We LOVE games at our house, and went through that phase too. Here are some things that helped us.
--Talk about how much fun it is to win, and how poor 'sister' hasn't gotten to win yet. Wouldn't it be sad if *you* never got to win? Won't it be nice when 'sister' gets a turn to win?
--This works best when 3 or more are playing, but it can work with just 2 too.... After someone wins, keep playing for a second winner, and a third winner, even when there is just one person left trying to get around the board, see how long it takes for them to 'win'.
--The rule at our house now is that the winner has to put the game away. Lately I've been hearing, "I want you to win (because I don't want to put the game away)."
--When I have bad luck with a game, I say my thinking out loud (modelling calm frustration), so kids know they are not the only ones who go through those emotions. "My goodness, when am I ever going to roll the number to start?!" And I let them see my laughing at my own crazy bad luck.
--Alternatively, sometimes I show what whining and tantrums look like, so they can see "themselves" in me. "Oh no, I just got the super long slide down!! WAAAAHHH!" They look at me like I'm an alien, and tell me to stop it. So all of a sudden I'll stop and say, "oh yeah, you're right, I don't need to cry about it. That's just what happens in a game sometimes." Sometimes I just say, "Oh no, I just got sent back to home, can I cry now?", and hear "NO, MOM!"
--And especially, games are supposed to be fun. If they start really going overboard with the frustration of not winning, explain that the game is supposed to be fun, and if the game is causing so much of a problem, then we don't have to play it right now.
Have fun!