Critical Thinking Part 5: The Gambler's Fallacy Video

Part 5 of the TechNyou critical thinking resource.

The resource covers basic logic and faulty arguments, developing student's critical thinking skills.

Suitable for year 8-10, focused on science issues, the module can be adapted to suit classroom plans.

The resource is found here:
https://education.technyou.edu.au/critical-thinking

Transcript can be found here:
http://technyou.edu.au/fun-stuff/videos/video-transcripts/

Continued in Part 6:
Critical Thinking Part 6: A precautionary tale
http://youtu.be/vjaqM4yd_RA

Animated and directed by James Hutson, Bridge8.
Written by Mike Mcrae and James Hutson

I used to ask 1st ...
I used to ask 1st year university students to go home and toss a coin 200 times, record the results and bring them to the next lecture. Just from looking at them I knew instantly which students did it honestly and which ones falsified? their results. Most people expect roughly 100H and 100T and this is correct. What they don't expect is the greater than 96% probability that there will be at least one run of 6 in a row within their 200. I borrowed the idea from Dr Theodore Hill.

the coin flip ...
the coin flip probability depends on how high up the flip and the fall (and the bounce of the coin on the surface). much the same? way buttered toast will fall butter side down, only because of the number of flips made from a relatively standard height of your kitchen table.

That covers the ...
That covers the second half of the video, yeah. They probably should have specified that the second half of the video is dealing with the fallacy 'post hoc ergo propter? hoc', not the gambler's fallacy. Perhaps the title should have been 'Causal Fallacies'.

For a conventional ...
For a conventional flat-disc type coin, any weight "on one side" will also be on the other, unlike with a six-sided die (for example). So actually making? a trick coin is much harder than that. Most coins in most countries are fair.

If a heads side of ...
If a heads side of a coin has more weight, it will be more likely to land heads down. And vice? versa.

1:12 Woot! I ...
1:12 Woot! I haven't heard the "Pac Man dying"? sound in over a decade. Nice to hear it again!

There's a premise ...
There's a premise flaw in the argument over what coin toss result to expect next.? Seeing 7 out of 9 "tails" results brings one to suspect that the coin is not fair after all and that the odds are greatly in favour of another tails. Pattern recognition is a tool by which we can determine probabilities in real world situations, and in fact this type of inductive reasoning is the basis for a lot of science.

Resently I read ...
Resently I read Dostoyevsky's "Gambler", and it was funny how well the gambler's fallacy was portrayed in? it, BEing a gambler himself, Dostoyevsky probably did believe himself that only a stupid gambler bets on a zero, after making a killing on it, when a smart gambler knows the zero isn't due for a while. However casino's make money because people believe they can outsmart the odds. Gambler's fallacy is a small part of it.

You make it sound ...
You make it sound like I'm trying not to be proven wrong or stupid. I thought we were having a normal conversation here, if I'm wrong so what? I'm not trying to be right or prove you wrong at all. Just trying to get something clear. Anyway, I see what you mean and agree that it has no effect on future result. The last coin flip has nothing to do with the next, but what I'm saying is the net? coin flips, have a probability of 50/50.

Oops, that should ...
Oops, that should be 1 in 3.2e29. Made a typo when doing the binomial calculation. See, this is how you do it. You go, "oh, I made? an error, oops!" And then you say "I made an error, here's what's wrong with what I said."

I'm well aware of ...
I'm well aware of how unlikely it is to flip 98 tails in a row on a fair coin (1? in 2.5e26), and if you did, it would be reasonable to question the coin's fairness. But if you have good reason to think the coin is fair, and you do flip tails 98 times in a row, that has no bearing on the probability of future events. Do you not understand this or are you just unwilling to admit fault? Stop responding with non-sequiturs.

You'd be pretty ...
You'd be pretty vexed if you flipped a coin 100 times and got 98 heads. You would expect roughly 50 50. This is the reason Carl Sagan says its unlikely that we are alone in? the universe.

