"Suppose that you receive five consecutive royal flushes in a game of poker. What explains this? You could have received them by chance, but that seems unlikely. A better explanation is that someone has arranged the decks in your favor."
Oh dear.
Any randomly dealt deck of cards will produce a sequence whose odds against are 52 factorial (52!). 52! written in full is: 80658175170943878571660636856403766975289505440883277824000000000000.
Amazing right? Why then doesn't the author claim divine intervention for any randomly dealt pack of cards given the extraordinary odds against that particular sequence appearing? Oh yeah, that's right – it's because he's committing a basic error in reasoning called the reference point fallacy. Just because a sequence of numbers might look significant to him does not mean that it actually is significant.
0/10. See me.
A royal flush is significant under the rules of the game of poker and even if it wasn't, his argument was that it is incredibly unlikely that you would get a royal flush
five times in a row. Getting a royal flush once is nothing special (except under the rules of poker), in fact you're four times more likely to get a royal flush than a hand consisting of the two and five of hearts, seven of spades, king of diamonds and jack of clubs. But, if you have been dealt that nothing special hand once, and then you are dealt it again, you'd suspect skulduggery. If you are then dealt it three more times, you'd be certain that the dealer is doing it deliberately.
There are several problems with the argument that I can see. Firstly, it is an argument by analogy. It is thus, fallacious. If I get dealt five royal flushes in a row, I would assume that the dealer had something to do with it. By analogy, I apparently must assume the creator of the Universe is like a poker dealer i.e. an intelligent being.
But poker dealers are humans. This argument by analogy therefore leads me to assume that God is a human.
Another problem is that we only know one Universe. If the analogy is correct, we are still on the first deal. Not only that, but we've looked at the cards we were dealt and have made up a game (or assumed a game) in which the winning hand consists of those cards.
As an addendum, your number of the possible ways of shuffling a deck of cards massively overestimates the number of different poker hands. There are, in fact, only (52 x 51 x 50 x 49 x 48) / 5! different poker hands because you are only dealt five cards and it doesn't matter which order you get them in. There are 2,598,960 poker hands, of which four are royal flushes.