IMO the Coin is a tricky thing. While you can argue that it balances the two player, the second player has the additional choice of when to use the Coin.
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.
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.