What does the Investiture Conflict casus belli cost?

piety; the amount depends on the titles, claims and distance, worked out when you declare.

Casus belli · Holy wars

Investiture Conflict

The war is called “Investiture Conflict”

Investiture Conflict is a casus belli in Crusader Kings III (holy wars). If the attacker wins: The attacker prevails, forcing the defender and their side to accept the attacker's stance on the appointment of the clergy. If the defender wins: The defender prevails, forcing the attacker and their side to accept the defender's stance on the appointment of the clergy. Declaring it costs piety. The war goal is worth 80% war score. Patch 1.20.0.3, from game/common/casus_belli_types/pam_wars.txt.

Quick answers (3)

What do you get for winning a Investiture Conflict war in CK3?: The attacker prevails, forcing the defender and their side to accept the attacker's stance on the appointment of the clergy (patch 1.20.0.3).
What happens on a white peace?: The quarrel over the appointment of the clergy stays unresolved, and each side refuses to yield.
What does the Investiture Conflict casus belli cost?: piety; the amount depends on the titles, claims and distance, worked out when you declare.

How the war ends

Attacker wins

The attacker prevails, forcing the defender and their side to accept the attacker's stance on the appointment of the clergy.

White peace

The quarrel over the appointment of the clergy stays unresolved, and each side refuses to yield.

Defender wins

The defender prevails, forcing the attacker and their side to accept the defender's stance on the appointment of the clergy.

If the war becomes invalid

The The Christian Church has ended; the Investiture Conflict is no longer valid.

Who can declare it

The game shows no text of its own for these conditions; the script is below.

Every holy wars war (the group's allowed_for_character) (24 lines of game script)

OR = {
	top_liege = this
	any_liege_or_above = {
		faith = prev.faith
		count = all
	}
}
faith = {
	NOR = {
		has_doctrine_parameter = unreformed
		AND = {
			has_doctrine_parameter = holy_wars_forbidden
			NOT = {
				prev = {
					has_character_flag = bonus_major_holy_war
				}
			}
		}
	}
}
herders_and_tributary_constraints = yes
pam_personal_pacifism_offensive_war_ban_trigger = yes
tgp_dynastic_cycle_offensive_wars_ban_trigger = yes
tgp_war_ban_all_ministers_trigger = yes

As written in game/common/casus_belli_groups/00_casus_belli_groups.txt.

Attacker (allowed_for_character) (4 lines of game script)

scope:attacker = {
	is_landed = yes
	pam_can_use_investiture_conflict_cb_trigger = yes
}

As written in game/common/casus_belli_types/pam_wars.txt.

Defender (allowed_against_character) (4 lines of game script)

scope:defender = {
	is_landed = yes
	pam_valid_investiture_conflict_target_trigger = yes
}

As written in game/common/casus_belli_types/pam_wars.txt.

Cost to declare

Costs piety. The amount is worked out when you declare (by the titles targeted, claims, distance and more), so the script is shown as written:

Cost (1 line of game script)

piety = medium_piety_value

As written in game/common/casus_belli_types/pam_wars.txt.

Source: game/common/casus_belli_types/pam_wars.txt and the English localisation, Crusader Kings III 1.20.0.3. “The attacker”, “the defender” stand where the game names the character; “…” marks other words it fills in during play.