To think of this intuitively, if you want to know the true probability of flipping a coin (almost 50/50) you have to get a really big sample to determine that it actually is 50/50. - Even with a sample of 1000 about 1/3 of your samples will be out by 3% (ie 515 to 485 or more)
By contrast, You need to flip very few coins to determine that coins usually land on one of their faces, and very rarely stand up on their edge after you flip them...
I saw a D-CA avatar and a post about coin flipping... I was about to start throwing things.
