Rav, can Bnei Noach play the lottery? And what about other games of chance (slot machines, roulette, etc.)—may Bnei Noach participate in those? In the case of these other types of games, is it permissible to play just for fun? And in any of these instances, is it acceptable to play with the intention of winning some extra money?

Just like Jews, Noachides can play the lottery, but cannot gamble, for it's considered a type of taking the other people's money without their willing & sincere agreement (a form of stealing). If it's not for money but just for fun, it's allowed to use "play money" or chips, or at the end, if everyone returns the money to its original owner. In short, not to earn "extra money" unless it's via Bingo or State Lottery, etc. where you actually depart with your money, even though you may get it back and even plus some additional money.