The probability of you getting 100 6's in a row on a fair die is dozens of orders of magnitude lower than your guy testing the die either getting it wrong, or l

The probability of you getting 100 6's in a row on a fair die is dozens of orders of magnitude lower than your guy testing the die either getting it wrong, or lying to you for any number of reasons. As for your second example, the problem is your own naive assumption of independence of all events. It is an extremely popular naive assumption, one I have ranted about how the school system accidentally teaches this more than once, but nevertheless is not a problem with the concept. I think you have correctly identified that your understanding of probability is wafer-thin. That's actually progress, a good thing, and not an insult. But you've misattributed the problems to probability rather than your understanding.