AlexSpl
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2VDV_forever: It doesn't change: 30 out of 151, meaning the Tower will fall. Although, I'll test it again. Maybe I missed something ;)
I checked, and the probability doesn't depend on the number of buildings.
It's not worth taking in-game probabilities too seriously, at least because the generation of a new pseudo-random number is influenced by the old one. In the context of a siege, this means that the effectiveness of the next shot from a ballista is influenced by the entire history of the battle.
You can also include information about the probability of inflicting specific damage in the reference. For example, what is the probability that an archer tower will inflict damage, say, 72, if the damage range is 68-102, etc.? I'm currently thinking about the "blind spots" in the physics of HoMM I. Are there any left? For now, only the not-so-accurate 1.77 (Diplomacy) comes to mind. Everything else seems to be in order.
Maybe I'm not saying anything new, but...
Let's assume that the attack of the attacking unit and the defense of the defending unit are equal, i.e., there are no damage modifiers.
Let there be N warriors in the attacking unit, and the damage range of each warrior is [min_dmg..max_dmg], then:
a) if N = 1, then all damages from the range are equally likely. The probability of inflicting specific damage is 1/(max_dmg - min_dmg + 1).
Example 1. One dragon inflicts 25 damage with the same probability as 50. The probability is 1/(50 - 25 + 1) = 1/26, but if there are two or more...
b) if N > 1, then damages located in the center of the range are more likely.
Example 2. Four nomads ([2*4-5*4] = [8-20]) are most likely to inflict 14 damage (probability 17.19%), while the probability of inflicting 8 or 20 damage is only 0.39%! The probability that the damage will be at least 75% of the maximum is 41.41%.
For comparison, three nomads inflict damage of at least 75% of the maximum with a probability of 31.25%.
If you build a graph of the dependence of the probability of a specific damage occurring (Y-axis) on that damage (X-axis), you will get a curve that looks like a bell.
You can get the exact probability values using programs.
The first line is the damage, the third is the probability of it occurring.
I checked, and the probability doesn't depend on the number of buildings.
It's not worth taking in-game probabilities too seriously, at least because the generation of a new pseudo-random number is influenced by the old one. In the context of a siege, this means that the effectiveness of the next shot from a ballista is influenced by the entire history of the battle.
You can also include information about the probability of inflicting specific damage in the reference. For example, what is the probability that an archer tower will inflict damage, say, 72, if the damage range is 68-102, etc.? I'm currently thinking about the "blind spots" in the physics of HoMM I. Are there any left? For now, only the not-so-accurate 1.77 (Diplomacy) comes to mind. Everything else seems to be in order.
Maybe I'm not saying anything new, but...
Let's assume that the attack of the attacking unit and the defense of the defending unit are equal, i.e., there are no damage modifiers.
Let there be N warriors in the attacking unit, and the damage range of each warrior is [min_dmg..max_dmg], then:
a) if N = 1, then all damages from the range are equally likely. The probability of inflicting specific damage is 1/(max_dmg - min_dmg + 1).
Example 1. One dragon inflicts 25 damage with the same probability as 50. The probability is 1/(50 - 25 + 1) = 1/26, but if there are two or more...
b) if N > 1, then damages located in the center of the range are more likely.
Example 2. Four nomads ([2*4-5*4] = [8-20]) are most likely to inflict 14 damage (probability 17.19%), while the probability of inflicting 8 or 20 damage is only 0.39%! The probability that the damage will be at least 75% of the maximum is 41.41%.
For comparison, three nomads inflict damage of at least 75% of the maximum with a probability of 31.25%.
If you build a graph of the dependence of the probability of a specific damage occurring (Y-axis) on that damage (X-axis), you will get a curve that looks like a bell.
You can get the exact probability values using programs.
The first line is the damage, the third is the probability of it occurring.