Preamble: The High-Stakes Principle. Imagine a group of players playing your game for ultra-high stakes: the losers are going to die. If your game does not continue to function properly in this scenario, you've got a design problem. Here are some of the most common ones:
This problem occurs when one player is forced to make an unmotivated choice which will probably or definitely throw the game to some other player. Usually this occurs during the final turns of the game, when one player can see clearly that he or she can't possibly win, but is still forced to take a turn. The kingmaker problem is the king of all design problems - it appears in most 3+ player games, and is almost impossible to eliminate completely. However, it's still the responsibility of the designer to minimize its occurrence or its bad effects as much as possible.
Possible Solutions:
Uncompelling solutions:
This problem occurs when two or more players are consistently able to gang up on the current leader to keep that player from winning. It can occur in virtually any 3+ player game in which the players have a fair amount of power to directly affect each other. If the game doesn't have a built-in drive to end (like a depleting deck of cards, tiles, etc.), it will continue indefinitely until someone gets bored or careless, and ends the game by kingmaking. If the game does have a built-in drive, players will bash the leader in the mid-game, and then play kingmaker in the end-game. Not all games with the kingmaker problem have the petty diplomacy problem, but all games that have the petty diplomacy problem have the kingmaker problem.
Possible Solutions:
Hidden-trackable information is only a true problem if it is being used as a solution for some other problem, such as kingmaker or petty diplomacy. If all the players have very good memories, then the problem that the hidden-trackable information is supposed to solve will crop up again. Try playing your game with all hidden-trackable information open. If the game still passes the High-Stakes Test, then the hidden-trackable info is harmless, and your use of it is a matter of taste.
A degenerate strategy is a way of playing a game that ensures victory (or perhaps a draw) all or most of the time. Degenerate strategies bypass the richness of decision making intended by the designer. A common example of a 2-player degenerate strategy is for the second player to mirror the first player's move every time. In some games, this can provide a guaranteed draw, or even a guaranteed win. It's difficult to come up with general principles for eliminating all degenerate strategies.
This problem occurs when players have too many options, or when there is often an objectively correct play which can be determined with lots of calculation.
Possible Solutions:
This means that it is too easy to accidentally reveal information that must remain hidden, too easy to accidentally make illegal moves without anyone catching it, or too easy to cheat.
Stagnation occurs when the structure of the game disadvantages whichever player chooses to move the game forward. The most common result is a game which refuses to end.