I've just reread the whole screed and although it doesn't specify when you get to the 50 pack part that the aces are returned and the deck shuffled it does appear that this is what he's doing. In that case his argument is flawed. Although the probability becomes incredibly small after a few aces are drawn it never formally becomes zero.
So his maths isn't the problem, it's his application of it that is.
If you read the next two webpages you'll see that he then applies this reasoning to the anthropic principle.
The problem is that the anthropic principle is a posteriori reasoning.
Jabba compares the probability that he was born to drawing an ace from the pack. He reasons that he's the ace of spades, his mother was the ace of diamonds and his father was the ace of clubs. the problem is that in reality he's the three of clubs, his mother was the six of diamonds and his father was the seven of hearts.
Jabba, I don't expect you to understand this, but give it a try. You were born because a certain sperm from your father joined forces with a particular egg from your mother. Now suppose that it had been a different sperm and a different egg a month earlier. Instead of getting Jabba your parents would have had a girl called Muriel who went on to be an English teacher. Let's suppose it's the same egg but a different sperm. Then your parents got a boy called James who became an engineer.
You're just an ordinary card drawn from an ordinary deck.
Your mistake is in thinking that, because the probability that you would be born given that all of the people you are descended from had a low probability of being born, you are somehow special. You aren't. The probability that Muriel or James would be born was exactly the same as the probability that you would be born. You're the three of clubs, Muriel would have been the nine of spades and James would have been the Jack of hearts. You're not special, you just happened to be the next card in the randomly shuffled deck.
In the example of the cards that you give we know a priori that there's a deck made entirely of aces. but suppose that you don't know that. Suppose that you have no idea how many packs there are or what cards are in those packs to start with. All you know is that you get a pack of cards and draw cards from it. What's the probability that the cards you draw are from a special pack? You have no way of knowing. You don't know what cards are supposed to be in a normal deck, you don't know how many decks there are and you don't know whether there are any special decks.
The probability that any given pack will be in a specific order is 8x10-67. And yet every single time you shuffle a deck it appears in an order with a probability of just 8x10-67. Does that mean that every single shuffle of a pack of cards is guided by a higher intelligence? Of course not.
When you shuffle a deck of cards it has to have one, and only one, configuration. Which configuration that happens to be is pure random chance (unless you're a very good magician!), but the probability of that specific configuration occurring was 8x10-67.
So the approach that Jabba takes in arguing that the probability of his being born is vanishingly small without a guiding intelligence is a red herring. The probability that Muriel would have been born was identically small, as was the probability that James would have been born.
Someone was going to be born, it just happened, by pure random chance, that it was Jabba. That's the way the standard deck of cards was shuffled. No supreme guiding intelligence required.
