In that article, he shows that giving the coin to p1 (the 2nd player, it's 0-based) gives a /disadvantage/ to p0 (the 1st player), so it is actually beneficial for the player who gets the coin.
It was much greater before the extra card and coin was added.
In the game it depends on the deck - for some decks, it's more useful than others, either due to particular mana curves, or to triggered effects (the coin counts as a spell, so can trigger cards like Gadgetzan Auctioneer or Wild Pyromancer)
> Ben: It's about three percent better to go first over second.
The 51% was mentioned is in a previous Blizzcon QA