Probabilistic Distribution

[Bigbusiness]

I have a car but I don't have a goat, so I woudn't mind the goat. If I win the car, I could sell it and buy a goat. Either way, I win

If you want the car, a goat will eat anything, so take off an item of clothing, slide it half way under the door and see if it is gobbled by a goat. The door that doesn't do this is more likely to have a car behind it

 

[frugi]

Thanks twalker I was being thick. Just drawing a flow chart now!

 

[TheBramble]

If you want the car, a goat will eat anything, so take off an item of clothing, slide it half way under the door and see if it is gobbled by a goat. The door that doesn't do this is more likely to have a car behind it

This is where you logical types come unstuck against the combined intellectual weight of us theoreticians.

What if the goat is (a) not hungry and/or (b) wants you to win the car? You may now find you're stuck on the horns of a dilemma (or should that be a dillama?)

 

[frugi]

I think he should stick with his original choice, but my chart is bound to be flawed.
If the host is more likely to tell the truth when there IS a goat behind the door then I'm definitely wrong!

Edit: I am wrong cause the host cannot say there is a goat or car when there is and be lying at the same time. One to work on...

Edit 2: Well if you assume the above then the chance is 50:50 whatever the contestant does. (see 2nd chart).

So, what am I missing here?

 

[Scripophilist]

Aha, Inveitable I would arrive on this thread at some point. I set up a website to try and explain some of the more basic laws of probability http://www.probabilitytheory.info, It's pretty basic but should address some of the points on this thread.

The big argument in academic circles about applying probability is whether trades are independant or not. I.e. does one trade or market move affect the outcome of another. There is loads of discussion and debate on this.

I did conceptualise a spreadsheet that took historic movement and projected it forwards. It works on a macro and major scale but all that inbetween is a little fuzzy.

One thing I have witnessed though is that Black Scholes were wrong!!! Pricing models using this equation don't reflect fair value very well IMO.

 

[TWI]

It certainly pans out something like that. I will see if I can dig out the proof as I do not have time right now to focus the mind on it.

 

[frugi]

Hello Scripophilist,

As you will see I shamelessly plagiarised an explanation of the gambler's fallacy from your useful website a few posts above. Sorry! Obviously I'm very happy to delete it if you wish, though it is a model of clarity.

*The big argument in academic circles about applying probability is whether trades are independent or not. I.e. does one trade or market move affect the outcome of another. There is loads of discussion and debate on this.

That is a huge relief as I thought it was just my basic lack of understanding that prevented my making a sensible decision about this.

Also, do you happen to know if I have I got the last goat/car problem right? The probabilities seem unrealistic so I suspect a schoolboy error in my calculations. Cheers.

 

[Roberto]

I have a car but I don't have a goat, so I woudn't mind the goat. If I win the car, I could sell it and buy a goat. Either way, I win

I think you maybe forgot something, BB: don't you have to take the goat across second, so that you can bring the sheep back in the boat before you take the car across? Or am I in the wrong problem?

 

[frugi]

There are grains to be had if you're not chicken, but to be honest the sheep fox things up a bit: please send it bleating back across the Styx.

 

[TheBramble]

One thing I have witnessed though is that Black Scholes were wrong!!! Pricing models using this equation don't reflect fair value very well IMO.

Hi Scripo. In new Market Wizards there a couple of traders whose companies used the imbalance inherent in the basic BS model to capitalise on trading opportunities. However, that was then - Now I would imagine few professional trading operations use the BS model without modification.

 

[Tuffty]

Originally Posted by Scripophilist
"I set up a website to try and explain some of the more basic laws of probability http://www.probabilitytheory.info, It's pretty basic but should address some of the points on this thread."

I had a look and was impressed. I was also confused. From the website it states:-

"Winning and losing runs
Are you a rotten gambler or just plain unlucky? You seem to have hit on a winning system when woe and behold you are struck down by a really bad losing run and with it your confidence. So, were you just unlucky?
If you know the probability of an event and how many times you will perform the event there is a forumla that will work out your maximun winning and losing runs.
Let us assume that S=The number of times you play this game / perform the event. In this case a coin toss. S=555 coin tosses. For success in this trial we will need to throw a head. There are only two events so our chance of success is 1/2 or 50%
Fire up Excel and type the following formula
=ROUND(LN(555)/-LN((1-0.50)),0)
Gives the answer = 9. In 550 throws you will get a maximun run of nine heads in a row."


Is this incorrect unless it is qualified with some probability? ie x% probability of 9 loosers in a row as you could get far more.

 

[TheBramble]

No, it's about right.

Another (shorter) calculation is 20*(1-Pw) = statistically valid maximum number of consecutive losing trades {where Pw is the probability of a Winning Trade}

Which is slightly more useful as it is completely independent of the number of trades (which of course, is always an unknown)

What's galling about these shorter equations is how close they are to an all-singling all-dancing Monte Carlo generated result (damn!).

 

[Tuffty]

Ah, Mr Bramble,
Your formula seems to be based on what is 'statistically valid'. How do you define 'statistically valid'? As you might have guessed I worry about such things as I may be dealing with the statistically invalid side of any such definition.

 

[TheBramble]

Too true. And as I've said elsewhere, just because something is statistically valid, doesn't mean to say it's how it's going to be. In this example, you could run for eternity and only ever experience half the number of consecutive losing trades - or double!

But given the majority of traders work with probabilities and statistical methods - it might prove useful to some.

I also keep a wary eye on (either for advantage or protection) those 'statistically invalid' conditions (aka Taleb's Black Swans), but don't build my trading strategy around them.

 

[donaldduke]

Tuffty,

It would appear to the longest losing streak thats probable doing approx 1000 trades.

As you draw more and more trades the probable longest losing streak gets bigger and bigger.
If you do a billion trades then a system thats right 90% of the time will probably still
lose 10 times a row somewhere in those billion trades. Even though the figure from the
formula is only 2!

1000 probably is significant for most traders.

The exception are day traders doing a 1000 trades a month,
whould expect to encounter longer losing streaks during their carear than that formula would suggest.

 

[frugi]

TWalker I would be extremely grateful if you had a moment to dig out the solution to the problem you set in post No. 17 as it is really doing my murphy in! Cheers

 

[Roberto]

Again, surely it's what we bridge-players call "restricted choice". In the original problem it must always be right to change your mind. In the amended version from post 17 it can't make any difference because the choice hasn't actually been restricted. N'est-ce pas? Or, as they say, "innit"?

 

[TWI]

Frugi,
I do not have the proof anymore myself, I will try to get hold of it from guy who sent me the problem.
I did originally believe after going through probabilities that it did not make a difference but the solution was pretty convincing that it did.

 

[theknifemac]

An intuitive answer here

http://www.comedia.com/hot/monty.html

Play the game yourself here

http://math.ucsd.edu/~crypto/Monty/monty.html
And more answers here

http://math.ucsd.edu/~crypto/Monty/montybg.html

And here

http://people.hofstra.edu/staff/steven_r_costenoble/MontyHall/MontyHall.html

And a slightly more mathematical proof

http://www.remote.org/frederik/projects/ziege/beweis.html


Stew

 

[JumpOff]

but your chance is now 50% not 33% sticking to your original door - so it makes no difference if you change or not?

as youve decreased your risk with the original choice of door wouldnt it make sense to stick with your winner?

which ever way you look at it, after the 1st door has been opened, you now have 2 choices so a 50% chance regardless if you stick or twist.

is this not correct?

I agree with you 13.
JO