In a case like Worms where there are concurrent actions and random reveal choices inside each turn... If some deterministic state and random number is created for each player at the start of the turn, then their inputs can be reproducibly mapped to the results of all the random choices. In that case you can just upload the inputs and let the server work out what happened based on the hash the player was given (i.e., let the server replay each player's inputs against that hash and figure out the result).

But the server is not another player. It's not a player at all. It's the arbiter of truth. So as you said:

>> The problem with this approach is that the latency to obtain the result becomes the roundtrip to the player with the slowest connection and back.

This is what I'm saying above. At some point games will just accept this and allow the player with too slow of a connection to be disadvantaged. To the extent that a server should tolerate slow connections, it is a handicap given by the game to players with slow connections.