I think I understand the concept of the Cortex system, adding the rolls for the skills together, and the Wikipedia page for the Cortex system says that I compare that roll to a difficulty number. In the Serenity RPG, where do I find the Difficulty number? The weapons don't have one, armour doesn't have one, is something missing from the book, or have I misunderstood the rules somewhere?
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There are two forms of Target Number rolled against in the Serenity RPG:
Most combat rolls are opposed; your TN is a roll by the opponent. If the opponent can't, won't or doesn't resist, the default number rolled against is a fixed value of 3 (p. 152, Innate Defense). This is adjusted for cover (p. 152, Cover).
If the target can resist, the target number Agility+Athletics/Dodge versus ranged, Agility+(weapon skill) to block melee attacks. Cover applies, too. (p. 152)
For ranged attacks, you modify your skill used by the range, not the TN. A not uncommon house rule is to adjust the difficulty instead - Since a skill step is 1 point average result change, Point Blank range's +1 Step would be -1 TN, medium ranges -2 steps as +2 TN, and long range's -4 steps as +4 TN.
Cortex's combat system is an "attack roll, dodge roll" system, not an "attack roll against an armour defense class" system. Almost all combat rolls are to resolve Opposed Actions (Serenity RPG, p. 143), which means you're going to be rolling to beat the dice result of the opponent. Weapons change what you roll to determine damage. Armour absorbs a number of wounds from the amount inflicted. Cover (p. 152) and things like that are modelled with a Difficulty Modifier to one or the other person's roll.
The rules for defense and attack are in "Defend Yourself", page 151, and "Inflicting Violence", page 153. In particular, note that the normal way to defend is by declaring a block (or dodge, or parry, or whatever) in anticipation of an incoming attack, so you declare it as part of a multiple-action turn, and the defense action kicks in if you're attacked after. If you don't do that you still get an (unskilled) Agility roll to determine the target number for the incoming attack. If you're entirely unaware of your opponent then you don't get to defend at all and their attack's difficulty is Easy (which is a TN of 3, which is literally easy for anyone with a bit of skill).
As for what skills are rolled in combat, that's covered in the Traits & Skills chapter, as well as a few additional notes on page 142 about non-skill (that is, attribute-only) rolls you can make. Various skills can be involved, depending on what actions are reasonable for attacking and defending within the context of the scene.