There are a number of possible strategies for the game, and the dynamics tend to change with different numbers of players. For example, with three players, you have the largest number of possible tied rounds. With two players, the game hinges on who can think one more step ahead than the last person, and your willingness to take risks. For instance, if your opponent had 2 red lights, playing a book (green) would not be a safe move. Likewise, your opponent might not expect you to make that one. Nash’s “game theory” could be put to good use here. Anyway, the best thing to do is to play semi-randomly, skewing toward your best chance of winning, especially in a larger group. There’s a surprising amount of strategy here for such a deterministic game.
Two Player Game
This becomes very much like a cross between chess and poker. Your ability to predict your opponent’s move will decide the victor of a given round.
Three Player Game
In this type of game, you have a couple of options for strategy. The most obvious being: anticipate what one of your opponents is going to play, and match it if you think it has the best chance of winning against the other guy. Another option is simply shoot in the dark. :) With the way the probability seems to work on this one, you’re just as likely to win as to lose in a given round, and more likely to tie than anything else.
This type of game is the most prone to ties, as Robert F. Caine has pointed out, it’s got the most possible. (You’ll have to ask him what the math on it is.) :)
Four Player Game
After having won a couple of these games, it’s apparent that the strategy isn’t actually as difficult as I had thought it to be. (I just needed some “lack of sleep” and four cups of coffee to figure it out. ;) ).
With a game of four players, your ability to win a round seems to come from whether or not you can predict which will be the more prominent object played. Here are what I recall the most likely winning combinations to be:
3 of one object, 4th wins
2 of 2 objects
3 objects played, one duplicate, object beating the duplicate wins.
Five Player Game
I still think that winning a five player game is more than 50% luck of the draw, unless perhaps you’ve been playing several rounds with the same people and are able to get an idea behind your opponent’s playing style(s).