Any Probability/Statistic majors among us?

[Vandiablo]

How can you determine the overall probability of a particular monster being picked to spawn?

Well, maybe there's some handy dandy equation or a simpler way, but if there isn't I'll point out that you would be better off calculating the prob that a monster won't spawn and then subtract it from one.

For instance, the prob for Balrog would be

P(Bal) = 1 - P'(1,Bal) P'(2,Bal) P'(3,Bal)

where P' = 1 - P, meaning prob of not getting picked, and
P'(k, Mon) is the prob of a monster Mon not getting picked in round k

For Balrog, P(3,Bal) is zero (impossible for Balrog to be picked third), so P'(3,Bal) = 1.

So
P(Bal) = 1 - P'(1,Bal) P'(2,Bal) (1) = 1 - P'(1,Bal) P'(2,Bal)

As you already know, we also have P(1,Mon) is equal to 1 divided by the count of monsters, in this case 9. So P(1,Bal) = 1/9 and thus
P'(1,Bal) = 8/9

So
P(Bal) = 1 - (8/9) P'(2,Bal)

oops gotta go