My advice would be to book at an out of town hotel, which allows cancellation up to 24 hours before the stay, without charge (there are a number of hotel chains that allow this as part of the standard terms & conditions).
I’m willing to bet that some of the hotels closer to the Olympic venues will not be able to sell all their rooms at the extortionate prices being asked – and you will be able to pick up a last minute bargain. If not, you will have the fall back of the already booked out of town hotel.