A while back, I was sitting at my desk and a fellow programmer wandered by and chuckled to himself. He turned to me and asked the following question "If I walk up to pay for something at the store and need 69 cents, what are the odds that I will reach in my pocket and pull out exactly 69 cents?".
I thought for a second and said "Probably like on in a gadgillion..."
Of course, him being an esteemed mathematician he smugly answered "WRONG, it is precisely 1 in 100"
After precisely 7 picoseconds I asked a couple of somewhat random questions:
#1 How many coins can you fit in your pocket?
#2 Is it possible to get 69 cents using just quarters?
#3 Do you always empty your pockets as soon as you have more than 100 cents?
He shut me down by saying "you're falling victim to the gambler's fallacy".
Let me do a quick explanation. The gambler's fallacy is basically explaining how people will irrationally think the probability of a future event is based on past events... even when they aren't. For example: If I flip a coin once and it lands on heads, I had a roughly 50-50 chance that it would land on heads. If I flip it again the probably is still the same that it will land on heads.
Interestingly enough, after a few hours, he came back and said "you know what, I think you're right, it probably is at least like one in a million". He went on to give some other questions that need to be answered in order to get an accurate probability.
#1 Do you collect antique coins?
#2 Do you have foreign currency in you pocket?
#3 Does your pocket have a hole in it?
#4 Do you HAVE pockets?
So, the next time someone is too stupid to understand simple things like the gambler's fallacy, make sure you aren't too smart to forget that the world is a really untidy and complicated place.