People who are not trained in statistics and randomness (and even sometimes those who are) tend to draw horrible conclusions about whether an event is random or caused. Fundamentally my question is - why is this true?
Note that I am talking about random from a statistical perspective, with the example of a series of coin tosses will show up heads on average 50% of the time.
Edit: Clarifying the definition of "random" that is used - it is a macro-scopic, probablistic definition, as indicated in the above sentence. I ignore whether it is causal on a microscopic level - for example, calculating every force and influence on the coin to determine that it is going to be heads this time. As humans can't calculate these factors, to us the coin toss is a 50-50 proposition. You could extend the question to situations with other probabilities, such as 70-20-10 percent for 3 different outcomes - that just makes the analysis more complicated. Note that it may still be useful to question this definition...
This point was driven home by a professor of finance who's class I attended, who said he could identify a true sequence of random numbers compared to one that was made up. He handed out 3 pennies and then left the room - 3 students flipped the pennies 50 times each and recorded the results - meanwhile, 3 other students made up a series of 50 heads/tails sequences they believed would represent random tosses.
I guessed at his method and suggested one of the people making up a sequence put a long string of heads or tails together (say 6 or 7). They did not, and he ended up being able to correctly determine which 3 of the sequences were "real" from the pennies and which 3 were the "fabricated" sequences. The real sequences of coin tosses all had at least one string of between 4 and 6 in a row.
Humans seem to feel that a sequence of coin tosses is not random when the same result shows up more than about 2-3 times in a row. This is clearly not a mathematically sound basis for evaluating whether something is based on a random or probablistic frequency curve, but it seems to be inherent to most people on an instinctual level.
What is the cause of this misperception? Does it have a name?