"We only ran the 2012 US Presidential Election one time, but that doesn't mean that on November 7th you should've refused a $10betthatpaidout$1000 if Obama won."

First of all, as non American I do not know what is specific about November 7th. Second, I think that some people may do not even know, that Obama has actually won.

"That's because we're considering results like HHHTHH or TTTTTT to be equally or more extreme, and there are 14 total possible cases like that."

It is not evident for me, because I am not familiar with statistics. I think where is a need to provide calculation, that there is two examples in form TTTTTT and HHHHHH and 6*2 like HTHHHH or HTTTTT.