According to the search results, royal guards are not allowed to laugh or show any emotion while on duty. However, it seems that they would not be fired for laughing, but rather they would get a stern talking to by their commanding officer. Some sources suggest that guards who laugh or smile while on duty might get a "telling off" or a fine, but they would not be fired. It is also worth noting that tourists are not allowed to touch a Queens Guard, and could cause serious problems if they do. While there are videos and stories of people making royal guards laugh, it is unclear what the consequences are for the guards involved.