Not to mention that nobody is going to post a thread "I went first in turn 2, 3, 5 and 7, while my opponent went first in the other 6 turns", even though that's exactly as unlikely.
Human intuition positively sucks at estimating probabilities and statistics. Just ask any RPG-gamer: "a fifty-fifty chance never happens, a one-in-a-million is a sure thing!"... That's not just a joke, it really feels that way. Partly because of confirmation bias and partly because human brains are no good at all with big numbers:
- Confirmation bias -- you don't remember all those one-in-a-millions which failed (because you already knew they'd fail, but the one which you actually made... you're still talking about it years later.
- Big numbers -- without a calculator and in at most ten seconds, answer the following question. How long is a million seconds: two days, two weeks, two months or two years?
There's a half documentary, half infotainment (but they did get the documentary part completely right!) by Derren Brown, called
The System. It nicely demonstrates "no matter how small the chance, if you try often enough, sooner or later it will happen". If you'd like, you can watch it online at
http://www.youtube.com/watch?v=9R5OWh7luL4 (for the people who are strictly anti-gambling: (1) it's just an example, (2) believe me, after having watched it entirely, you'll agree that this in no way promotes gambling... if anything, it is discouraged).