.. solving the same block as a pool? Do they carry on solving the puzzle or does everyone move on to the next block?
First one to solve it gets the prize, and the game starts again

I understand that part... The higher probability being for the pool, so does that mean the solo miner is still hashing? How does the solo miner know when a block has been solved before them?
Also does a miner that has 1Gh/s mine each hash at the same rate as someone that has 100?
~Foyz