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Offline red1rabbit
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Posts: 5
#16
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You are absolutely right; if you have 10 Gorgons, there is a 100% chance they will kill one monster from the enemy stack, but more than one might die. Everything falls within a range; the probability that 1 will die is 1-100%, and the probability that all 10 will die is 0.00000000001 (you need to multiply the probabilities; 0.1 raised to the power of 10). This gives us a range from 1 to 10, with the probability of the event expressed as a percentage.
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Offline Heroes13
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Posts: 257
#17
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red1rabbit
You are absolutely right, if you have 10 Gorgons, there is a 100% chance that they will kill one monster from the enemy stack, but more than one might die; everything is within a range. The probability that 1 to 10 will die is 1-100%, and the probability that all 10 will die is 0.00000000001 (you need to multiply the probabilities, 0.1 raised to the power of 10). So, we have a range from 1 to 10 with a probability event in percentage terms.

From each group of ten, one unit can die.
1-10 units - maximum 1 unit
11-20 - maximum 2 units
21-30 - 3 units, and so on.
It is difficult to say with what probability this will happen. You can rely on the data provided above with the formula, but I think they are not correct. Here, the probability is not for the entire quantity as a whole, but somehow calculated for each group of ten separately; otherwise, I cannot explain it. It is better not to dwell on this question.
Мой ник Heroes, и никто не вынесет меня
Скажу я вам, мои друзья.
Я некромант, я маг великий, и армия моя
Непобедимая, огромная!
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Offline KycoK_3a6opa
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Posts: 74
#18
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KycoK_3a6opa

Another question about the table:
01-------10%
02-------19%
05-------41%
10-------65%
11-------68%---30%
15-------79%---45%
20-------88%---61%
21-------89%---63%---35%
25-------93%---73%---46%
30-------96%---81%---59%
31-------96%---83%---61%---37%
40-------98%---92%---77%---57%
I'm just curious how this table was obtained...
Where did you get all these percentages? What formula did you use to calculate the probability, for example, for the 31st Gorgon with 4 units?!
Stop hard - Go Pro!:smile49:
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Offline Znich
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Posts: 16
#19
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Hello everyone!
I noticed a peculiarity of Gorgons: the "Gaze" ability works particularly well against all snake-like creatures. This applies not only to level 7 creatures, but also to Medusas, Fly Snakes, Nagas, and Wyverns. I don't remember about Basilisks.
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Offline Valgarv
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Posts: 2
#20
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KycoK_3a6opa
I'm just curious how this table was obtained...
Where did you get all these percentages from? What formula did you use to calculate the probability, say, for the 31st Gorgon with 4 units?!

It's all quite simple and is calculated using Bernoulli's formula. However, it's important to consider that the probability we need is a sum.
That is, how the algorithm works when calculating the skill's activation.

There are n cows. This means we randomly generate a number n times, for example, from 1 to 100. Let's say the number from 1 to 10 appears k times. Then, the algorithm checks how many dozens of cows we have in the stack, i.e., it divides n by 10 and rounds up, resulting in the number d. If the resulting k is greater than the number d, then the number of creatures dying from the gaze is d. If k is less than or equal to d, then the number of creatures dying is k.

To calculate the probabilities in percentages, you need to use Bernoulli's formula.



where


Using this formula, we calculate the probability that k cows out of n will use their ability with a chance of p = 10% (or 0.1) for each. But there's a catch: in the algorithm, we also perform, let's say, a truncation based on the number d. That is, in reality, when a stack of n cows attacks and we are interested in the chance of how many will die from the gaze, we must sum all the probabilities when k is equal to or greater than d.

For example, we have 11 cows, and we are interested in the chance of killing two units with a deadly gaze.

We get: according to Bernoulli's formula, the probability that 2 out of 11 will have a value from 1 to 10 is P(2) = 0.21308126895; 3 out of 11 is P(3) = 0.07102708965; P(4) = 0.0157837977, and so on, up to P(11) = 0.00000000001.

Then, we add up all these probabilities, since they are all favorable to us. The result is:

P = 0.30264312 (or the 30% that is in the table)

I hope I explained it not too clumsily
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Offline dnaop-wr
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Posts: 1,011
#21
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I explained it correctly (although I've never needed advanced mathematics in my life – everything could be solved at a simpler level). But it's better (easier) to use a table. Moreover, there are also upper limits, and chance is not a guarantee, no matter how much you calculate it. With a table, you don't need to memorize the whole thing, just the principle of its construction – and you don't have to worry. It's like the Lord's Prayer.
Техника в руках индейца мертва.
Справочник по НоММ-4 http://handbookhmm.ru/pamyatka-dlya-heroes-iv.html
Памятка по НоММ-3 http://handbookhmm.ru/pamyatka-dlya-homm-iii.html
и HotA http://handbookhmm.ru/vyishla-obnovlennaya-pamyatka-dlya-homm-iii-hota.html
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Offline Valgarv
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#22
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dnaop-wr, well, I answered the direct question about where these numbers in the table come from and how it is generated.
And yes, of course, it's better to use it.
As for higher mathematics, where did you find it here? This is just a simple probability theory.)
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Offline KycoK_3a6opa
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#23
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Valgarv
It's quite simple and calculated using Bernoulli's formula. However, you need to consider that the probability we need is a sum.
That is, how the algorithm works when calculating the skill's activation.

There are n cows. This means we generate a random number n times, for example, from 1 to 100. Let's say we get the number from 1 to 10 k times. Then, the algorithm checks how many dozens of cows we have in the stack, i.e., it divides n by 10 and rounds up, obtaining the number d. If the resulting k is greater than the number d, then the number of creatures dying from the gaze is d. If k is less than or equal to d, then the number of creatures dying is k.

To calculate the probabilities in percentages, you need to use Bernoulli's formula.



where


Using this formula, we calculate the probability that k cows out of n will use their ability with a chance of p = 10% (or 0.1) for each. But there's a catch: in the algorithm, we also perform, let's say, a truncation based on the number d. That is, in reality, when a stack of n cows attacks, and we are interested in the chance of how many will die from the gaze, we must sum all the probabilities when k is equal to or greater than d.

For example, we have 11 cows, and we are interested in the chance of killing two units with a deadly gaze.

We get: according to Bernoulli's formula, the probability that 2 out of 11 will get a number from 1 to 10 is P(2) = 0.21308126895; 3 out of 11 is P(3) = 0.07102708965; P(4) = 0.0157837977, and so on, up to P(11) = 0.00000000001.

Then, we add up all these probabilities, since they are all favorable to us. The result is:

P = 0.30264312 (or the 30% that is in the table)

I hope I explained it not too clumsily)
Thank you very much! This is exactly what I needed. :smile20:
Stop hard - Go Pro!:smile49:
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