Yes, one coin flip ...
Yes, one coin flip is a Bernoulli trial, and the number of heads in multiple coin flips follows the binomial distribution. However, that doesn't mean that previous flips affect future ones (in fact, binomial requires independence). The notion that flipping 98 tails in a row means that heads are likely to occur is wrong, and doesn't follow from what you just said. There is no "law of probability" to satisfy, and? no requirements for how random events turn out.

But this is an ...
But this is an event in an event, you know what I mean? You flipping a coin 100 times is one event that has its own probabilities. And then each coin flip has? its own probability which is exactly 50 50. Does that make sense?

You've gotten this ...
You've gotten this a bit wrong. When you flip a coin 100 times, assuming fairness, the expected number of heads is 50. That doesn't mean that you expect to get 50 heads every time, it means that if you do it a bunch of times and average the number of heads, you should? get something close to 50. The odds of flipping heads 50/100 times on a fair coin are about 8%. So what you really should expect is to get an equal split 8% of the time when flipping a coin 100 times.

That's simply not ...
That's simply not true. The chance of flipping heads on a fair coin is 0.5. The chance of flipping heads on a fair coin given that you just flipped 98 tails in a row is also 0.5. These events are independent, and the past outcomes? do not affect the future ones. The chance of flipping a head after 98 tails is just as good as flipping a tail after 98 tails. The distribution of n more flips is identical, whether you just flipped 98 tails, 98 heads, or 49 of each.

It takes research/ ...
It takes research/data* to prove an argument, not necessarily? science.

lol?
lol?

Oh no,? Dave's ...
Oh no,? Dave's syndrome.

I just watched that ...
I just watched that episode. The moving wall. Spooky.? :P

@MrBoo88 "I can't ...
@MrBoo88 "I can't decide, maybe I should flip a coin, hope it explodes and kills me"? - Black Books. (can't say it couldn't happen either).

Correlation does ...
Correlation does not? imply causation.

this actually? says ...
this actually? says that science gives us results that are most likely correct!

Coins can land? on ...
Coins can land? on their side.

Probability doesn't ...
Probability doesn't work that way. With 100 perfect coin flips,? the odds of it being EXACTLY a 50/50 split is about 8%, assuming my math is right. I think the formula is (n choose n/2)/(2^n), n being 100. 40 heads and 60 tails is about 1%, and the probability of it being BETWEEN 60/40 and 40/60 is about 96.5%. The trick is that as n grows arbitrarily large, the standard deviation, as a FRACTION of n, becomes arbitrarily small.

your studio stole ...
your studio stole an audio sample in the pacman game? for this video... whoops

0:40 "just aren't ...
0:40 "just aren't there"... all the patterns we see are constructed, and are real, in our minds. What you mean is that only some of them tell us something useful about the world. 0:45 "50%". You are assuming an ideal coin, and ideal coin flipper, which? you did not state. You need to factor in the chances that the coin and/or flipper may be biased, and by how much, and for what reason.

"The Coin" argument ...
"The Coin" argument excists only, and only, as logical? and in theory, but if you take one coin and throw it 100 times you should get equal 50/50 heads and tails, but you won't. We (sometimes) see patterns that are not proven to be there, but no matter that science proves and tests patterns it often relies and has its ground in theory, thus unproven and, paradoxically, pattern like.

I considered ...
I considered magneto being in the? area. I also considered shooting him if so, so as to get my reality back. But it hit me, the guy can really stop a bullet cant he? So I set out to master the kamehameha wave, which he has no influence over, considering this is pure ki. When I first started it was quite messy really. Goku makes it look so easy. You have to be as still as a rock when executing it, which was a task in and of itself, seeing as the thing has much leverage.

Or you're related ...
Or you're related to Erik Lehnsherr? and need to band with others who can inexplicably alter the laws of probability as well.

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