If something claims to be random, it also means that it’s predictable. After all, it has to live up to the randomness. Is that right?

Well.. I can’t always decide for myself. Consider a perfectly fair coin. Let’s say you’ve done 50 tosses and only 13 were heads. The next 50 could go anyhow; they are, after all, independent experiments, right?

But on the other hand, if the Law of Large numbers must catch up, then there is a rather high chance that the next 50 should have more heads than tails in the next 50. Right?

(Note: This argument is incorrect. Find out why for yourselves)

As I see it, even though we know that mathematically, the next experiment is independent of the previous one, we, in practical life, so often bank on the Law of Large numbers to even things out (even though mathematically it’s not supposed to work that way):

Consider a game of Mafia. You have to make up your mind on whether a person A might be the healer or not, say. Now, of course you’ll go by what A says/does, etc. But suppose that A was the healer in the previous game, and allotment of roles happens via a perfectly random method each time. Now, though maths says that in this round, A has an equal chance of being healer as anybody else, our practical sense will surely assign a small weightage against A being healer now.

Some of you might still be thinking that you are the perfect mafia player who judges only by players’ actions. Well, suppose you’ve narrowed down the possible healers to A and B, and now there’s absolutely nothing left to differentiate between the two. Who would you pick?

My point is simple: Just because our brain *understand*s probability well(I got a 10 on the Probability Course), does not mean it *follows* probability well (I’d pick B any day). Our brain just knows one thing: If something is truely random all the time, that in itself is a pattern.

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*Related*

http://en.wikipedia.org/wiki/Gambler's_fallacy