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Probability 101
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Probability 101

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Probability 101

In the process of writing this post, I've discovered a large part of the problem. The definition of randomness you will find on dictionary.com, and elsewhere, is incorrect.

It states

"of or characterizing a process of selection in which each item of a set has an equal probability of being chosen."
Randomness | Define Randomness at Dictionary.com

This is wrong wrong wrong wrong wrong. Any half decent mathematician will tell you, and I hope I will be able to explain why.

My dictionary (Collins, English, ISBN 000433078-1) defines random (statistics) as:

"having several possible experimental values any one of which is uncertain and depends on chance."

The key difference, is that it mentions nothing about equal chance.

Wikipedia states:

A random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions.

Randomness - Wikipedia, the free encyclopedia

There are several very wrong schools of thought which seem popular related to simple probability.

1-"Two outcomes = 50/50", linked to the notion that "random things are always 50/50 or 33/33/33 etc" (aka, dictionary.com-itus)

This is wrong, probably comes from fair die and dice roll examples from school. As stated before, if you play the lottery (and we'll ignore modelling the balls with physics models etc etc). It is random chance whether you win or not. However it is certainly not a 50/50 proposition (unless you buy a lot of tickets . and even then you won't be profitable). Another example would be drawing a heart off the top off a full deck of cards, there are two outcomes, draw a heart, don't draw a heart, but the chance of doing it is 1/4.

I don't know if I can explain it any better than that, providing the maths would just cause further confusion, @Fat Tails or somebody else might have a better approach.

2-"Since you believe you can predict the odds of the very next trade, why do you take losing trades? Just skip those"

I don't even understand this train of thought tbh. Perhaps @Big Mike could expand on it. If something has a 60% chance of happening...it has a 60% chance of happening, that doesn't magically mean I know when it will happen and when it will not.

Again an example. If you roll a fair die, I can "predict" that you'll roll a 2-5 with 5/6 accuracy. I can say you will roll a 2-5 83% of the time. I can bet you that you'll roll a 2-5 every time you roll it, and be correct 83% of the time, thus having an edge if I get good enough odds. I'm not saying I'll know when you'll roll a 1 and won't bet you on that roll though, that's ludicrous. Nor does it mean that rolling a 2-5 on a fair die isn't a random event.

Not trying to have a go at anybody (hence why I quoted Mike, if he takes offence he can ban me), I just think this should be sorted out as I think a basic understanding will help people's trading.


Next time, Monte Hall

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Hotch View Post
In the process of writing this post, I've discovered a large part of the problem. The definition of randomness you will find on dictionary.com, and elsewhere, is incorrect.

It states

"of or characterizing a process of selection in which each item of a set has an equal probability of being chosen."
Randomness | Define Randomness at Dictionary.com

This is wrong wrong wrong wrong wrong. Any half decent mathematician will tell you, and I hope I will be able to explain why.

My dictionary (Collins, English, ISBN 000433078-1) defines random (statistics) as:

"having several possible experimental values any one of which is uncertain and depends on chance."

The key difference, is that it mentions nothing about equal chance.

Wikipedia states:

A random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions.

Randomness - Wikipedia, the free encyclopedia

I also would subscribe to the definition of Collins/Wikipedia. A random process is simply a process which is non-deterministic. The outcome of a non-deterministic process cannot be predicted, as it cannot be attributed to one or several causes.

A random process can be typically described by a probability distribution. This does not imply that the probability distribution is known. The definition "... process of selection in which each item of a set has an equal probability of being chosen" does give a general description of a random process, but just refers to the discrete uniform distribution.


Hotch View Post

"Since you believe you can predict the odds of the very next trade, why do you take losing trades? Just skip those"

I think it is just a joke. Trades are always non-deterministic, and hence the outcome of a single trade is unpredictable. Finding an edge means to identify a probability distribution which is skewed in your favor.

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I was actually going to start a thread about this, but, since you decided you ruin my plan, I guess I'll post it here instead.

Knowing basic statistics and probability is practically a must for every trader. I would advise (again) new traders start with a statistics course before they pursue any other trading education.

There are so many excellent free resources these days, here is one of them:
UC Berkeley Webcasts | Video and Podcasts:

UCLA has an ebook/wiki devoted to the subject:
Probability and statistics EBook - Socr

Grinstead & Snell is an excellent resource:
Untitled Document

The man responsible for modern quantative finance, Ed Thorp, has put his "Elementary Probability" online also:
http://edwardothorp.com/sitebuildercontent/sitebuilderfiles/ElementaryProbability.pdf

I started with this book:
Amazon.com: Cartoon Guide to Statistics (9780062731029): Larry Gonick, Woollcott Smith: Books

This has a lot of good explanations of a lot things, including probability:
Archives | BetterExplained


One should note that probability quickly gets "complicated" and require an understanding of calculus, but finite/discrete probability is accessible for all.

I would, of course, recommend everyone to take advantage of the excellent math (and physics) courses at MIT's OpenCourseWare (http://ocw.mit.edu/courses/ocw-scholar/), but I understand that not everyone will be inclined to do so. It will be exciting to see if any of those will be offered through MITx this fall.


