[WildTurkey]

Inference, not absolute proof. For example the coin toss examples above. Fifty heads in a row. What does it mean for the next toss?

The probability for getting 50 heads in a row is the same as the probability of getting any predefined sequence. For example the following sequences have the same probability:

HHHHH HHHHH HHHHH HHHHH HHHHH HHHHH HHHHH HHHHH HHHHH HHHHH

HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH

[bvw]

You must make an overly strong assumption about the coin and toss to say that. Here we don't see the toss, nor are we able to subject to coin to any scrunity -- just the result of the toss. Fifty heads in a row means the coin or toss is rigged -- almost a complete certainty.