[ColinDabritz]

It helped me to think of it this way: Alice is guessing that their coins are different (one possibility) and Bob is guessing that their coins are the same (the other possibility), so from either direction they are covered.

[yukinon]

Thanks. I think this was the reply that actually helped me understand this.

[imdsm]

Yeah it still took a minute. The way I realised it was Bob is covering them for the same flips, so if he flips H, he covers if Alice flips a H too. But if she flips a T, Bob is no longer covering her, but she knows when Bob isn't covering her, if she guesses for the opposite, she'll cover them. 100%.

The next level is: Eve joins the game, and the coin gets another side.