10-20-2009, 06:28 AM
Solved it.
I was trying to calculate the probabilites based on how many combinations an enemy appeared in in relation total number of combinations. Instead, you must calculate the individual probability to generate each particular combination. The sum of these probabilities for all combinations will be 100%; to get the probability of any one monsters spawning, you must only sum the probabilites of the combinations in which the particular enemy appears in.
From the first example of my first post, 1/36 isn't the probability to pick a Soul Burner itself, but rather the probability of picking that particular combination in that particular order (Doom Guard, Soul Burner). This requires that you keep track of how many possibilites there are to pick from based on previously chosen enemies.
For example, opposed to a die which will always have 6 possible outcomes regardless of a previous roll, the number of possible enemies to pick to spawn will depend on what was picked previously. If Doom guard is picked first, the restrictions on the "size" will limit the next choice to 4 enemies, hence the DG/SB combination has a 1/9 * 1/4 = 1/36 probability of being generated. If Soul Burner is picked first, however, the game can still pick any of the remaining 8 enemies, hence the SB/DG combination has a 1/9 * 1/8 = 1/72 probability of being generated. The total probability to generate Doom Guards and Soul Burners is the sum of these two probabilities 1/36 + 1/72 = 1/24.
It is not the occurances of a particular enemy in different combinations that must be summed, but the probabilites of those combinations that must be summed to determine the overall probability.
I was trying to calculate the probabilites based on how many combinations an enemy appeared in in relation total number of combinations. Instead, you must calculate the individual probability to generate each particular combination. The sum of these probabilities for all combinations will be 100%; to get the probability of any one monsters spawning, you must only sum the probabilites of the combinations in which the particular enemy appears in.
From the first example of my first post, 1/36 isn't the probability to pick a Soul Burner itself, but rather the probability of picking that particular combination in that particular order (Doom Guard, Soul Burner). This requires that you keep track of how many possibilites there are to pick from based on previously chosen enemies.
For example, opposed to a die which will always have 6 possible outcomes regardless of a previous roll, the number of possible enemies to pick to spawn will depend on what was picked previously. If Doom guard is picked first, the restrictions on the "size" will limit the next choice to 4 enemies, hence the DG/SB combination has a 1/9 * 1/4 = 1/36 probability of being generated. If Soul Burner is picked first, however, the game can still pick any of the remaining 8 enemies, hence the SB/DG combination has a 1/9 * 1/8 = 1/72 probability of being generated. The total probability to generate Doom Guards and Soul Burners is the sum of these two probabilities 1/36 + 1/72 = 1/24.
It is not the occurances of a particular enemy in different combinations that must be summed, but the probabilites of those combinations that must be summed to determine the overall probability.