In the same vein as the most counterintuitive theorem awards, which theorems do people think seem obvious (or are generally declared as such) and then have quite tricky proofs? I'll get it going with the Jordan curve theorem (http://en.wikipedia.org/wiki/Jordan_curve_theorem ) although I personally am not convinced it is that 'obvious' a statement myself (hence the quotation marks around obvious). Specifically, I could imagine there being some quite pathological Jordan curves. Anyway, what does everyone else think (bearing in mind, given the right machinery, some statements do become quite obvious)?

On the same topic as above: in researching for my essay I discovered an interesting result concerning the game of Hex.

The Hex Theorem states that every complete game of Hex must result in a win. There is however a stronger result which depends on the Jordan Curve Theorem that states that there is a winner... i.e. one of the players wins, not both. This certainly seemed to me to be more obvious than the initial fact.

Owen.

is the a similar theorem for tic tac toe, that states if both players make perfect play then the game is a tie

Yes.

What about Tiddlywinks?

or even chess

As well as the the fishbase search problem...