[Truper]

I think those decisions are made on the client machine when a battle is watched. As I understand it, the host passes the starting state of a battle and a random seed to the client (as well as the battle's result). If you want to watch it, the client has to duplicate the decision-making process so it can display the results. Otherwise the host would have to pass all the events of a battle to the client, down to the Last sword thrust, resulting in really huge turn files.