Who wins the race for multiple valid blocks mined at the same time?
When there's a fork, part of the network will mine to find the next block in one branch and part in the other branch. Whichever part finds the next block first will determine the winning branch.

A miner who finds a block will want to spread it widely and quickly. This makes sure there are many other miners who saw his block first, and thus a high probability that the next block will be found by one of those.