Probability theory etc

This is a discussion on Probability theory etc within the General Trading Chat forums, part of the Reception category; Sounds like there will be an interesting prog on subject topic Radio 4 @ 9.00 (8.00GMT) by prof Marcus de ...

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Old May 29, 2008, 10:02am   #1
 
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Probability theory etc

Sounds like there will be an interesting prog on subject topic Radio 4 @ 9.00 (8.00GMT) by prof Marcus de Sautoy - he's generally worth a listen and good on the maths of music.

On now!

(Sharky 29/10/14: A podcast of the radio program is available here: http://downloads.bbc.co.uk/podcasts/...0529-0900a.mp3 and is linked from this page: http://www.bbc.co.uk/podcasts/series/iots/all)
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Last edited by Sharky; Oct 29, 2014 at 10:11pm. Reason: Added link to the radio show
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Old May 29, 2008, 10:47am   #2
 
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0007 started this thread One major point that came out from this talk was how counter-intuitive probability theory is. Some lessons there for trading perhaps? eg - isn't it difficult to believe and act upon the facts and what you see happening, rather than what you think or want should happen.

No new lessons there then. Just need to work on my mental discipline!

(prog is normally available for "listen again" on BBC website - though it's still got last week's at present).
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Old May 29, 2008, 10:48am   #3
 
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Way over my head but interesting that statistically you only need 23 people in the same room to have a good chance of 2 of those people having the same birthday. But 250 people to have to be in that room for a better than evens chance of someone else having the same birthday as yourself.
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Old May 29, 2008, 10:51am   #4
 
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(prog is normally available for "listen again" on BBC website - though it's still got last week's at present).
On again Sunday evening 9.30 pm
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Old May 29, 2008, 1:17pm   #5
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Way over my head but interesting that statistically you only need 23 people in the same room to have a good chance of 2 of those people having the same birthday. But 250 people to have to be in that room for a better than evens chance of someone else having the same birthday as yourself.
most of probability theory is relatively easy. When you get Stochastic processes, Martingales, queuing, diffusion processes, percolation's etc. . . . then things can get pretty intense.

Also there are counter intuitive paradoxes about protocols that you see in probability theory (see prisoner's paradox) and also other famous paradoxes like Simpson's paradox.
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Old May 29, 2008, 3:32pm   #6
 
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Originally Posted by 0007 View Post
Sounds like there will be an interesting prog on subject topic Radio 4 @ 9.00 (8.00GMT) by prof Marcus de Sautoy - he's generally worth a listen and good on the maths of music.

On now!
very good. just listened to it.

one clever example is the one about getting 5 heads, and how people "feel" that the next one has to be a tail, as "its due a turn".
imagine instead of flipping the coin, you put it in a box and lock it away for 20 years.
open the box after 20 years and then ask "do you still think the next one is due a tail"?

gets people to think how the coin cant have a memory, and how people connect things when there is no actual connection.
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Old May 29, 2008, 3:42pm   #7
 
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Computer Laboratory - Probability

^ Very good free notes from a short corse on probability. Starts out assuming no knowledge and quickly covers some relatively advanced stuff.
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Old May 29, 2008, 3:46pm   #8
 
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. . .

one clever example is the one about getting 5 heads, and how people "feel" that the next one has to be a tail, as "its due a turn".

. . .

gets people to think how the coin cant have a memory, and how people connect things when there is no actual connection.
Actually, when you make that (of the order of) 10 heads in a row, what's the chances of the next one also coming up heads the answer is actually >99%.

Why?


Because the chances of that happening (ie 11 heads in a row) are far less than the chances that a mistake was made and a rigged coin was used. (serious)
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Old May 29, 2008, 4:20pm   #9
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Actually, when you make that (of the order of) 10 heads in a row, what's the chances of the next one also coming up heads the answer is actually >99%.

Why?


Because the chances of that happening (ie 11 heads in a row) are far less than the chances that a mistake was made and a rigged coin was used. (serious)
the chance of getting another head GIVEN that 10 heads have already occurred is STILL one half, it does not matter what has happened before.

However to get 11 heads in a row is 1 in 2048. Coin tossing is a stochastic process, known as a Markov Chain.

And to prove something is rigged is rather (how shall we say) "difficult". You can never really be "certain", but you can say with 98% or 99% that something is rigged and that should about resolve it. The reason for this is because you are using probabilistic tools/measures on a probabilistic system, hence your answer cannot be deterministic in that sense.
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Old May 29, 2008, 4:38pm   #10
 
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The coin toss theory has been many an interesting and argumentative discussion.

Even if you flick 15 heads in a row, lock it up for years or do it in 5 minutes, use the same person or 15 different people, the odds on the next flip is still 50-50.

This is because the coin has no memory....but...

Law of odds do,

therefore over whatever time, by whoever, the coin will become closer to 50-50 the more times it is flicked...so

If you've had many heads in a row, at some time, not necessarily the next flip or the next several but at some time/flick/event it will have to pull in (close to) the equal amount of tails.

(this even includes whether one side is decimally heavier than the other)

The same rules apllies to the Roulette table, even though they have 1 green/neutral or 2 on european tables, this is why they have a minimum outside bet rule followed by a maximum to prevent people from (constantly)winning this way. This swings the odds in the houses favour by around 2%, this means that you will win small amounts most of the time, but at some point the ball will give 12 reds/blacks busting the player.

(above example uses doubling up method and is proved to work - scientifically and actually, hence why casino's have moved the goal posts to prevent it)
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