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Comment by tjic | Hacker News Reader

if we’ve just observed the coin appear as heads 29 times in a row, what are the odds that the same coin will land on heads on the 30th toss?

Many people would argue that the chance of this happening is less than one in a billion, as we just calculated. However, that answer is blatantly wrong.

Bullshit.

If a coin lands heads 29 times in a row, Bayesian analysis tells us that the chance of the coin not being fair, the experimenter lying to us, aliens influencing the outcome, etc. are all a lot higher than we might have expected a priori.

If I saw a coin land head 29 times in a row and was offered a bet on the next flip, I'd put some real money on it turning up heads.

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You're nitpicking unnecessarily. When asked a 'do the trains collide?' math question, do you point out all the safety precautions in place that would prevent the collision?

You're missing my point.

The original post was arguing "people are stupid and credulous".

I am arguing that, no PEOPLE ARE NOT STUPID - they are finely evolved to operate in the real world. If you present people with a REAL WORLD PROBLEM and they come to EXACTLY THE RIGHT ANSWER (as opposed to the "desired" theoretical answer) then the problem is with your ability to quiz people, not with people failing to be smart.

You're missing my point

I think you are missing your own point. Faced with 99 head tosses, you think the 100th should be heads because it proves the system is gamed (eg. the coin is biased).

The article addresses people who believe that faced with 99 head tosses, they think the 100th should be tails (because it is "due").

In other words, the people in the article behave as if they believe that the system in independent (not gamed) but reach the wrong answer.

But your argument supports the opposite of the classic gambler's fallacy. The traditional mistake is to expect the 30th flip to be less likely to be heads, because 30 in a row is rare. So peoples' intuition is even less appropriate to the real world than probability theory is.

Desired theoretical answer: 1/2.

Your answer: bet on heads

"EXACTLY THE RIGHT ANSWER": Less than a one in a billion chance of heads.

_IF_ the draws are independent, it's not bullshit and you just lost a lot of money. In the example around which the article is written the draws are very much independent.

I saw somewhere a similar article with pictures of "randomness". The point was it's very counter-intuitive: random events tend to look very un-evenly distributed. Here lots of zeroes, here lots of ones. Given the big number of "draws" in the Lottery, it's not at all unusual to see a number appear or not appear for a while. So you don't even have reason to suspect foul play.

> _IF_ the draws are independent

That's a big IF.

Let's do an experiment with people: we ask them to stand in a road, then we tell them that in a moment a hologram of a fire truck will come at them. They are requested to stand in the road. 30 seconds later a massive firetruck appears to race at them, lights going, siren blaring. Sunlight reflects off of the chrome. The guy in the driver seat is wearing a helmet and a black jacket, and scowling. The license plate is "113 GHR".

The experimental subject steps out of the road.

"Dummy!" we yell... we TOLD YOU that it was a hologram.

The candidate isn't a dummy. He just trusted his experience and his own sense a lot more than he trusts one word from you.

And your point is? This is Occam's Razor. It's much more likely that it's a real truck. Also the stake vs the gain is too big.

I'm talking about a state organized lotterie. Given the huge risks involved in cheating, the fact that the profit margin is assured even without cheating and the fact that there is no one person or entity who really cares about bigger profits (state owned and managed), I'd say the same Occam's Razor would say the draws are very likely independent.

Such a great illustration for the article.

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