Since I’m working on the new dice system for With Great Power, this kind of stuff is on my mind.
Just looking at dice systems, most of them have certain “points of articulation” like an action figure. Places where inputs from the fiction or from player decisions can affect the probability of the roll. One of the tasks of good design is to determine what those points of articulation are, map them clearly to their triggers in the game, and be certain you have a good understanding of what consequences each decision will have on the probability.
Let’s look for example at D&D 4th edition. The basic roll is d20 + bonus number versus a difficulty class or defense value. Where are the points of articulation in this single dice mechanic? Each item in that formula is its own point of articulation: the die roll, the bonus number, and the difficulty class/defense value.
The game puts in lots and lots (and lots) of different ways to change the three parts of this equation. For dice rolls, there are special abilities, usually race-related, that will allow you a re-roll, or allow you to add a d6 to your roll, or allow you to roll twice and use the better one. Access to these abilities is almost always determined in character creation, but their use is decided in play. The bonus number probably has the most ways to alter it: Level bonuses, ability score bonuses, special powers, weapon bonuses, and gaining combat advantage, just to name a few. The defense value will change through the use of abilities, and some powers allow you to attack different defenses than other powers.
In play, these points of articulation drive players to weigh the options when creating their characters, driving them to design characters that do one type of thing very, very well. In play, it encourages players to look for opportunities that combine bonuses of different sorts into the same attack. Movement is encouraged, since positioning can gain you multiple bonuses. This supports the kind of exciting, action-intense combats that D&D 4e was built to create.
As a designer, these exceptions can be the real meat of your game. They are where the players get to take fate in their hand and shape their own probabilities by the choices they make. Players love doing that. Make sure that the choices they make reflect the basic premise of the game. When your points of articulation do not match up with the tactical, exploratory, or thematic decisions that the premise demands, your game will earn the title “broken.” And deserve it.