Well, your coin flip analogy, when just skimmed over without much deeper thought, sounds very clever, and one might walk away from it thinking that it is true. Only this is a problem, in my opinion similar to how evolutionists think, that just sounds clever because no one is thinking long (or correctly) about the details.
I find this type of problem exists in many people who think they are intellectual, by virtue of the fact that they said something which sounds hard to disagree with, and others will say oh that sounds smart-I am a believer too.
Well, here is the problem with your coin analogy, in case anyone, including yourself, missed it:
Your coin tossing tournament doesn't guarantee at all that someone will call ten flips in a row correctly. In your tournament, during each round, who gets to make the call? You have two people, but only one can make the decision of what they are calling. So in order to proceed to the next round, there is no guarantee at all that you made a correct prediction, only that you may have been standing there, while someone else made the incorrect prediction. In that sense, every single person in the world, except the guy who made the incorrect prediction got it right. And thus your game won't work. So I gladly challenge you to find someone to get ten correct guesses in a row, with just a few people and a few coins. How much are we wagering.
In life, I have found, it is easy for many people to think a lot, and still totally miss the obvious.