EddieM,
So huge mathematical odds against one particular scenario occurring are irrelevant if that scenario has occurred.
There is no need to explain the uniqueness of a particular deal from a random shuffle ie no one rigged the deck.
Not sure what you mean, but the card example illustrates that even in something as mundane as dealing out a randomly shuffled pack of cards, the outcome is almost certainly unique (at this moment in time) due to its incredible improbability, but you just did it.
I don't think the odds make it 'almost certainly unique'.
Like tossing a coin that has just come up heads ten times in a row and is just as likely to come up heads or tails next toss. Prob of 0.5 each toss if we discount edge.
Each deal is as likely as any other to appear. The fact that an individual deal has appeared does not affect the frequency of other outcomes.
So when we are presented with a deal, and say in wonder 'what are the chances of that?' , we have to remember that it is as likely to have occurred as any other deal.