There's this book that deals with Games Theory where the author tells the following story:
Two math students had to flip a coin some 150 times and note the results for homework.
The results for Student A
101011010000010101111010000000100001000111110111
111000010100001111000010101101111001011111000011
110101000000000000011011111111110101100110000101
000000000011111001111000111011111111000000101001
The results for Student B
011010010110101001010110001110101010100101110110
101100101110111011000110100101010101101101010101
101101010100101101111100101010100110001010100010
100101011011010111000110110111000110110101011000
Next day, a quick look and the teacher approved Student A for doing what was told and reprehended Student B for cheating.
While both results showed near identical number of outcomes for both heads and tails, it was clear to the teacher that Student B must have thought something like "heck, 150 times? Why bother, I'll just write the results on the fly and no one will notice".
We can bet Student B was not a gambler since we're too familiar with the chaotic nature of Roulette decisions and thus we'd recognize the results from A as likelier to happen than B's.
While both sides of a coin have equal chances, streaks do happen with a certain regularity. This was the point of said homework. The Math teacher knew about it from studying. We know about it from experience.
Old news to some, nevertheless it's good to see some evidence in a scientific book.
Science is empirical afterall, so it's where Math and Gambler's Fallacy meet.
Streaks can happen and WILL happen, just none of the parties can exactly pinpoint when. And it's where they clash.
Each decision is independent, bearing no relation to the last and the next, blah, blah, blah.
OK, but with strings of numbers I believe it's a different story. Shame we can't just walk into a casino and bet the next 12 numbers will be predominantly Red or something. Congrats! You win 1 unit!
Not without B.R.a.G...
what if student b did flick the coin for 150 times and got 150 heads could happen, just like roll 6 dice and get 6 ,6's, its happened and a person won a car at a fete
This is not true, you can not tell if b was cheating.
You can get 150 events with only singles and series of two and two series of three.
There is no way to tell how random works.
For me this is rubbish.
Well you can tell that to Professor Jordi Deulofeu. He wrote the book.
I don't tell him nothing, because i know i am telling the truth.
Just because B did not come with any sequense larger then 456 so does it not mean he or she was cheating.
I have many times seen 150 trails with series of three and below and the other way around.
I assume when you have simulate several hundred tousen trails nothing is unknown.
You name the topic - Interesting fact about Randomness - and what is the facts ? what is the point ?
You can guess that some one has cheating, but you can not be 100% because a random sequense for 150 trails can be beyond average.
Quote from: ego on Nov 29, 10:27 AM 2014
I don't tell him nothing, because i know i am telling the truth.
What??
QuoteJust because B did not come with any sequense larger then 456 so does it not mean he or she was cheating.
I have many times seen 150 trails with series of three and below and the other way around.
I assume when you have simulate several hundred tousen trails nothing is unknown.
You mean nothing is known... well the chapter continues and there's a brief explanation on why the teacher didn't recognize the results as truly random. I can transcribe it if you're interested.
QuoteYou name the topic - Interesting fact about Randomness - and what is the facts ? what is the point ?
You can guess that some one has cheating, but you can not be 100% because a random sequense for 150 trails can be beyond average.
I thought the point was clear: streaks and chops will happen with a certain regularity and it's good to see some evidence of it published in a science book.
BTW, here's an interesting video about random numbers. At 02:45 the presenter starts on bashing on computer simulations.
link:s://:.youtube.com/watch?v=SxP30euw3-0 (link:s://:.youtube.com/watch?v=SxP30euw3-0)
Quote from: ego on Nov 29, 08:53 AM 2014
This is not true, you can not tell if b was cheating.
You can get 150 events with only singles and series of two and two series of three.
There is no way to tell how random works.
For me this is rubbish.
I actually don't think this is "rubbish" at all. The professor is right. There is actually about 200 trials on here. Student B had no streak last longer than 5. That is not realistic and just to prove it I would love for you Ego to pull out any of the 185 smartlive spins on here and show me a streak where there are only 2 or 3 streaks in it and nothing more. Theres hundreds to choose from. Don't have the time? Don't worry about it I did the homework for you. There's nothing even remotely close to what you claim you have seen. Played a lot of roulette and I'm not to blind to know that in 200 spins there's certainly going to be at least one streak of 6 in a row and extremely likely to find many more than that. But go ahead and try to prove me wrong. I'm with the professor.
Quote from: wyldegibson on Nov 29, 02:31 PM 2014
There is actually about 200 trials on here. Student B had no streak last longer than 5.
The 5-streak was my mistake transcribing. There are no more than 3 heads or tails in a row for StB. The teacher found the results to be too regular.
Quote from: psimoes on Nov 30, 06:11 AM 2014
The 5-streak was my mistake transcribing. There are no more than 3 heads or tails in a row for StB. The teacher found the results to be too regular.
Even more to my point...the professor is completely right. In 200 trials you will never see only chops of 2 or 3 as the highest streaks. I'm not sure why Ego would ever think that because I find him to be very intelligent and mostnof the time on cue but he's very off here. I'm sure after he looks at any 200 spin sequence he will rethink his earlier stance.
Yeah from what I read, seems to be of great merit.
Now, the book on Games Theory is part of a collection. Other volumes talk about Pi, Golden Ratio, Prime Numbers and all that. It's for educational purposes. Nothing cutting-edge there, really. So what's presented is quite established. Hence I take it for a fact.
Another interesting thing it's there's no talk about the Law of the Third anywhere in the book.
Quote from: psimoes on Nov 30, 08:15 AM 2014
Yeah from what I read, seems to be of great merit.
Now, the book on Games Theory is part of a collection. Other volumes talk about Pi, Golden Ratio, Prime Numbers and all that. It's for educational purposes. Nothing cutting-edge there, really. So what's presented is quite established. Hence I take it for a fact.
Yes I can't really see how it helps us in our gambling endeavors except that we will get some decent streaks eventually but hard to know when to capitalize precisely. As far as this being a fact though I am indeed with you and the professor
Has anyone heard about Sierpinski's triangle?
See the first 2 mins of the video. It proves in a way the law of Large numbers is right and it is interesting to see how Chaos forms identical non-linear structures and substructures within the predetermined conditions.
link:://youtu.be/fUsePzlOmxw (link:://youtu.be/fUsePzlOmxw)
As you see below, n is the number of vertexes, r being the distance between the dots and the associated vertex.
(link:://mathworld.wolfram.com/images/eps-gif/ChaosGame_1000.gif)
I wonder if this could be of some use for roulette!