Do web farms help to reduce latency caused by physical distance?

There are many causes of high latency but I’m only interested with the one caused by physical distance between client and server.

Web/server farms utilize multiple servers coupled with load balancers are used to distribute the processing load. From what I read, these servers in a web farm are usually situated close together (eg. in the same datacentre). This does not really help with latency if a client is too far away.

Is there such thing as a distributed web farm? where the servers making up the farm are distributed across geographical locations in an attempt to reduce latency to clients worldwide?

I’m trying to set up game servers around a geographical region and hope to minimize this latency. There’s no player-versus-player feature, therefore there’ll be no issue from latency connecting players. The player will just play “against” the game server like Farmville. The player’s progress will eventually be synced with all game servers. The player can login from anywhere in the world and he/she will continue from where he/she last left off. Is there a way to just route a player to the nearest game server automatically instead of having the player choose which game server they wanted to connect to?