Critical Thinking Part 5: The Gambler's Fallacy 

"So while our brains see patterns,...it takes science to prove that these patterns are real." Awesome line. Keep them videos coming!

If you flip a coin 99 times and it always comes up heads, what is the probability that it will come up heads on the next flip? The statistician will tell you 50%. At some point you have to start believing that the coin isn't perfectly balanced.

Gamblers Fallacy is weird. Each individual toss is 50/50, but if you bet on frequencies (3 heads frequencies are more common then 4 heads frequencies) then it isn't 50/50 anymore (I think). It's hard to really grasp why those two situations can't be correlated in a useful way when betting.

There *is* a pattern in there: ultimately, on a long enough timeline, the average number of heads/tails will be 50/50. How many times you need to flip to get within a specific approximation of 50% is where there is no pattern. Two tosses might be all you need. Maybe 10, maybe a million.

Great video! I work in PR for an online casino, and people are always asking me if this or that "betting system" will work. Betting systems actually exploit the gambler's fallacy because they tell people to bet on the expectation that a certain outcome is 'due' in roulette, craps or slots. If only people thought a bit they'd realize that if a betting system could beat the house, casinos would go out of business in a flash!

I generally consider myself as a rational thinker, but this thing almost *always* goes against my intuition despite the fact that I know it's wrong.

this reminds me of the monty hall problem. why it gets constantly misunderstood *is* because of the gamblers fallacy, what this guy talks about here.. only now, ive been able to put it into words.

OK: A = the probability that a coin flips head 3 times in a row B = the probability that a coin flips head 300 times in a row Is A = B or A > B?

I'm a professional translator and I'm currently working on translating the series into Russian for the people from the Zeitgeist movement. It'll be completed in a couple of days. If you wish, I can contact you when I'm done and send the text broken down into same pieces as they appear in the video. I read my YT PM regularly, so you may reply there directly.

it's actually pretty arguable that this is a fallacy to an extent. obviously the idea of being on a roll is a fallacy, however, i would argue that getting the same result multiple times in a row on a 50% chance is less likely than getting mixed results. for example, if you had just decided you will flip the coin 10 times, it is extremely likely that both results will show up at some point during the 10 flips. the odds of only one result showing up consecutively for all 10 flips is extremely low. the idea is not that each flip of the coin lowers the chance of it landing on a specific side. it is always a 50% chance. but getting the same result from a 50% chance several times in a row has a separate percentage chance that needs to be calculated. flipping heads twice in a row has a 25% chance of happening. this is not a 25% chance of getting heads on a second flip, but rather a 25% chance overall, for both of the flips. this is because you are combining two 50% chance actions.

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.

I know this has a lot to do with definitions and philosophy but he said in one sentence that the next flip of the coin is 50/50 *CHANCE* . And in very next sentence, he says that LUCK has nothing to do with it. Explain that please... and (2) also, how do these two different things jive? If you bet money beforehand that 10 flips of a coin would produce 5 heads, but after first 6 flips produced 6 tails in a row, wouldn't you say that the probability of the next flip would be heads? (given the average of ten flips) It seems like a paradox between betting on the group chance and individual chance. Someone smarter please explain.

It's not because "our brains find patterns" it just makes sense, the odds are very unlikely to get a big streak of one or the other, but no one talks about that.

Incredibly useful and generous resource.

It's so easy to misunderstand the gamblers fallacy. Getting heads on one toss is 50%. However in a series of 4 coin tosses there's a 6.25% chance of 4 heads in a row. Some who misunderstand the gambler's fallacy will say "no, since it's always 50% - you're just as likely to get 4 heads in a row than anything else". Which is incorrect. It's hard to intuitively grasp the difference between a series of 4 compared to the 4th toss. You can't say that the 4th toss will be more likely to end up a certain way because of probability. But you can say ahead of time that 4 heads in a row is unlikely. Each toss is 50% - but if you count a series of 4 tosses that's 50% ^ 4.

Getting permission to have them redubbed is tricker, but we'll keep your request in mind and will let you know. Thanks!

i found Vsouce Veritasium and this channel this night... my brain is about to explode!!!

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

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.

Casino's don't make money because of the gamblers fallacy. That is quite a poor example. The gamblers fallacy would set the casino to break even after a long period of business (assuming non-skill based games). Casino's make money because the odds of the games are in their favor (and other sketchy tactics).

This'll help me understand the Jurassic Park novels and love them even more.

Reason I say this was because I was messing around tossing a coin I chucked in the air on to my table it landed on the table, started to spin, then stopped in the up right position. It was awesome.

I agree, I was just pointing out that it generally makes more sense to speak of probabilities than certainties, since correlation can never truly prove causation. This is why scientific theories are called "theories". It makes sense to assume such fundamental things are real as, if nothing else, a methodological assumption. Thinking any other way would lead to solipsism.

This is confusing to me. It's saying that a coin is equally probable to land on heads 10 times in a row, as heads 5 times out of 10. I'm not a gambler, but seeing a coin land heads 9 times would have me immediately call tails on the next flip. Would that specific case make me land in the gambler's fallacy? So now I'm speculating: In a real gambling situation the games are more complex than simple coinflips, making the real patterns harder/impossible to determine, leading to this desire to find a pattern where there are none, which is what the gambler's fallacy is all about. Am I onto something?

