The initial posting is now complete - questions and discussion is welcome to commence

The mathematical system is currently built to take into account a number of things:
1) How many creature types are currently available to enter the dungeon?
2) What is the player's current factional mix of creatures?
3) How does each creature type feel about the player's current factional mix?
4) What is the player's current alignment?
5) How does each creature type feel about the player's current alignment mix?
The big formula can be written as this:
Probability of Creature Appearance = Base Probability + Factional Modifier + Alignment Modifier
In the 2 alignment system the formula can be written as:
P = [1/n] + [Cfh(Fh) + Cfc(Fc) + Cfu(Fu) + Cfg(Fg) + Cfd(Fd)] + [Calc(Alc) + Cage(Age)]
In the 3 alignment system the formula can be written as:
P = [1/n] + [Cfh(Fh) + Cfc(Fc) + Cfu(Fu) + Cfg(Fg) + Cfd(Fd)] + [Caae(Aae) + Caoc(Aoc) + Capv(Apv)]
Where:
P = Probability of creature appearance
n = Total number of creature types currently available for recruitment (i.e. threshold conditions have been met)
Cfh = Creature Faction Coefficient for Humans
Cfc = Creature Faction Coefficient for Corpars
Cfu = Creature Faction Coefficient for Undead
Cfg = Creature Faction Coefficient for Constructs (Golems)
Cfd = Creature Faction Coefficient for Denizens
Fh = Human proportion of player creature population
Fc = Corpar proportion of player creature population
Fu = Undead proportion of player creature population
Fg = Construct proportion of player creature population
Fd = Denizen proportion of player creature population
Calc = Creature Alignment Coefficient for Law-Chaos continuum
Cage = Creature Alignment Coefficient for Good-Evil continuum
Alc = Player alignment on Law-Chaos continuum
Age = Player alignment on Good-Evil continuum
Caae = Creature Alignment Coefficient for Altruism-Egotism continuum
Caoc = Creature Alignment Coefficient for Order-Chaos continuum
Capv = Creature Alignment Coefficient for Peace-Violence continuum
Aae = Player alignment on Altruism-Egotism continuum
Aoc = Player alignment on Order-Chaos continuum
Apv = Player alignment on Peace-Violence continuum