September 18, 2016 — Shop Talk with Gene, Chris and Goggs

[Spectre73]

Am I the only one waiting to hear from Goggs how many people need to be in the room to share your birthday!,Gene cut him off before the reveal.

No - I've been thinking about that too and without looking at the net I guessed 12. A little out then

 

[Goggs Mackay]

No - I've been thinking about that too and without looking at the net I guessed 12. A little out then

And that is a perfectly reasonable guess, the point of the tale is to illustrate just how unintuitive many aspects of chance and statistics are to the average person. If anyone is at all interested, a quick search online will provide many great examples, the great thing being is that for most of the best ones, nobody needs any math ability etc and the examples are usually very easy to grasp real-world examples.

Another classic is that if I toss a coin 10 times in a row, and it comes up heads all 10 times, what are the odds of the 11th toss being tails? (It's normal to fall into the trap of thinking, well, it has to land tails sometime, and heads are already well over-represented etc; the tendency is to then think 'It must be tails' turn now, so you would answer that you think there is now a greater chance of tails coming up, after all those heads in a row - but the answer for a coin toss is that regardless of how unlikely the results have been prior, any coin toss will still have a 50:50 chance of coming up whichever side.
I think the explanation is that most of us understand that if you did ten thousand consecutive coin tosses, the final tally should approximate 5000 heads to 5000 tails. Bearing this in mind, when we are faced with a relatively unlikely series of even odds coin tosses that are heavily weighted to one side, we instinctively think that chance will 'kick-in' and start to even things up and bring the unlikely tally closer to the 50:50 we know should be the correct odds on whatever side coming up. We have to remember that a single coin toss has a 50:50 chance of either coming up, and no matter what has gone before, any single toss will still have those odds.
There are numerous more interesting and surprising results. I may have a look to find any really great ones. I hope my explanation hasn't confused anyone!

 

[Wade]

Nice post but It could have been a little shorter Gordo.

 

[technomage]

Nice post but It could have been a little shorter Gordo.

And it could have been a lot nicer, let me tell you. That Goggs is downright rude. I don't know why he hasn't been banned yet.

 

[technomage]

And that is a perfectly reasonable guess, the point of the tale is to illustrate just how unintuitive many aspects of chance and statistics are to the average person. If anyone is at all interested, a quick search online will provide many great examples, the great thing being is that for most of the best ones, nobody needs any math ability etc and the examples are usually very easy to grasp real-world examples.

Another classic is that if I toss a coin 10 times in a row, and it comes up heads all 10 times, what are the odds of the 11th toss being tails? (It's normal to fall into the trap of thinking, well, it has to land tails sometime, and heads are already well over-represented etc; the tendency is to then think 'It must be tails' turn now, so you would answer that you think there is now a greater chance of tails coming up, after all those heads in a row - but the answer for a coin toss is that regardless of how unlikely the results have been prior, any coin toss will still have a 50:50 chance of coming up whichever side.
I think the explanation is that most of us understand that if you did ten thousand consecutive coin tosses, the final tally should approximate 5000 heads to 5000 tails. Bearing this in mind, when we are faced with a relatively unlikely series of even odds coin tosses that are heavily weighted to one side, we instinctively think that chance will 'kick-in' and start to even things up and bring the unlikely tally closer to the 50:50 we know should be the correct odds on whatever side coming up. We have to remember that a single coin toss has a 50:50 chance of either coming up, and no matter what has gone before, any single toss will still have those odds.
There are numerous more interesting and surprising results. I may have a look to find any really great ones. I hope my explanation hasn't confused anyone!

I'm confused, but maybe that's because I haven't heard the episode yet.

 

[Randall]

And that is a perfectly reasonable guess, the point of the tale is to illustrate just how unintuitive many aspects of chance and statistics are to the average person. If anyone is at all interested, a quick search online will provide many great examples, the great thing being is that for most of the best ones, nobody needs any math ability etc and the examples are usually very easy to grasp real-world examples.

Another classic is that if I toss a coin 10 times in a row, and it comes up heads all 10 times, what are the odds of the 11th toss being tails? (It's normal to fall into the trap of thinking, well, it has to land tails sometime, and heads are already well over-represented etc; the tendency is to then think 'It must be tails' turn now, so you would answer that you think there is now a greater chance of tails coming up, after all those heads in a row - but the answer for a coin toss is that regardless of how unlikely the results have been prior, any coin toss will still have a 50:50 chance of coming up whichever side.
I think the explanation is that most of us understand that if you did ten thousand consecutive coin tosses, the final tally should approximate 5000 heads to 5000 tails. Bearing this in mind, when we are faced with a relatively unlikely series of even odds coin tosses that are heavily weighted to one side, we instinctively think that chance will 'kick-in' and start to even things up and bring the unlikely tally closer to the 50:50 we know should be the correct odds on whatever side coming up. We have to remember that a single coin toss has a 50:50 chance of either coming up, and no matter what has gone before, any single toss will still have those odds.
There are numerous more interesting and surprising results. I may have a look to find any really great ones. I hope my explanation hasn't confused anyone!

All factors considered truly random ( no cheating or fixing ), the tendency to consider over-representation in a coin-toss where 10 out of 10 are the same result is perfectly reasonable, and the statistical chance is also 50:50. So both are correct, because mathematically the statistical chance of 50:50 = 50% probability, which translates to 5 times out of ten, and this has been well established. So although one side of a coin could conceivably continue to come up the same indefinitely, each toss reduces the likelihood that it will: Introduction to Probability and Statistics

 

[Goggs Mackay]

Thanks for proving my point, again...
There's some substance to what you are saying, but as visually shown here - in the way you can't seem to segment things into paragraphs, with breaks, it's somewhat the same as the way you talk when co-hosting.
As I said from the start, I was making constructive criticism.
I never said that I didn't care for your opinion.

