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
Quote from: TwoCatSam on March 03, 2009, 05:05:14 PM
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
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
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
HI
Try This nolinks://en.wikipedia.org/wiki/Random_walk (nolinks://en.wikipedia.org/wiki/Random_walk)
Specific cases or limits of random walks include the drunkard's walk and Lévy flight.
cheerz
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
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
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
People.......
If anyone would care to read the full text the the author's words, I will scan and copy it in.
Sam
I would love to take a look please Sam
TSK
Yes, please.
I'd like to read that too. :)
Thank you.
Gents.....
Thanks for your interest. The scanning will be posted soon.
Sam
Maybe something to play while "waiting" to play your actually bet ????
flat bet it & hover around breaking even.....
Thx Sammy....
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.
(https://www.vlsroulette.com/proxy.php?request=nolinks%3A%2F%2Fimg10.imageshack.us%2Fimg10%2F9066%2Fscan0001k.jpg&hash=0d662cff627cd3bcad7ed707a29d606f1bd541e6) (nolinks://img10.imageshack.us/my.php?image=scan0001k.jpg)
(https://www.vlsroulette.com/proxy.php?request=nolinks%3A%2F%2Fimg10.imageshack.us%2Fimg10%2Fscan0001k.jpg%2F1%2Fw906.png&hash=0473228c0389d646942aa7d1733cd371cb4b08d2) (nolinks://g.imageshack.us/img10/scan0001k.jpg/1/)
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
He is saying the coin is flipped 20,000 times. For it to be tHtHtH..etc..for 20,000 flips would defy all logic and probability.
Perhaps the other book will explain it more completely.
Sam
Doesn't make sense to me.
Player A steps up to a table and sees - R B R.
Player B sits down at the same table one spin later and sees - B R B.
The table can't make the supposition true for both A and B over the next xxx spins.
So it all depends on the point at which each person begins their observation...?
I mean, we can't all start at exactly the same place in any spin sequence!
The first thing I thought was how long do we have to track the event to know if a side is pulling ahead?
Let's say we take 100 spins. So let's for argument sake say that after 100 spins, reds are 65 and blacks are 35. How do we know that after 200 spins black won't be 120 and reds 80? How do we know that those first 100 spins was actual part of a red's lead? Maybe just a bad streak in the black's lead (if that made any sense.
Think is I guess we have to be there from spin 1. How many do we track though to know which will be dominant?
Also if we stop at the end of the day and the wheel is shut down till tomorrow, do we start a new session or go on? Then let's say we start every day with new session. What happenes if let's say the dealer takes 5 minutes to sort out everyones chips and to respin. Does that affect the outcome? Or is this really only true for no interruptions and continues coin flipping? Alot of questions ... I guess alot of testing then!
Interesting though Sam.
Cheers
Jakk
Jakk
I have the feeling the book from which Molodinow took the idea will have much more detail in it. Let's just flip coins. I would take a minimum of two flips and a maximum of three for h or t to become the leader. HH HtH.......either way heads is dominant. In the first, HH, heads is 100% greater than tails. In the second, HtH, heads is 66% greater.
I am reading it this way: If you flip a fair coin and you get two heads, HH, then the chances are 88 to 1 that heads will remain in the lead for the entire 20,000 flips. Why 20,000? Why not three or four? It would be HHH, in which case you would have a winner. Or HHtH in which case you would have a winner.
I read him as saying if you have HH, there is an 88 to 1 chance you will get HHH. If you have HtH, there is an 88 to 1 chance you will get HtHH or HtHtH.
So instead of a 50% chance of hitting Heads, you have an 88 to 1 chance of hitting Heads.
Makes no sense to me. I should maybe stop reading books!!
Sam
Hi
My thought would be that in the first few spins one side of the coin could lead,the next 100 the other and the next 1000 flips the next. The patterns could be short ,meduim or long at the end of the day it is al random. In 2009 heads could be dominant next year tails could be.
To use this in our advantige as we all know is to use triggers,strategies.......but beware of randomness.
;)
Regards
MAX
This phenomenon is well explained in another book, which is a good practical book on probability (with some math, but mainly just arithmetic) -
nolinks://nolinks.amazon.com/Taking-Chances-Probability-John-Haigh/dp/0198526636/ref=sr_1_1?ie=UTF8&s=books&qid=1236365969&sr=1-1 (nolinks://nolinks.amazon.com/Taking-Chances-Probability-John-Haigh/dp/0198526636/ref=sr_1_1?ie=UTF8&s=books&qid=1236365969&sr=1-1)
There's even a formula which tells you how many "changes of lead" there will be in X number of spins.
The trouble is, roulette isn't really a game of probability, so it's hard to see how this kind of information can help. After all, there are any number of stats you can come up with but do they actually give you any help in predicting the next number? I think you need physics for that.
IMO if you can take anything from this particular info, it should be that it's better to bet with the wheel rather than against it. In other words, don't bank on a change of direction, instead "go with the flow".
Tangram
Thanks for that.
Sam
Its the law of large numbers and isn't exploitable in the short term. You can do the same thing on Roulette Xtreme. Do 100,000 spins and you'll see that black or red takes an early lead and usually maintains the lead. So what, its useless info in the short term. If red is in the lead for a million spins, that doesn't mean there won't be lots of long black streaks.
Spike
I merely find it a curiosity. Like the birthday paradox or whatever you call it.
You're right. It's not exploitable or it would be common knowledge.
I'm the kid who would rather take apart a clock to see why it ticked than play baseball.
Sam
Tangram
I found the book used and bought it. What's twelve bucks anyway? I find this phenomenon fascinating even if it leads nowhere.
Sam
I'm sure you won't regret it Sam, but just be prepared for some head-scratching moments! Like I said, the math in the book isn't heavy, but you have to be thinking clearly to understand some of the concepts.