Randomness and outcomes. Math people please help!

[TwoCatSam]

On page 13 and 14 of his book, THE DRUNKARD'S WALK, Leonard Mlodinow gives an example of coin flipping.   The gist of it is this:  When you begin flipping the coin, either heads or tails will—sooner or later—assume the lead.  Basically he states that one might expect the lead would change many times during the course of 20,000 flips, but writes this.  (I paraphrase, but the content is the same.)

But the mathematics of randomness says the lead will not seesaw.  In fact, the most probable number of changes in the lead is 0, and it is 88 times more probable that the decision that took the lead—heads or tails--will lead through all the 20,000 flips.

Me again.  I have gone to Random.org and used their coin flipper to test this a little.  You can flip 16 coins at a time.  I am surprised at the number of times this phenomenon occurs.  If heads takes the lead, there will be more heads than tails in the sixteen flips.  Same with tails.

In all of the studies on randomness I have done, all the books and articles I have read, I have never come across this mathematical statement.  It is totally new to me.

Here's the question:  Is he correct in what he says?

Here's the big question:  How do we make money from it?

Sam

[Gavioli]

But the mathematics of randomness says the lead will not seesaw.  In fact, the most probable number of changes in the lead is 0, and it is 88 times more probable that the decision that took the lead—heads or tails--will lead through all the 20,000 flips.


Here's the question:  Is he correct in what he says?

Here's the big question:  How do we make money from it?

Im not sure if i understand corectly what he means with zero, but if he mean even then yes. Because everytime one side takes the lead, even=0 must happen first. And we cant make any money from this because we dont know when the change will happen.

Cheer

[TwoCatSam]

Gavoli

I read it to mean this:  If heads assumes the lead in the beginning, it is 88 times more likely that heads will maintain the lead throughout the 20,000 flip trial.  The 0 merely means that it is less likely (closer to 0) to change leads and 88 times more likely to maintain the lead.

Sam

[Gavioli]

Ok, I understand now what he means. I think it is law of large numbers or something like that. Use wiki and im sure you will find an answer.

nolinks://en.wikipedia.org/wiki/Probability_theory

nolinks://en.wikipedia.org/wiki/Law_of_large_numbers

[Breeze88]

HI


Try This nolinks://en.wikipedia.org/wiki/Random_walk


Specific cases or limits of random walks include the drunkard's walk and Lévy flight.



cheerz

[TwoCatSam]

My question is:  Is the man right?

When I start flipping a coin and heads takes the lead, is it 88 times more likely that heads will retain the lead through 20,000 spins.  This statement sounds incredible to me.  IF he is correct and it is 88 times more probable the lead will stay the same than change, I feel a system can be built around this "fact".

Sam

[Marven]

It sounds incredible to me as well. I can't think of a reason why one side should maintain the lead just because it showed first.
If that was true though, it would sure be very useful. Any form of predictability is.

Marven

[TwoCatSam]

Marven

Not because it showed first, but because it pulled ahead first.  BRR..........Red pulled ahead of black.

He puts in a footnote about a book written in 1957.  It is still in print after 52 years!  I have ordered it from my library and if I can't get it, I will spend the $74 and tax to buy it.  This book supposedly goes more into detail about the phenomenon.

Sam

[TwoCatSam]

People.......

If anyone would care to read the full text the the author's words, I will scan and copy it in.

Sam

[The Spiders Kiss]

I would love to take a look please Sam
TSK

[esoito]

Yes, please.

I'd like to read that too.

Thank you.

[TwoCatSam]

Gents.....

Thanks for your interest.  The scanning will be posted soon.

Sam

[xman1970]

Maybe something to play while "waiting" to play your actually bet ?

flat bet it & hover around breaking even.....


Thx Sammy....

[TwoCatSam]

OK, youse guys read this and tell me if I'm misunderstanding it......

If you click "Open link in a new window", it is much easier to read.  Position your cursor in the test and right click.

[esoito]

Thanks for the scan.

I can confirm your interpretation thus:


Quote:  "In fact, the most probable number of changes in the lead is 0..."

I take this wording to mean that they come out alternately: HtHtHtHtHt...  (i.e.  each leads for exctly the same number as the other...therefore, there are zero changes in the lead...)

And in the case of tHHHtHHHH your interpretation of the rest of the quote as being "...it is indeed 88 times more likely that heads will retain the lead through 20,000 spins." is how I would interpret it, too.

Ooooer...our hearts beat as one, Sam!

Hope this helps.

[esoito]

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