We've cruised the BI several times. The answer is formal nights are what you want them to be. Some dress ultra formal, some smart casual, some very relaxed. There will be tuxes & gowns, nice jeans, & everything in between. My DH wears slacks, collared polo shirt, a sport coat if it's chilly. I wear slacks & dressy top. We travel with carryon only so no room for formal wear. We've never, ever had a problem.