Oldie but Goodie

[TheBramble]

It's always fun to debate the MH Problem and everyone is agreeing without possibly realising it.

The difference is one of perspective: Whether one looks at the contestant's probability from the outset or AFTER one of the booby-prize doors has been opened (eliminated).

Frugi is dead right (and very elegantly demonstrated in his diagram). From the initial position, switching will lead to a 2:3 probability of winning.

The situation AFTER MH opens a door could be considered on it's own as a separate probability issue. As RT mentions above.

The thing is, the whole point of the first post in this thread was not to debate the answer provided in that post, but to ask if there are lessons for traders.

I think the subsequent train of the thread's development is a very real lesson on trader psychology....

 

[roguetrader]

Ok I try once more before I leave it. Play my game. In RT's game there are 100 doors, one prize and you pick one. Your chance of picking the correct door is 1%. The chance of the prize being behind the other 99 doors collectively is 99%. Now RT removes 98 of those other doors, do you still think that the odds are 99% that the prize is behind the remaining door.

 

[roguetrader]

Do you believe if I have flipped 3 heads in a row on a coin toss that the odds on the next flip have changed?

 

[roguetrader]

The thing is, the whole point of the first post in this thread was not to debate the answer provided in that post, but to ask if there are lessons for traders.

I think the subsequent train of the thread's development is a very real lesson on trader psychology....

Hmmn i couldn't see anything comparible between the game and trading, but thats just me. The problem tho is the answer was part of the consideration in that question surely, and therefore if the logic in the answer was flawed it would have to be addressed first.
Maybe in my case it's "trivial things occupy simple minds" so on that note I am going to bow out of this discussion.

 

[jimvt]

Do you believe if I have flipped 3 heads in a row on a coin toss that the odds on the next flip have changed?

No of course not, but that's entirely different!

As for the 100 door game, although "common sense" says no, read (all of) this:
http://www.grand-illusions.com/monty.htm

Anyway , enough is enough......no more from me either.

Cheers

 

[roguetrader]

He has a 50:50 choice of doors, yes, but one of them has a greater chance of hiding the prize, regardless of whether it is chosen.

Anyway I'll leave it there - I guess we'll just have to disagree on this one

Frugi mate do that for my 100 doors example below please.

 

[frugi]

Ok I try once more before I leave it. Play my game. In RT's game there are 100 doors, one prize and you pick one. Your chance of picking the correct door is 1%. The chance of the prize being behind the other 99 doors collectively is 99%. Now RT removes 98 of those other doors, do you still think that the odds are 99% that the prize is behind the remaining door.

Yes, as long as the 98 doors removed by RT do not have a prize behind them, as before. The only time you will lose if you change your original choice is if your original choice was the prize, the chance of this being 1% as you say. Thus there is a 99% chance that changing original choice, once the 98 losing doors have been removed, will win.

Do you believe if I have flipped 3 heads in a row on a coin toss that the odds on the next flip have changed?

Of course not. Are you calling me a fallacious gambler lol

 

[roguetrader]

No of course not, but that's entirely different!

As for the 100 door game, although "common sense" says no, read (all of) this:
http://www.grand-illusions.com/monty.htm

Anyway , enough is enough......no more from me either.

Cheers

LOL jimvt, what can I say, except "I'm still not havin' it!" food for thought though.

 

[Ingot54]

Originally posted by RogerM"
In the explanation section it says that the key to the paradox is the fact that Monty knows where the prize is and so never picks that door. If he didn't know, then 1/3 of the time he'd uncover the prize and the game would be void and you'd have to play again.

Still doesn't explain why the toss of a coin example above doesn't work tho'.

The key is that MH knew :

a) Which door not to open, in which case the contestant MUST switch in order to win
b) The contestant had chosen the winning door, in which case it did not matter which door MH opened

The lesson for traders is don' t trust Monty! Do your own research.

 

[Ingot54]

... and the reason the flip-of-the-coin approach does not work, is that coins can' t think, therefore they can' t choose to present a red herring to you.

...and another lesson here for traders ... develop a strategy that out-performs the flip-of-a-coin and all you need do is manage the choice - manage the risk.

 

[talkingcents]

Flip of the coin

When making a decision in life if you flip a coin the probability in making the right decision is 50/50 !.
So if you apply just a little sensible logic to the problem you should move the probability a few points in your favour and so your profitable trades should exceed the unprofitable trades.
Just a thought!