OK, smarty-pants, what's the best move?

[Pascal]

Spoiler: Show

The 4 possibilities are:

First coin: H, Second coin: H
First coin: H, Second coin: T
First coin: T, Second coin: H
First coin: T, Second coin: T

But you know that the first coin is heads, so you can remove both the predictions which involve the first coin being heads. Which therefore leaves:

First coin: H, Second coin: H
First coin: H, Second coin: T

Therefore 1 in 2 chance?