This isn't what the results say. The win rate for the player who goes first ("Player 0") rose from 41% to 61% when the player who goes second ("Player 1") was not given The Coin.
This is summarized in the text:
> The Coin basically makes what used to be a first player advantage into a first player disadvantage. Not bad for a single card!
User dtech already found the source for me (: -> https://news.ycombinator.com/item?id=8020232
The Coin does indeed give you advantages with no downside. However, the reason why you get the coin has to do with the mechanics of Hearthstone. In the case where The Coin didn't exist, you would be at a severe disadvantage if you didn't go first.
In Hearthstone, since you can generally control where your minions attack, going first gives you tempo. If your opponent didn't have the coin, as the player going first you could permanently maintain your tempo and win with regularity (depending on what cards you draw). In card games it is important that tempo be something that can change in the course of the game in order to make things more fair.
The first player has the advantage of going first. That is a given advantage, with no choice involved. It is harder to "waste" that advantage. The Coin, on the other hand, is much more linked to choice (when to use) and therefore, easily wasted. It is also an additional "thing" for the second player to think about when playing, while the first player doesn't have this burden.
If you want some real-world stats about going first vs. second, try the stats from Arena Mastery[1], which more or less match what Bilzzard has said anecdotally: with the second player getting the coin, going first is still a slight advantage.
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
Then I read an article about The Coin on OP's blog: http://buddypanda.com/?p=65 and I don't think that the simulator is that useful. Maybe I'm too dumb to understand this, but my intuitive idea is that a card like The Coin gives you various advantages and no disadvantages, since it is an extra card that comes for free and gives you more flexibility. How come then, that the simulator says that the player actually wins more games without The Coin?
Hearthstone isn't mainly about random encounters between AI opponents, but to gain advantage in material over your opponent over the course of the game. Sometimes, 1hp, 1 card, 1 round is sufficient to decide over victory or defeat. If the simulator neglects hero abilities (as in The Coin article), my guess would be that it's not too accurate.
However, I thought that a simulator for Hearthstone would be a great idea. I think you're onto something here, but I'd like to see a few more use cases that match my intuition I gained from playing hundreds of games of Hearthstone.