Monster creation in dungeons

[--Pete]

Hi,

At least my first program is somewhat interesting. It can output all possible combinations (most recorded was 10,270 on dlvl 3 - not counting dlvls 4-6 which take at least an hour of computing to determine) for a level and lists how many combination each monster appears in.

Starting from this, I think the probabilities could be easily calculated without resorting to Monte Carlo methods.

Let us say that a given level has N distinct possible combinations. Each of those combinations has M(k) monsters, with k = 1 to M. Each combination can then be chosen in M(k)! ways. The total ways (not distinct) the level could be populated is then

T = Sum (k = 1 to M) of M(k)!

The total number of ways a particular monster can be on that level is

t(monster) = Sum (k = 1 to M) of {M(k)! if monster is included in the combination; 0 if not)}

Then, the probability of that monster appearing on that level is t(monster)/T

I haven't thought this out in detail, but on first blush, I think it should work and with less than fifteen thousand combinations per level it shouldn't take an unreasonable computation time.

--Pete