The serial killer vigilante has [quoute]Her hidden strike is considered equivalent to a sneak attack with the same number of dice for the purpose of meeting prerequisites or using abilities that depend on sneak attack.
Does this include effects that change the dice size of sneak attack, from effects like the Extreme Prejudice feat, the Knifemaster rogue sneak stab, the skulling slayer bold strike or the waylayer ambuscading sneak attack?
How does that work when attacking a dex denied opponent?
You already answered your own question.
Her hidden strike is considered equivalent to a sneak attack with the same number of dice for the purpose of meeting prerequisites or using abilities that depend on sneak attack.
It is not sneak attack it just allows you to use hidden strike to meet prerequisites or abilities that depend on sneak attack. Things that modify sneak attack have not effect on hidden attack. So if you want to pick up a feat or a prestige class that has a prerequisites of sneak attack you can use the number of dice of hidden attack to fulfill that prerequisites. If you have an ability that only works when you use sneak attack you can use it when you are using hidden attack.
Does dealing d8 damage with your sneak attack depend on you having sneak attack then?
Assuming it does (because you cant increase the damage die of your sneak attack unless you actually have sneak attack, thereby making it "depend on sneak attack") would that increase the reduced hidden strike damage to 1d8?
You realize that hidden strike already does 1d8 damage? Hidden Strike is actually a little better. It can affect those that are not aware of you or who consider you there allies.
RAW they are separate abilities. If the GM wants to consider them interchangeable that is his right but that is a house rule.
So you're actually saying it doesn't count as sneak attack even though it is "considered equivalent to a sneak attack" when using the abilities i mentioned whose effects modify (and therefore "depend on" having/being able to use) sneak attacks?
Or are you just saying it doesn't modify the reduced 1d4 hidden strike damage, meaning feats like extreme prejudice do nothing for a serial killer?
Im not invested one way or the other, just trying to clear it up.
Excellent. thanks.