Flaw #3 seems flawed to me. There are 52! possible ways to shuffle a deck of cards but a game is only played using a small subset. Suppose there are 4 players, then you need 2 times 4 plus 5 is 13 cards. The remaining deck of 39 cards can be shuffled in 39! ways without affecting the game. These possibilities are still included in those 52! of total possibilities. In case of 4 players there are only 52!/39! possible games that can be played. This is still a larger number then the 4 billion mentioned in the article but it doesn't dwarf the 4 billion as the 8*10^67 does.