06-22-2003, 10:30 PM
(This post was last modified: 06-22-2003, 10:31 PM by the Langolier.)
My goal here is to determine a formula for how many monsters of a given type I will find on a given level in an X number of games (100, 250, 5000, etc). As in example, I am trying to calculate how many balrogs will spawn on dlvl 15 in 2500 games. The easiest way to do that for any number of games would be to calculate the average fractional amount of that enemy per game, and then simply multiply that number by the number of games. This would be like a game that spawned every monster that could spawn on a given level - I would like to calculate what percentage of the level each monster constitutes (the percentages should add up to 100%). An example would be level 15 that spawned balrogs, drakes, cabalists, three witch classes, magistrates, steel lords, and doom gaurds, but only 15-30 of each type constrained to their relative occurances (more withes than mages because they are more likely to spawn in one game). It is easy to see that this is quite a chore for level 15, and much more so on earlier levels where many other monsters types can spawn.
Jarulf's Guide has a section that deals with monster generation, but I can't find quite what I need. In section 5.3.2, it gives a routine that is used to determine what enemies appear on a level based on which monsters can appear on that level and their sizes. Essentially it works like this:
Randomly pick a monster from the types that can appear on the level
Subtract the size of that monster class from 3614 (the max size for one level)
Repeat until there is no monster that has a smaller size than what is left
To see how it works, we will look at dlvl 15 when balrogs and SB's spawn.
Balrogs randomly chosen first (size 2200)
Remaining size = 3614 - 2200 = 1414
At this point, only drakes and witches has a size smaller than what is left, so the remaining choices are: Azure drakes, Snow witch, Hell spawn, Soul Burner
Sould burners randomly chosen (size 980)
Remaining size = 1414 - 980 = 434
No monster have a size smaller than what remains - end monster selection.
Using this method it is easy to compute the various possiblities of spawned monsters for dlvl 15 including balrogs/drakes, balrogs/SB's, tri-witch, etc. Further down in the guide there are tables that list the probabilities of a certain monsters spawning on given dlvls. The problem I am having is relating these percantages to what monsters actually spawn. Is there any way to use those percantages to calculate a monsters fractional occurance?
The guide mentions that 185 monsters spawn per level on average. Will the number of monsters that spawn of each type be divided equally? If two monster types spawn on level 15, will each one constitute 50% of that level? If three types spawn, will each type constitute 33% of that level? I know that level 16 is a special case, and that I always find a greater number of knights than I do advocates. Does anyone know the generation for this level, such as knight-to-advocate ratio?
My guess is that I will have to calculate them by hand. First you have to determine to total number of all monster combonations that can exist per level. Go through each combonation one by one and calculate the total number of enmies of each monster type based on an average of 185 total monsters. Once you have the totals for every monster type, divide that number by 185 multiplied by the total number of combonations possible. Summing up the fractional amount for each monter type should equal 185. Is this method correct (just to double check myself in the event I do need to do this). Any help with ideas to simplify the calculations would be appreciated.
Take an example where there are only two possible combonations that a level can spawn with: balrogs/drakes or balrogs/snow witches. 92.5 balrogs will spawn in both cases because in each case they make up half of the level, giving a total of 185 balrogs spawned. 92.5 drakes will spawn in the first case, 0 in the second. 0 snow withces will spawn in the first case, 92.5 in the second. The totals for each monster class for these two possible combonations are as follows:
Balrogs: 185
Witches: 92.5
Drakes: 92.5
Now divide of each of these values by 182*2 because that is the total number of monsters that have spawned in the 2 cases. We end up with a level that spawns with 50% balrogs, 25% witches, and 25% drakes. Note this doesn't mean those are the probabilities an enemy of that type will spawn of the level (which is the information giving in the guide). Using these percentages it is easy to see that after 1000 games, 500 balrogs, 250 witches, and 250 drakes would have spawned.
Jarulf's Guide has a section that deals with monster generation, but I can't find quite what I need. In section 5.3.2, it gives a routine that is used to determine what enemies appear on a level based on which monsters can appear on that level and their sizes. Essentially it works like this:
Randomly pick a monster from the types that can appear on the level
Subtract the size of that monster class from 3614 (the max size for one level)
Repeat until there is no monster that has a smaller size than what is left
To see how it works, we will look at dlvl 15 when balrogs and SB's spawn.
Balrogs randomly chosen first (size 2200)
Remaining size = 3614 - 2200 = 1414
At this point, only drakes and witches has a size smaller than what is left, so the remaining choices are: Azure drakes, Snow witch, Hell spawn, Soul Burner
Sould burners randomly chosen (size 980)
Remaining size = 1414 - 980 = 434
No monster have a size smaller than what remains - end monster selection.
Using this method it is easy to compute the various possiblities of spawned monsters for dlvl 15 including balrogs/drakes, balrogs/SB's, tri-witch, etc. Further down in the guide there are tables that list the probabilities of a certain monsters spawning on given dlvls. The problem I am having is relating these percantages to what monsters actually spawn. Is there any way to use those percantages to calculate a monsters fractional occurance?
The guide mentions that 185 monsters spawn per level on average. Will the number of monsters that spawn of each type be divided equally? If two monster types spawn on level 15, will each one constitute 50% of that level? If three types spawn, will each type constitute 33% of that level? I know that level 16 is a special case, and that I always find a greater number of knights than I do advocates. Does anyone know the generation for this level, such as knight-to-advocate ratio?
My guess is that I will have to calculate them by hand. First you have to determine to total number of all monster combonations that can exist per level. Go through each combonation one by one and calculate the total number of enmies of each monster type based on an average of 185 total monsters. Once you have the totals for every monster type, divide that number by 185 multiplied by the total number of combonations possible. Summing up the fractional amount for each monter type should equal 185. Is this method correct (just to double check myself in the event I do need to do this). Any help with ideas to simplify the calculations would be appreciated.
Take an example where there are only two possible combonations that a level can spawn with: balrogs/drakes or balrogs/snow witches. 92.5 balrogs will spawn in both cases because in each case they make up half of the level, giving a total of 185 balrogs spawned. 92.5 drakes will spawn in the first case, 0 in the second. 0 snow withces will spawn in the first case, 92.5 in the second. The totals for each monster class for these two possible combonations are as follows:
Balrogs: 185
Witches: 92.5
Drakes: 92.5
Now divide of each of these values by 182*2 because that is the total number of monsters that have spawned in the 2 cases. We end up with a level that spawns with 50% balrogs, 25% witches, and 25% drakes. Note this doesn't mean those are the probabilities an enemy of that type will spawn of the level (which is the information giving in the guide). Using these percentages it is easy to see that after 1000 games, 500 balrogs, 250 witches, and 250 drakes would have spawned.