Interestingly, I remember something that said that some statisticians tend to take "1 in 100" as "beyond chance". Of course, it's very context dependent what your rule of thumb will be. So if you go and drive to work, you assume the chance of you crashing and dying is so low (1 in 50,000 or less?) as to be "beyond chance" and you get in the car and go. On the other hand, if you make a nuclear power station that has a 1 in 50,000 chance of blowing up and killing a load of people, you don't take that. Now, that's just focusing on risk avoidance, but you can see the context dependence. sshole 17:47, 16 May 2010 (UTC)
About the Falsification section
The Andromeda example is quite wrong. The argument would be true if Andromeda emits only one photon at a time in a random direction with a huge interval between 2 consecutive photons. On a clear night with Andromeda in your field of view, the probability that a photon from it hits your eye is about 100% due to the huge amount of photons that it emits per second in every direction.
The 10-sided dice argument is also wrong. The probability of rolling some sequence is 100%. But the probability of rolling a particular sequence that you defined in advance is 10^-51. Did it happen at least once to anybody? Of course not.