Not so fast!
On Princess, the final say on evening attire always rests with the staff aboard each ship. The chart in the Cruise Answerbook in the Princess's cruise information package gives the typical number of evenings that require casual, semiformal, and formal attire on a particular cruise, but I have taken several cruises on which the actual numbers have deviated. Generally, cruises with very few days at sea might have more casual nights than specified in the table while cruises with a lot of days at sea might have fewer casual nights than specified in the table. Additionally, exchanges of semiformal and formal nights are quite common. Anybody who is going on a cruise that's longer than seven days should plan on three formal nights -- and four or more formal nights if the cruise is two weeks or longer.
I always bring an extra semiformal outfit with me. An extra shirt and an extra necktie do not require much space in a suitcase, and that way I'm prepared for unforeseen circumstances that could happen a couple different ways.
>> An invitation to dinner at the Captain's Table demands semiformal attire (except, of course, on formal nights when it demands formal attire) -- and it's extremely gauche to "send regrets" to an invitation from the captain while embarked aboard his vessel.
>> I have been on a few Princess cruises where there have been opportunities to attend special events that required semiformal or "business" attire. It would be a shame not to be able to attend such an event just for lack of suitable clothing.
Although one can buy an outfit at the ship's shop if one is in a bind, but it would be unfortunate to have to do so. The ship's laundry and dry cleaning service can come to the rescue if you planned for too few semiformal or formal nights, but not if you didn't bring any attire at all in the respective category.
The fact that there are no scheduled semiformal evenings does not mean that one can safely leave semiformal attire at home. I would bring a sport coat, a dress shirt, and a necktie "just in case" on a cruise with no scheduled semiformal evenings. I'm bringing dress slacks, dress socks, and dress shoes for wear on causal nghts anyway, so they are no additional burden, and I certainly can wear the sport coat over a "golf" or "polo" shirt on casual nights if the dining room, the theater, the casino, or whatever other space turns out to be a bit chilly in the evening. For ladies, many dresses suitable for wear on semiformal occasions would also pass for "smart casual" so it's really just a question of bringing an evening outfit that can go either way.