips for your weekly wages for the next 20 years, you are not likely to notice the diff between one side of the coin and the t'other.
Yeah, very true. Also, even when 50/50 distributions are statistically sound, they operate over the long haul -- which means they can often look "fixed" to the short-haul human attention span. For example, if you ask people to write up a list of the result of 100 random coin flips (i.e. HTTHHTHT for heads and tails), they'll usually underpredict the amount of HHHHHHHHHH or TTTTTTTTTT streaks. They assume that after a couple of flips, the 50/50 rule will force an alternate flip to break a streak. That isn't actually true in reality; if you flip a coin 1,000 times you'll get a number of seemingly "improbable" one-sided streaks.
So not only would we require an enormous amount of flips to detect a 51% probability -- but looooong before we detected that bias, we might have given up angrily, suspecting that the coin if "fixed" because it produced a seemingly-crazy streak of 25 "heads" in a row.
While our brains may be excellent at crunching statistics subconsciously, when we pay conscious attention to probability, we really suck at it.
Hmm, something about this article doesn't jive with the original paper that dealt with this task. The lab that did the work actually did construct a coin-flipping machine to handle the mind-boggline numbers of repetitions necessary to eliminate error, but the finding wasn't the the original orientation determined the outcome, rather that the dynamics of the energetic flip could be tailored to produce a predictable outcome. I'll track that article down soon...
If you find it, post it, for sure!
Personally, I've always carried one of those "heads, I win" and "tails, you lose" coins just for those random but probable coin toss situations.
