When I worked in tech support, there were many cases where people reported impossible symptoms. The good technicians were the ones that were able to systematically go back an question the assumptions that they made, which forced them to believe the impossible. Like, a room can’t just cause a computer to power off, or a monitor cable can’t cause a keyboard error.
Someone asked me a common probability question today that made me question my assumptions. If you have a fair coin that has a fifty-fifty chance of turning up heads or tails on each throw, and you just flipped the coin 500 times getting heads each time, is the coin more likely to turn up tails on the next throw to even out the experiment and bring the results back to 500H and 500T by the time 1000 trials were made.
This is a common misconception in probability and statistics. There is a force that tends to make the results even out, so when you go too far off to one side, the results will compensate and you will get a string of results from the other side. You commonly see it with people that play the slots. Machines that haven’t had a win in a while are due for a winning spin. In the model each event is independent of the others and therefore past and future events have no effect on the next event in the sequence.
My question is why doesn’t our experience and instinct tell us that flipping a coin behaves like a series of independent trials, and instead we expect it to compensate for the past, and why that instinct can make things worse.