Probability - How does it work?!

The problem (as usually stated) is what are the chances of flipping a head 100 times in a row. Rather than in an arrangement of 100 coins what percentage of possible arrangements feature XXXXX (XXXX being whatever you are measuring).

Hey Help! I think I've been following most of this. Though straight up I should say I've no maths training. But whereas I can see Teome's reasoning I find it hard to see what you are getting at. Maybe you can clarify.

As Teome suggested, if you think of it as sequences, in a set of 100 restricted coin tosses the chances of ending up with 1 tail at some random point along the line and 99 heads is 100 times more likely (given that it has 100 different sequential possibilities than the single sequence possibility of all 100 heads). If this is correct (and unless I've misread, I think we're all agreed it is) then I dont see the relevance of your continuing argument about all sequences being *individually *equal in possibility.

Contrary to what you are claiming, I would say that Teome has phrased the argument in the manner in which we face it in everyday life: When we say that 100 heads or 100 tails is near impossible, we don't mean it is less likely as an individual sequence than 99 heads with specifically the second toss being a tail, or 99 heads with the 55th toss being a tail, etc. What we normally mean is that the chance of picking out that one random sequence is astronomically smaller than simply betting on ANY of the massive massive number of other undisclosed random sequences.

No? (Apologies if, despite my best efforts, I just sounded like a tellytubby)