I often do make much shorter bullet-point style paragraphs but I couldn't really be arsed at the time, I was in a hurry but I did want to provide the answer because it was brought up by a forum member.

I could point you to some horrendous wall-of-text posts, many being consecutive ones from the same poster. Makes my 3 paragraphs on chance look positively stunted.

I agree you haven't done anything other than criticise constructively but to be honest, reading between the lines I think you simply dislike me and probably always have, which is fine.

 

[Goggs Mackay]

Just thought I'd point out an interesting comparison I just did (roughly), between the length of my paragraphs sans breaks in the offending post about chance and odds, and several articles written for the Mysterious Universe website.

My longest paragraph in that post is of the order of around 160 words. Compare this with the many articles over on MU (a favourite site/show of mine), which are often from 180 - 230 words long! Seems like I'm not the most wordy or lacking in decent paragraph breaks in my posts.

So I would urge anyone with a disdain for overly-long paragraphs to write immediately to their local MP or equivalent elected politician. Seems like there is an epidemic of badly formatted content that is just not acceptable to the contemporary reader. Heaven forbid such a reader should ever look at an archived copy of a famous broadsheet newspaper, such as 'The Times' of London. Back in the day, the 1800's and early 20th century, newspaper pages were often absolutely covered in text with almost no paragraph breaks! The scandal! It must have driven discerning readers over the edge and into madness....

 

[marduk]

All factors considered truly random ( no cheating or fixing ), the tendency to consider over-representation in a coin-toss where 10 out of 10 are the same result is perfectly reasonable, and the statistical chance is also 50:50. So both are correct, because mathematically the statistical chance of 50:50 = 50% probability, which translates to 5 times out of ten, and this has been well established. So although one side of a coin could conceivably continue to come up the same indefinitely, each toss reduces the likelihood that it will: Introduction to Probability and Statistics

Being pedantic about it, while it decreases the liklihood within that set of the odds of it continuing to come up the same side, the important bit that people miss is that the coin is outcome independant: the prior flip is actually irrelevant.

So while the odds of it coming up 11 times heads on 11 tosses is smaller than 10 times out of 10, the 11th flip is still 50/50 odds if looked at independantly. The coin doesn't care or know what the last flip was, or can 'choose' the next flip to align with statistical chance.

 

[Goggs Mackay]

Exactly, Marduk. If you know any other good non-intuitive examples of the understanding of risk (or lack thereof), please post one!
There are factors to do with risk that people are generally pretty good at, even when totally ignorant of the rules behind it, and conversely, there are areas of understanding risk that most of us do very badly at, probably because some gel with our experiences and intuition whilst others run counter to our common-sense.

 

[technomage]

I need to take a plane trip but haven't flown in 18 years or so. Statistically, the safest way to travel, but I feel much more comfortable driving and I did everything I could to scuttle my trip to no avail. Woe is me.

 

[Randall]

Being pedantic about it, while it decreases the liklihood within that set of the odds of it continuing to come up the same side, the important bit that people miss is that the coin is outcome independant: the prior flip is actually irrelevant.

Actually that's not the case and the studies in the paper I linked to clearly demonstrate that prior flips are far from irrelevant. You can even do it yourself if you want by graphing out a series of "prior flips" or just doing the statistical math.

So while the odds of it coming up 11 times heads on 11 tosses is smaller than 10 times out of 10, the 11th flip is still 50/50 odds if looked at independantly.

Sure, but the argument that's being made isn't that each flip is being looked at independently. It's that even if you look at a series of prior flips, the odds are still 50:50 ( they're not ).

The coin doesn't care or know what the last flip was, or can 'choose' the next flip to align with statistical chance.

Agreed. That's why it's possible that a coin might continue to come up only one way or the other on and on into eternity. The thing is. That's not what actually happens. For whatever reason we don't fully understand, over time, things like coin tosses tend work out according to statistical probability.

 

[Randall]

I need to take a plane trip but haven't flown in 18 years or so. Statistically, the safest way to travel, but I feel much more comfortable driving and I did everything I could to scuttle my trip to no avail. Woe is me.

You know how statistics are. Depending on the premise, they can be probably be spun this way and that way to either benefit the airlines or the benefit of the car companies. I doubt that the statistics used for car crash fatalities took into consideration individual factors contributing to each accident that could be removed from the majority of incidents. They we're probably all lumped together as one big statistic, including poorly maintained vehicles, those driven by impaired or incompetent drivers, those who were driving in hazardous conditions, and those who were driving dangerously on purpose.

Remove all those variables from how you drive, and compare them to how many people are likely to die if your airplane catches fire at 30,000 feet or is hijacked by madmen, or shot at with missiles, or the pilot is having a bad day and decides he's going to go down in a blaze of glory, and well, you're probably right to be nervous regardless of the statistics. Hopefully that makes you feel better ... ... lol.

 

[technomage]

You know how statistics are. Depending on the premise, they can be probably be spun this way and that way to either benefit the airlines or the benefit of the car companies. I doubt that the statistics used for car crash fatalities took into consideration individual factors contributing to each accident that could be removed from the majority of incidents. They we're probably all lumped together as one big statistic, including poorly maintained vehicles, those driven by impaired or incompetent drivers, those who were driving in hazardous conditions, and those who were driving dangerously on purpose.

Remove all those variables from how you drive, and compare them to how many people are likely to die if your airplane catches fire at 30,000 feet or is hijacked by madmen, or shot at with missiles, or the pilot is having a bad day and decides he's going to go down in a blaze of glory, and well, you're probably right to be nervous regardless of the statistics. Hopefully that makes you feel better ... ... lol.

Thanks a lot.