Although the Worms games are turn-based, gameplay typically involves performing a lot of actions within one turn. Walking, jumping, using utilities (which don't end your turn), and finally firing a weapon. Many of these actions can trigger an event with a random outcome, which should ideally be unpredictable and un-manipulatable, such as which weapon will be found in a weapon crate, or how long the fuse of a mine with a random fuse will be.
In a peer-to-peer game, the server is just another player, and should not be considered intrinsically more trustworthy. Ignoring latency, it's possible to implement a scheme of securely generating random data, in which everyone produces a verifiable hash (commitment) of a random number, and after everyone announced their hash everyone announces their random number, which is then XORed together to produce the outcome (see e.g. Keybase's "Cryptographic coin flipping"). 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.