Last edited by Lornz; March 24th, 2012 at 02:29 PM.
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Lornz View Post
I was actually going to start a thread about this, but, since you decided you ruin my plan, I guess I'll post it here instead.

Bwahahahaha! Success!

Dovie'andi se tovya sagain.
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Hotch View Post
In the process of writing this post, I've discovered a large part of the problem. The definition of randomness you will find on dictionary.com, and elsewhere, is incorrect.

It states

"of or characterizing a process of selection in which each item of a set has an equal probability of being chosen."
Randomness | Define Randomness at Dictionary.com

This is wrong wrong wrong wrong wrong. Any half decent mathematician will tell you, and I hope I will be able to explain why.

My dictionary (Collins, English, ISBN 000433078-1) defines random (statistics) as:

"having several possible experimental values any one of which is uncertain and depends on chance."

The key difference, is that it mentions nothing about equal chance.

Wikipedia states:

A random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions.

Randomness - Wikipedia, the free encyclopedia

There are several very wrong schools of thought which seem popular related to simple probability.

1-"Two outcomes = 50/50", linked to the notion that "random things are always 50/50 or 33/33/33 etc" (aka, dictionary.com-itus)

This is wrong, probably comes from fair die and dice roll examples from school. As stated before, if you play the lottery (and we'll ignore modelling the balls with physics models etc etc). It is random chance whether you win or not. However it is certainly not a 50/50 proposition (unless you buy a lot of tickets . and even then you won't be profitable). Another example would be drawing a heart off the top off a full deck of cards, there are two outcomes, draw a heart, don't draw a heart, but the chance of doing it is 1/4.

I don't know if I can explain it any better than that, providing the maths would just cause further confusion, @Fat Tails or somebody else might have a better approach.

2-"Since you believe you can predict the odds of the very next trade, why do you take losing trades? Just skip those"

I don't even understand this train of thought tbh. Perhaps @Big Mike could expand on it. If something has a 60% chance of happening...it has a 60% chance of happening, that doesn't magically mean I know when it will happen and when it will not.

Again an example. If you roll a fair die, I can "predict" that you'll roll a 2-5 with 5/6 accuracy. I can say you will roll a 2-5 83% of the time. I can bet you that you'll roll a 2-5 every time you roll it, and be correct 83% of the time, thus having an edge if I get good enough odds. I'm not saying I'll know when you'll roll a 1 and won't bet you on that roll though, that's ludicrous. Nor does it mean that rolling a 2-5 on a fair die isn't a random event.

Not trying to have a go at anybody (hence why I quoted Mike, if he takes offence he can ban me), I just think this should be sorted out as I think a basic understanding will help people's trading.


Next time, Monte Hall

I'm no mathematician, but I think we are confusing 2 different concepts because we are using them interchangeably, Probability and Odds. Probability measures the chances for an event occurring against a total number of occurrences. Odds measure the chance of a singular event occurring as opposed to not occurring. Notice the words 'total number of occurrences' in the description for probability, and 'single' in the description for odds.

The odds of the single next coin flip to be heads or tails, the single next trade to be winner or loser is 1 to 1, some here have expressed it as 50/50.

The probability of the next coin flip to be heads based on the 'total' 1000 flips before it, the next trade to win or lose based on the 'total' 1000 trades observed before it, is variable depending on the distribution of heads/tails, or wins/losses observed in the last 1000 (total) occurrences.

So, single next trade considered by itself, odds 50/50. Single next trade considered in light of the last 1000 total historical trades, win probability 10%, 20%, 60%, 70%...etc.

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I see there is not much interest in the Berkeley course, but hopefully some will watch this:



As for odds vs probability:

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monpere View Post
Probability measures the chances for an event occurring against a total number of occurrences. Odds measure the chance of a singular event occurring as opposed to not occurring.

I disagree with that particular statement.

Let us say assume that there is a 40% probability that I am wrong. In that case

-> the probability that I am right are 60 % (the numerical value is 0.6)
-> the odds that I am right are 6:4 (the numerical value is 1.5)

If you talk about a probability you talk about the ratio of favourable to all occurences. If you talk about the odds you talk about the ratio of favourable to unfavourable occurences.

Or maybe this is just an odd philosophical discussion on probabilities.


Last edited by Fat Tails; March 25th, 2012 at 05:47 AM.
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Lornz View Post
I see there is not much interest in the Berkeley course, but hopefully some will watch this:

As for odds vs probability:

You beat me by a few seconds by shamelessly posting a video, where I tried to explain it with my own words. That is unfair!

At least the guy in the video said the same thing, so I do not need to comment it.

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The whole discussion regarding coin flips is pretty meaningless, and even more so when people redefine mathematics on the fly.

I've posted this before, but it deserves to be in this thread as well.
http://www.espenhaug.com/ScientificCoinFlipExperiment.pdf

Do you believe that markets are random, @monpere?

Do markets have a 50% chance of continuation and reversal at each tick?

People keep saying that each trade is 50/50, without declaring a stop and profit target.

Is a 1:1 and a 1:50 both 50/50?

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