Ignore Bait: Highest IQ, Many Questions, Odds makers invited...

[David in FL]

As when humans default to their feelings and emotions, we typically don’t make the correct choices.

That’s an extremely accurate statement and reflects the current leadership, and state of affairs in this country…

Sadly, too few people are capable of critical thought. Relying instead on emotion and feelings. Oftentimes driven by others who understand that and use it to forward their agendas by appealing to the weak-minded through emotional based rhetoric.

 

[straightline]

Lol, must be an election year.

 

[justnum]

The arithmetic is clear enough. No argument. It's cool to have a little ( a lot would be better) exobox thinking though.

VaPool brought up conspiracies and they're so easy to debunk because the means (of conspiracy) are off limits. Reminds me of The Amazing Randy vs Uri Geller on Carson a ways back. Occurred to me back then they could be using identical "powers" to prove their side. One to perform the trick and the other to debunk it. TV show... Frankly I have enough faith in the human intellect that the species' that spawned all the legends - and generically identical and global ones at that, had a pretty good idea of what their experiences were.

Great point if Americans had not created tv shows and media entertainment, then America would be similar to European countries.

The Euros are starting to come around, some countries have decided to change policies based on actions of a country performing special military operations. I do hope they form a response to combat countries performing covert espionage operations. However the economics of that response require more collaboration.

America is re-educating the world and the world is slow to adopt. This paradox is similar to how math is taught in the US versus outside of the US.
You can see it here on this thread with the people repeating arguments about fractions, its like their entire communication system breaks down and just loops to infinity and beyond.

 

[DCMike]

Just some idle conversation here, voicing my confusion. I read about a computer generated coin flip years ago. I think they let it run billions of times or more. There was a high run of one side winning every flip of around 20-22 times. This was wildly improbable as the next highest run was under ten I believe.

Here is where I get confused. If the first twenty flips would have been all heads, the odds of the rest of the series being fifty-fifty remain the same. If there was a thousand flip run of all heads, the trial from there on out would still have fifty-fifty odds. It seems to me if the overall statistics are to remain fifty-fifty, then the tails side would have to do some catching up either with long runs of it's own or a series of shorter runs.

If the odds are fifty-fifty, after a billion flips shouldn't the results be within a very close percentage of fifty-fifty? The computers say that one side might be 10-15% ahead of the other. If so, I say the odds weren't fifty-fifty. Seems like if one side is well ahead the other side has to be favored over the following run if you can stay with it long enough.

This confusion is why I am much more inclined to wager than gamble. I hate to sound like Bert Kinister but my last wager was for a chicken dinner. A single backcut shot, a bad shot to bet against me on. To quote Bert, "Winner, Winner, chicken dinner!"

Hu

Interesting thought experiment! I would have to agree: that the real deal with coin tossing is eerily surprising.

Although the average number of heads has to "even out" to fifty-fifty (law of large numbers), the total number of heads do not. In fact, for totals, the deviations from expectation grow at a rate proportional to half the square root of number of tosses.

So for example, for an idealize fair coin, after a million tosses there is (only) a 68% chance that the total number of heads is between 499500 and 500500, which is just +/- 500 deviation from expectation. (500 being half of the square root of a million)

After a trillion tosses, there there is only a 68% chance the total is within 499999500000 and 500000500000 which is +/- 500000 from expectation.

The size of the deviation grows, but just at a rate slower the the number of tosses, because "square root of n" grows more slowly than "n". This allows the law of large numbers (which is for the average, not the total) to still be true.

An anomaly in the beginning (such as 20 heads in a row) would be absorbed into these expected deviations

The notions above are due to the deMoivre-Laplace theorem (essentially the first "central limit theorem") proven in the 1700s. The deMoivre-Laplace theorem has a Wikipedia entry if you're interested.

William Feller's 1950 textbook devotes an entire chapter to fluctuations in coin tossing. So many interesting and non-intuitive things.