
Flipping 10 heads in a row - a small probability demonstration - ColinWright
http://singingbanana.tumblr.com/post/9166555322/flipping-10-heads-in-a-row-full-video-by
======
jonkelly
My favorite related demonstration is to do a "tournament" where you start with
64 people and eliminate the 1/2 who don't flip heads each round. Some
"amazing" flipper will get through 5 to 7 rounds and win. Something to think
about when you see a mutual fund manager who beats the market 7+ years in a
row.

~~~
Estragon
There's a con based on this: send half your marks a prediction that the stock
market will go up next week, and half a prediction it will go down. Repeat
next week, restricting to whichever set received the correct prediction. After
five weeks, you'll have a group of people who think you've accurately
predicted stock market movements for five weeks in a row, and some of them
will be prepared to pay for your next prediction.

~~~
billmcneale
I remember reading this anecdote to explain the anthropic principle:

[http://beust.com/weblog/2010/08/17/fun-with-the-anthropic-
pr...](http://beust.com/weblog/2010/08/17/fun-with-the-anthropic-principle/)

------
praptak
"Sir, you must be the greatest archer in the world - everywhere around on
walls, trees and fences there are targets, each with your arrow exactly in the
middle. How did you achieve such greatness?"

"I paint the targets after shooting."

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grantbachman
A quicker way to do this would be to take a container full of 1024 coins and
dump them onto the ground so they're spread out. Put all the coins that landed
heads up back into the jar and continue this process 10 times. However many
coins you have left are the number of coins that landed heads up 10 times in a
row.

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fendrak
This is why probability is such a useful math: it turns our intuitive
reasoning on its head and gives us solid descriptions of the processes at
hand. Another great example of probability in action is the Monty Hall Problem
(<http://en.wikipedia.org/wiki/Monty_Hall_problem>). Totally unintuitive
process, but unarguable results.

~~~
cj
I just threw together a quick simulation of the Monty Hall problem if anyone's
interested: <https://github.com/Paton/Monty-Hall-Paradox-Simulation> .. really
fascinating.

~~~
hadronzoo
I also have one for Matlab/Octave that allows you to change to door count to
get a better feel for what's going on: <https://gist.github.com/411593>

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Tichy
So what is the world record of number of heads in a row? I fear this video
could start a very time consuming coin flipping craze...

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mihaifm
It's called Ion Saliu's paradox or The Fundamental Theory of Gambling. If you
have an event with probability 1/n and repeat it n times, the probability of
realizing the event at least once is is about 1-1/e = 0.63 (for high enough
values of n).

His calculations were correct, showing that chance of failure was 37% and
success 63%.

~~~
Peaker
And also interesting to note that if you repeat n times, you will get on
average 1 realization of the event (Sometimes 0, rarely n).

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ErrantX
The Derren Brown episode he mentions is well worth a watch if you enjoyed this
- he doesn't deal so much with the mathematical side, but the idea of using
misdirection to show something unlikely happening simply through consistent
trial.

Edit: the show is called "The System"

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te_platt
Ha! That's nothing. One time I got 12 yatzees in a row. One day I was playing
Yatzee and got 2 in a row. That was exciting but I was impatient so I wrote a
program to play for me. Eventually my program made 7 in a row but that was
still taking too long. I calculated how long it would take to have a greater
than 99% chance of getting twelve in a row and decided I needed to get a life
more than I needed to keep the program running. Then I figured as long as it
was really the computer doing it and not me it wasn't too much to imagine a
Platonic universe where my program already had been run an infinitely long
guaranteeing that I got 12 in a row. I don't have a video of it though so
kudos to SingingBanana.

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SoftwareMaven
I've been listening to _The Drunkard's Walk: How Randomness Rules Our Lives_
[1] by Leonard Mlodinow. It is a great introduction to how probability works,
the history of randomness and probability in science, and how randomness
affects so much of what we do. very interesting look at the math without
getting too caught up in the math.

[1]
[http://www.amazon.com/gp/product/0307275175/ref=as_li_ss_tl?...](http://www.amazon.com/gp/product/0307275175/ref=as_li_ss_tl?ie=UTF8&tag=theworlofsoft-20&linkCode=as2&camp=217145&creative=399369&creativeASIN=0307275175)

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pkulak
Actually, if you flip a coin 1024 times, the probability of getting 10 heads
at some point is about 63%.

I was actually wondering about this myself the other day
([https://plus.google.com/101522949595361604155/posts/Vhdist7x...](https://plus.google.com/101522949595361604155/posts/Vhdist7xFeV)),
and so I build a little script to calculate it. Calculating the probability of
a run is actually not very straight forward.

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hadronzoo
It's relatively easy toss a coin and always get heads (for both biased and
unbiased coins):
[http://books.google.com/books?id=tTN4HuUNXjgC&pg=PA317#v...](http://books.google.com/books?id=tTN4HuUNXjgC&pg=PA317#v=onepage&q&f=false)
(Jaynes's Probability Theory: The Logic of Science, Section 10.3)

