Nice idea, bitcoin.me. How would you adjust the odds when/if they changed?
you don't, ... the wagers themselves do. parimutuel betting: http://en.wikipedia.org/wiki/Parimutuel_betting
bitlotto and satoshi dice are two forms of blockchain-based online betting. parimutuel could be another.
because the payments go through the peer-to-peer network and not through some website, it could be run from a country where it isn't illegal to offer. the website simply shows the bets and the current odds.
one of the difficulties with betting for parimutuel is that everyone waits until the last minute to wager as the range for the odds becomes narrower. using the blockchain would be a little frustrating as you don't know if the current block will be mined before the bet closing (e.g., before the start of the race).
this betting system would be suitable for just about any contest.