I'm putting off work, and I just realized I think during my last spurt of working I actually finished the main thing I was working on tonight...so I guess I am just putting off going home?? What is wrong with me? I guess I still have to log my time and answer a few emails or something, I must be putting that off.
Anyway, has anyone else ever been confused by the gambler's fallacy? This comic made me think of it. http://www.qwantz.com/archive/000298.html
I have never been able to get this one. OK, I get it that it makes sense that every time I flip a coin, the odds of it coming up heads are 50/50. But I also get that it is likely for 100 coin flips to come up roughly half heads and half tails, and so it is unlikely for 100 coin flips to come up all heads or all tails. So if you've had 80 flips that are heads so far, isn't it more likely that the next one will be tails?
It's not- people are always stressing that it's not, but I don't get it! I fail basic probability. I even read this website that seems to be made just for me, and I STILL don't get it at all! http://vegasclick.com/gambling/fallacy.html
Although T-Rex's description in the first two panels actually helped, with the difference between what happens in the long term vs. when you are predicting the correction to take place (in the short term). Anyway, here is a website that does a pretty good job of explaining it, if you are interested. I think it is starting to make sense now. Maybe.
http://wizardofodds.com/askthewizard/fallacy.html
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Probability really upsets me. I never, even understand it and eventually just say "Ok, I get it" so that people will stop trying to explain it to me. I'm going to check out these links to see if they help me understand.
I don't know if this will help, but it might...
A couple has 9 children and are expecting a 10th. What is the likelihood that the next child will be a boy?
... 50%? Assuming that, scientifically, boys are equally likely. Is the idea that the past doesn't matter, the probability is just always 50% every time? But I thought that that IS what I've always thought and that that is actually wrong...
Ok, I just read up on this and this corresponds with what I already thought, but seems to go against the rules of probability that I've always heard // hated? So I continue to be confused.
Also, wasn't this discussed at length in Rosencrantz and Guildenstern Are Dead?
Yes! It was in Rosencrantz and Guildenstern are dead, and the fact that they keep getting heads over and over is supposed to make it creepy I think. But if it's a 50/50 chance each time, maybe it should not be creepy? So confused. Movie maven, I like your example. I think I'm like Laurie in that I get why it's a 50/50 chance all the time, but I don't know how to reconcile that in my head with the overall trends caused by probability. Arg.
You're confusing the probability of an individual event with the probability of the entire series of events.
Think of the odds of flipping two heads in 2 a row - 1/4 (or 1/2 x 1/2).
The 3rd flip still has a 1/2 chance of being heads even though the overall odds of flipping three heads is 1/8 (1/2 x 1/2 x 1/2).
And yes, I probably have to thank Mr. Ahl for that. Sigh...
You have a blog? Hi!
R&G opens up with a bizarre stretch of heads, and it should be creepy. Sure, each individual coin has a 50% chance of landing heads, so the long streak of heads is possible, just really unlikely. No single coin toss should be surprising; getting heads is just as likely as getting tails. But getting 80 heads in a row is very unlikely, so it would be creepy (or be very good evidence that you've got a weighted coin).
Here's how I think about independence. What would it take for the outcomes of past coin flips to influence outcomes of future coin flips (thus violating independence)? Is there some Probability God out there who messes with the universe to make sure the most likely scenarios take place all the time? "80 heads to 20 tails so far; hmm, better intervene here and start making that coin go tails more often." But there is no such God. Plus, why would he ever let things get past 50/50 to begin with? So there are no such cosmic forces at work that affect future outcomes to balance out past unlikely sequences.
Now imagine you're sitting on that run of 80 heads, but still believe the coin is fair. Of the next 20, the most reasonable thing for you think is that, most likely, half will come up heads, and half tails. That's the same thing you should have thought when you started: The last 20 of your flips are most likely going to come out 50/50 heads/tails. If you really do believe the coin is fair the whole time, the first 80 outcomes shouldn't affect your beliefs about the last 20.
Jamin, that explanation was perfect! Thank you!
Jamin, the last paragraph got through to me- thanks!
MentalJewelry, expressing it in a mathematical formula actually helped a lot, to see the 1/2 there in the equation. Thanks!
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