A commenter explains that the most interesting claim (51% bias) is not explained correctly in the article. Humans flipping a coin add a bit of precession (spin) that biasses the toss. The "odd/even time in the air" analysis is incorrect -- that only matters if it is possible to stop the coin before the first flip.
Yep. To see this, consider a coin flipped into the air so that it's tilted 45 degrees with the floor and spinning only around the vertical axis. To a casual observer it will appear as if the coin is tumbling but in fact one side faces up 100% of the time.
This video from Numberphile goes in depth about this: https://www.youtube.com/watch?v=Obg7JPd6cmw . The guy talking, is Persi Diaconis, is the main author of the paper this article is based upon.
If the coin has a substantial thickness, is it still accepted as a coin? I think not. How much density differential do you need to generate a 1% bias in a coin no thicker than any existing UN member currency?
The paper ends with "The caveats and analysis also point to the following conclusion: For tossed coins, the
classical assumptions of independence with probability 1/2 are pretty solid."
I think this link botches the explanation for 51%. 51% is because of precession, as explained in the paper[1]. With enough precession the coin will always come up heads if it starts out heads. That's how magicians control coin tosses.
He tries to describe it in terms of HTHTHT. Coins do not have memory. They don't know if they've previously flipped 3 times, 4 times, or 1e308 times. If you draw from [HTHTHT..HT] randomly, you'll get 50% heads and 50% tails. Change that to [THTHTH..TH] and the answer is the same.
With precession the answer changes because it stays in the initial state longer. As the paper points our "Keller showed that in the limit of large initial velocity and largerate of spin, a vigorous flip, caught in the hand without bouncing, lands heads half the time." Keller assumed no precession.
edit: I just saw that in the comments they point this flaw out. It gets hand waved away by the author as a "oversimplification" that he made. My opinion is that it is okay to simplify, but not to the point of being wrong. The explanation is not how probability works, at all.
The most interesting part to me was this
"A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity." (https://en.wikipedia.org/wiki/Flipism)
I assume that was as the result of using the tossing machine, but I really thought it would not have been that frequent.
I have this happen a lot when tossing on wooden floors with a gap between the boards - basically the coin gets stuck in the gap. My brother and I got quite good at deliberately doing this.
I have never had it happen on a flat surface and I must have tossed 10,000 of coins in my youth.
heyitsnick|10 years ago
The house edge for slots games is anywhere from 2% to 15%+ and is one of the worst bets you can make in the casino.
Blackjack, video poker and some bets on craps are the only times in a casino where the house edge shrinks to below 1%.
wozniacki|10 years ago
plonh|10 years ago
letstryagain|10 years ago
shuriu|10 years ago
He also has done research on the randomness of shuffling cards: https://www.youtube.com/watch?v=AxJubaijQbI . Pretty cool stuff!
jmount|10 years ago
plonh|10 years ago
qznc|10 years ago
RogerL|10 years ago
He tries to describe it in terms of HTHTHT. Coins do not have memory. They don't know if they've previously flipped 3 times, 4 times, or 1e308 times. If you draw from [HTHTHT..HT] randomly, you'll get 50% heads and 50% tails. Change that to [THTHTH..TH] and the answer is the same.
With precession the answer changes because it stays in the initial state longer. As the paper points our "Keller showed that in the limit of large initial velocity and largerate of spin, a vigorous flip, caught in the hand without bouncing, lands heads half the time." Keller assumed no precession.
[1] http://statweb.stanford.edu/~susan/papers/headswithJ.pdf
edit: I just saw that in the comments they point this flaw out. It gets hand waved away by the author as a "oversimplification" that he made. My opinion is that it is okay to simplify, but not to the point of being wrong. The explanation is not how probability works, at all.
zw123456|10 years ago
I assume that was as the result of using the tossing machine, but I really thought it would not have been that frequent.
danieltillett|10 years ago
I have never had it happen on a flat surface and I must have tossed 10,000 of coins in my youth.
soup10|10 years ago
https://www.youtube.com/watch?v=ZQSIx3CU9rA
raymondh|10 years ago
coldpie|10 years ago