When you attack with advantage you draw two modifiers and take the highest resulting damage.This means that if you curse one monster a different monster can draw the curse later, but a boss shouldn't. I believe there are exceptions for bosses and allied monsters that appear in some scenarios. Standard monsters all share the same deck.Each player character has their own modifier deck, not shared with other characters, except that character's own summons, which share their deck.There is a shared limit among players of 10 blesses and 10 curses and a separate shared limit among monsters of 10 blesses and 10 curses. Any remaining at the end of a scenario are also removed. They are removed from the deck when drawn and do not have the same reshuffle effect. These are special cards that are temporarily added to a deck throughout a scenario. Bless cards are also x2s, but with a different symbol and curse cards are x0s with a different symbol.Modifier decks do not get shuffled until one of three things happens: Either you run out of cards in the deck, in which case you shuffle it immediately or you draw the x2 or x0 cards (marked with a 'recycle' symbol) in which case you shuffle at the end of the round or you reach the end of the scenario and decks are reset for the next.Attack 3 drawing -2 becomes attack 1 then resolves. Attack 3 drawing x2 becomes attack 6 then resolves. So attack 3 drawing a +1 becomes attack 4, then resolves. If it has a value you just apply that to the damage of the attack. Each time any character makes an attack they draw a modifier from their deck.This is useful for seeing the enemy modifier deck.

You can also mouse over a character and information about them, which includes their passives, statuses and current remaining modifier deck will pop up in the tooltip. In mission while holding 'TAB' or clicking the icon immediately above the icon marked 'here' in the previous image: Out of mission, the icon appears for each character: You just need to mouse over or click it, depending on situation. I've added rings and the word 'here' in the following images to mark the symbol you are looking for. You can see your modifier deck in a number of places.

Aul and auxl attack modifier