
The Coin Flip: A Fundamentally Unfair Proposition? (2009) - gluxon
http://econ.ucsb.edu/~doug/240a/Coin%20Flip.htm
======
heyitsnick
"1% may not sound like a lot, but it's more than the typical casino edge in a
game of blackjack or slots."

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

      Blackjack, video poker and some bets on craps are the only
      times in a casino where the house edge shrinks to below 1%.
    

Care to cite your source for this or are you a gaming industry insider?

~~~
PhantomGremlin
There's no need for a source. It's common knowledge. Many books, websites, and
research papers have extensively studied those games.

Edward Thorp is a mathematician who did a lot of analysis about blackjack over
50 years ago.[1] He's a seminal figure in this field.

Here's one site I recall mostly because it has a memorable name:
[http://wizardofodds.com/](http://wizardofodds.com/)

[1]
[https://en.wikipedia.org/wiki/Beat_the_Dealer#History](https://en.wikipedia.org/wiki/Beat_the_Dealer#History)

~~~
ChristianBundy
_> There's no need for a source. It's common knowledge. Many books, websites,
and research papers have extensively studied those games._

It's obviously not common knowledge to the person that's asking the question.
:~) Thanks for the source though.

~~~
mod
That one person doesn't know it doesn't mean it's not common knowledge.

That said, the edge is not always below 1%. It varies based on the rules. Some
games don't allow a surrender, for instance, which changes the edge pretty
drastically.

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plonh
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.

~~~
letstryagain
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.

~~~
thret
This is a trick that can be learnt with practice. If you spend a lot of time
around gamblers, don't ever accept a coin toss proposition.

~~~
jahnu
Doesn't the person not tossing the coin get to call though?

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letstryagain
If you call tails, I catch the coin and show it to you. If you call heads,
I'll catch the coin and invert it before showing it.

~~~
jahnu
Ahh right. People I know usually call after the flipper catches and covers it.
So they would have to have some technique for flipping it as they raise their
hand to reveal the coin. Difficult but I guess not impossible.

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shuriu
This video from Numberphile goes in depth about this:
[https://www.youtube.com/watch?v=Obg7JPd6cmw](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.

He also has done research on the randomness of shuffling cards:
[https://www.youtube.com/watch?v=AxJubaijQbI](https://www.youtube.com/watch?v=AxJubaijQbI)
. Pretty cool stuff!

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jmount
My small take: [http://www.win-vector.com/blog/2015/04/i-still-think-you-
can...](http://www.win-vector.com/blog/2015/04/i-still-think-you-can-
manufacture-an-unfair-coin/)

~~~
plonh
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?

~~~
jmount
Persi Diaconis did a lot of experiments- the biases are very low.

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qznc
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."

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RogerL
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.

[1]
[http://statweb.stanford.edu/~susan/papers/headswithJ.pdf](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.

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zw123456
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](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.

~~~
danieltillett
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.

~~~
PhantomGremlin
I once attempted to hand a quarter to a convenience store clerk. Somehow we
dropped it during the exchange. The coin rolled about 8 feet and went thru a
tiny gap between two large cardboard boxes on the floor.

I'm sure I could have stood there for an hour attempting to drop a coin onto
the floor and have it roll into that gap, and I would have failed.

~~~
danieltillett
I had a similar situation in which a coin I tossed managed to end up stuck in
a small gap in the celling. I remember having to get up on a chair on top of a
table (I must have been under 10 at the time) to get it out. Good times :)

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soup10
Good to know! Relevant clip of some very entertaining gambling by two poker
pros:

[https://www.youtube.com/watch?v=ZQSIx3CU9rA](https://www.youtube.com/watch?v=ZQSIx3CU9rA)

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raymondh
See also:
[http://www.stat.columbia.edu/~gelman/research/published/dice...](http://www.stat.columbia.edu/~gelman/research/published/diceRev2.pdf)

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coldpie
Mostly off topic, but boy do I enjoy articles that use the word "tosser"
innocuously.

