For a movie, or a book, or a dance, or a song, you never really know what's coming. You can infer based on what you know of the skill of the author, the genre and culture in which the work is set and made, and so on. But you never know for certain. It could change in a moment; the book may suddenly pick up, the dance change direction, the song change rhythm. The author may, at any moment, take the work in a new direction.
For a board game, with the rules laid out in front of you, the author can explicitly take you in a new direction only if the game requires you to bring heretofore unrevealed external media - a movie, a piece of music, a paragraph of text - into the game play during the game. For the typical abstract, roll-and-move, or trivia game, you've seen everything the author put into the work the moment you've read the rules, and sometimes the moment you've read the back of the box.
Barring the author having you consult external media during the game, if you have imagination and experience with similar games, you can do a fair job of envisioning what the experience with the board game will be like. The dice may be screwy and you may pick all the wrong cards, but a trivia game is a trivia game, an economic game is an economic game. The other players will be the main unexpected factors in the game.
However, there are exceptions to this. Games like Go or Chess looks and initially play like simple abstract games. However, there are depths in these games that reveal themselves after several plays, depths that you could not have expected or understood from simply reading the rules.
Discoveries like these can occur in other games. Many of these will be bad, when you come to realize that the game is not really balanced or enjoyable for certain reasons. Some of these will be good, when you come to realize that there are hidden, novel, pleasurable experiences in the way the game mechanics interact.
Sometimes this is the voice of the author, whose twists remain unrevealed until the game is experienced. Often, it was a happy accident to the author as well, who discovered these twists the same way that you did.
For games, as well as for any well crafted media, even after these twists are revealed, and even after you know when to expect them, you should be able to enjoy experiencing them repeatedly.