A core function of the DM is to be the referee for the rules. This chapter will provide guidance on how to go about doing that, especially when you're not sure yourself how to interpret the rules.
Before getting into the details on how to make various judgment calls when running the game, it's important to understand a bit about the intent of the game and your role as the DM. Above all else, the game is about having fun in a cooperative manner. Triptycho is not a competitive game; as such, the main thing for you to consider is: which ruling will lead to everyone having more fun? If that question has an obvious answer, then you know how to make your ruling.
That said, it's still important to be as fair and impartial as possible. You don't want to get caught making a ruling in one situation that lets one of your players do something a teeny bit against the rules because it's cool, but then prevent another player from doing the same thing later because in that case it would break your scenario design in half and make things boring for everyone else. While facilitating “fun” is certainly your primary goal, that doesn't mean that you always say “yes” to every rule-breaking thing your players come up with.
Because this is something of an artform - and the specific answers change depending on your unique group of players - you have to accept that you're going to make some mistakes. The best thing to do in these situations is to communicate openly and honestly. If you make a ruling that comes back to haunt you in a new situation later, just tell the players that you didn't foresee this and will be making determinations differently moving forward. If you feel it useful or necessary, go ahead and let the player break the scenario in half that second time, and use the results as an example of why you'll be making different decisions in the future. Just make sure you talk about it so your players know what's going on.
In practice, most of the actual rules decisions you have to make will revolve around how cards interact with each other. Many cards have unique effects written in their text - effects that can result in murky circumstances when certain cards wind up being played at the same time. For example, what do you do if someone plays an Action with text stating that it automatically hits, but the Reaction played in response has text stating that the attack automatically misses?
In the case of cards contradicting each other, you have two options. The first and simplest option is just to pick the result that most benefits the players. This will prevent players from feeling cheated by questionable circumstances, and bending the odds slightly to benefit the players is rarely a bad thing.
This doesn't work for everyone, however, as some may find that it feels rather artificial, and some players are adept at finding ways to make sure such cases come up often and always in their favor. In these cases, use the following priority rules in order to determine which card or effect wins out:
Let's go back to our previous example and see how this works. Let's assume the player played the Action and one of your Adversaries played the Reaction. If the player's Action required spending a Karma point, then the Action's automatic hit effect takes priority over the Reaction's automatic miss effect because that gives it top priority. This is true even if the automatic hit is implicit (such as due to lacking a Hit entry). Therefore, the attack hits.
Now let's assume no Karma was spent. If the player's Action automatically hits because it lacks a Hit entry, but the Reaction has text that states that the attack automatically misses, then the Reaction wins out. That's because the Reaction's text is explicit on the card while the Action's text is implied through reading the normal rules. Therefore, the attack misses.
What about if the player's Action was played from hand, didn't require spending Karma, and has specific text stating that it automatically hits? Well, if the Adversary's Reaction was played from its card, then the player's Action wins out because cards from hand get priority over effects written on enemy cards. Therefore, the attack hits. But what if the adversary instead played the Reaction from its hand? In this example the Reaction wins because Reactions are always played after Actions. Therefore, the attack misses.
Since Assists and Interrupts get priority over the other types of cards regardless of all other circumstances, these should always be judged in reverse order of play. Unless otherwise specified, these even override Karma plays. What happens if a player spends Karma to play an Action that says it automatically hits, but an enemy plays an Interrupt that states that the attack automatically misses? The Interrupt always beats the Action, so the attack misses.
How do constant effects fit into this? For instance, imagine you've given a player a (completely broken and very ill-advised) piece of Gear that has as an effect that all their attacks automatically hit. You'd treat this as an effect from Gear (see #4) that was played first (see #5).
In the case of two contradicting constant effects, try to pick the specific over the general. For example, a player might be wearing Gear that gives them Fire Resistance 1 as a constant effect, but they enter into a magically warded dungeon that eliminates all player Fire Resistance. In this case the dungeon should be considered more specific than the Gear, so the best ruling is that the player loses the Fire Resistance. After all, how else could these magic wards have any useful effect?
The best case would have the dungeon text specifically state in which circumstances it overrides player Fire Resistance. The text might state that it overrides Gear but not temporary buffs applied within scenarios. In this case you know exactly how to make your rulings. But it's impossible to account for every circumstance, so eventually you'll have to just make a call. Go with what you feel would lead to the most fun, and remember: your rulings are final, but you can always decide to make rulings differently in the future if you dislike how something worked out!