~~~
hadronzoo
If Google is filtering those pages, here's an earlier version of that chapter:
<http://omega.albany.edu:8008/ETJ-PS/cc10i.ps>

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mathattack
This is interesting psychology. Eventually 10 in a row has to happen. But
would you bet 50 cents to win 51? At what point is it Bayesian statistics that
tells you not to make the bet? (That somehow the coin is loaded)

~~~
notaddicted
You can assess the fairness or bias of the coin:
<http://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair>

If you wish to start with a probability distribution assuming a degree of
fairness you can do that and it won't be so prone to fluctuation of the start.
I don't know anything online about this offhand but check out "Data Analysis A
Bayesian Tutorial" by D. S. Sivia section 2.1.1 for a worked out example.

Once you're doing that, then you need to calculate the optimum amount to bet.
If the betting will continue indefinitely then a sensible thing to do would be
to bet to maximise the expected logarithm of your bankroll, which you
calculate with the Kelley criterion:
<http://en.wikipedia.org/wiki/Kelly_criterion>

If you only get to make one bet then you may just want to maximise expected
value.

EDIT: didn't explain how to translate the fairness distribution into win/loss
odds because I don't know offhand, you could always simulate.

------
hackermom
Amazing patience.

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corin_
Two thoughts on this post/submission. The first is that it's really pretty
shoddy, I mean why did it need to be filmed, why not a written (or even to
camera) piece that just explains the logic. Anyone who doesn't believe it
after having it explained isn't going to believe it after a video of an
experiment that could so easily be edited to show 1000 heads out of 1000
flips.

The second is, even if it was presented better, is this suitable for HN? Sure,
the topic of probability is suitable, but this is on such a basic level that
surely most, if not all, HN readers already comprehended it.

That said, here's hoping that, if people are going to insist on upvoting it,
it can at least spur some interesting discussion. With that aim, here's a
tangeant:

It's always interesting in gambling how, no matter how mathematically smart
someone is, it's incredibly easy to let your heart make decisions for you when
money is on the line. Whether it's betting red on roulette because it landed
black 6 times in a row, or betting big on a blackjack hand because you've lost
your last few in a row and surely it can't keep going.

Even though, as you place the bet, you're thinking "I know the last X spins
don't _actually_ have any impact...", you can't help but feel the urge.

~~~
blauwbilgorgel
I like the philosophical implications of: if it is possible, with enough
trials, it will happen.

I remember using this argument against the proposed creationism view of my
religion teacher. If it is possible for life to emerge on a planet, given
enough time, it is bound to happen. Likewise: given enough games of Go, one
game will end with a perfectly ordered black-white spiral. This then led to
the tangent of: Is it possible for God to exist in our world?

The same with the possible worlds model of modal logic. If something is
possible, there is a world were such is the case. That could mean that, if
time travel or travel between possible worlds is possible, there is a world
out there, where they discovered this. They could travel between possible
worlds and teach these other worlds how to travel too.

As soon as something that crosses the boundaries between worlds is even
remotely possible, in the end it should permeate through all possible worlds.

~~~
derleth
> Is it possible for God to exist in our world?

This isn't the same kind of question, assuming the Abrahamic conception of
God, because that God is logically inconsistent. So, if the Abrahamic deity
exists, reality is inconsistent, so what right do we even have to consider it
reality? Therefore, the Abrahamic deity cannot exist in the real world.

(Nope, no lightning bolts.)