For each individual coin flip the chance is 50 50. However the odds of getting heads heads heads heads heads heads heads heads is very low. So I guest its how you luck at it.

It's happening right now - eps 3 or season 2 up real soon :)

This is my favorite video of the series !!!

@Neoplantski 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.

Thunder _is_ caused by lightning..

Cause and effect is one of the most fundamental observations of the universe and is the basis of all the laws of physics, everything that exists in the universe and everything that has happened and will ever happen. If you're taking the position that nothing can be known for certain, then sure, cause and effect might not exist, the universe itself might not exist, we might all be dreaming right now etc. But if you're genuinely skeptical about cause and effect then you might as well know nothing.

To be slightly more accurate: you have a 50% chance of winning a coin toss, *assuming that the coin is evenly weighted*. If tails appears to be doing improbably well, it is possible that it is doing so because the coin was not evenly weighted, and your assumption was false.

flipping a coin never seemed like a good example to me...you could just get used to flipping it with such finesse and precission that it will always land heads/tails....so its not

This is just so brilliantly made!

@Alexthebling 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.

We've received offers to write transcripts for the videos in other languages. Would you like translate to Russian?

In the real world, yes. For the sake of argument and demonstration, as here, one has to assume or agree that the coin is fair.

Hi Semyon - yeah that would be great. PM it to us when you're done. Thanks!

Good series, worth showing your kids.

Im really thankful i never had a gambling problem because how else could i have ever afforded my drug problem!

@TinQuasimodo 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.

"our brains are too good at seeing patterns, it sees patterns that aren't there" That's not being good at seeing patterns, that's actually bad at seeing patterns. Our brains are bad at seeing patterns.

You defined the fallacy well . . . But I wish you would have disproved it rather than go off on a tangent about the history of probability. The part that got me was understanding that the probability of flipping H H H H is equal to H H H T So while, yes, it’s very unlikely to flip 10 heads in a row; it’s equally unlikely to flip 9 heads and 1 tails!

Actually there is more like a 49.9% chance of tails. 0.2% chance of it landing on the the edge, unless forced to a down position.

We took this is school. Good info.

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

Very true, but if I toss a coin 99 times the probability should be close to 50/50 or else there is some external influence. If I get 98 tails,out of 99, while not impossible, this is highly unlikely, and in such a case, its hard to say, but I would be right to assume that the law of probability will be satisfied at some point, and start picking out heads, because its more probable that heads will show up, then that the stupid simple coin will break the laws of probability and give me more tails.

@vgmjbpkcdmqd 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?

Okay but what about Dynamic Bayesian Networks?

Great video, homie.

I had a Reese's Peanut Butter cup once, and got a throat infection the next day. never ate them again, even though I liked it. Same fallacy I think.

@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).

What will Season 2 involve?

Is it a good kind of hurt? ;) You know we have season 2 coming up? :)

Awesome video!

Good work

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

This really true

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

Einstein: God does not play dice with the Universe.

Right. But a coin might land on its side = neither head nor tail... :)

Nice.

Correlation does not imply causation.

Coins can land on their side.

2:22 No Audis allowed

Though it's hard to admit, in the end we don't even know that cause and effect exist. There are quite a few things like this everyone assumes; otherwise we couldn't have science.

What a stark description of gamblers from the editor of National Review..................

I move a penny. The penny has been moved. Cause an effect. I can prove that i caused the penny to move.

Here from empyrean

Psychopaths will not understand that. They believe themselves the most.

@vgmjbpkcdmqd 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.

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

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

here from xqc stream LUL

I'd say there is a greater chance the coin would land tails. When I was a kid I developed the skill to dictate the results of my indoor coin flips to an accuracy greater than 95%. It all boiled down to precise muscle memory and subtle tricks. If you pay attention to the side the flipper starts on each time, a flipping habit could skew the 50/50 probability, for instance: When the flipper starts on heads, it lands heads. When the flipper starts on tails, it lands tails. He naturally rotates the coin when placing it on his thumb causing a 'heads-tail-heads-tail' pattern however, the individual probability for each flip is not 50/50. If I expand on my initial statement I'd *want* to say there is a greater chance the coin would land tails, but in all honesty I'd have to be there in person to make my prediction.

Talk louder, man. I can’t hear you

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.

I am a victim of gambler's fallacy, i can't warp up my mind to understand something like in this example , if i toss a coin 10 times the chance that i will get only head 10 times in a row is (0.5)^10 and if you say 9 of that is head it's (0.5)^9 that's 0.19%chance of happening, it's obviously 99.81% more likely to be a tail and you are telling me it's 50%. i hate my brain i still can't convince it.

@vgmjbpkcdmqd 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.

@MrNoosphere lol

Don't be so hard on yourself though. Part of that was likely instinct, which is an unguided process. Blame the fallacy on natural selection. :P

Oh no, moment's of this video are so very terrible and so very horrible.

Most of us dont. thats why we have religion.

This series would be useful if it wasn't so obviously geared towards attempting to convince people of politically correct narratives such as Global Warming, Evolution, Vaccinations and such. It's presented as a way to think logically and in an unbiased fashion but subtely, and deceptively, it places these subjects in the midst of logical discussion, presenting them as fact, without actually discussing the logic and science behind them. Disappointing