Posts from Tactics for the Swamp (Fortress).

serpent's lair - you kill serpents inside (up to 90), and you get wyverns (up to 12) for free. And the terrain is simply amazing.

Hey everyone, can you explain the principle behind the Gorgon's gaze? I tested 20 "Alpengold" units against 10 "Amur" units. The heroes have no defense or attack skills and no artifacts. The Gorgons have the "Blessing" spell for maximum damage. The Angels fly in, the Gorgons attack, dealing 248 damage, and one Amur dies, and two more are affected by the gaze. Seven remain. And they all have maximum health of 200! 600 - 248 = 352 damage from the gaze. But! No matter how many times I attack, their health remains full, and the number of Angels decreases due to the "Mumu" gaze. Therefore, the gaze affects the number of units, not the damage. So, the question is: what is the principle behind the gaze of death?

Guys, explain the principle of the Gorgon's gaze. I tested 20 "Alpengold" against 10 "Amurs."

Let me explain. Each Gorgon has a 10% chance to inflict the Death Gaze. But that doesn't mean that 10 Gorgons will have a 100% chance.

There's a formula, again from mathematics: :cool:
1-(1-0.1)^n, where n is the number of Gorgons. In your case, with 20 Gorgons:
Chance = 1 - (0.9)^20 = 0.878 = 87.8%
A 99.9% chance gives something around 70 Gorgons, if I remember correctly.

Furthermore, the number of units that can be affected by the gaze is calculated randomly within the range
from 1 to (n/10)+1 (rounded down). In your case, 20 Gorgons will affect from 1 to 3 creatures.

87.8% chance to affect from 1 to 3 creatures. That is:
29.26% to kill 1 creature,
29.26% to kill 2 creatures,
29.26% to kill 3 creatures.
I hope I explained it clearly? :)

...
I hope I explained it clearly? :)

Dirty, I'm sorry, I understand that you're good at math, but... no matter how much higher math I studied in college, I never had to use it in real life - everything could be calculated much simpler with almost the same accuracy. Therefore, I will suggest my version.
It's well said in FizMIG: 1 cow has a 10% chance of stunning 1 enemy with its gaze, and a stack of 10 cows has a 100% chance of doing so. This is quite consistent with mathematical statistics - everything tends towards the average value. That is, a stack may not stun anyone, it may stun 2 enemies, etc., but on average it will be 1.
Now about the situation. 20 cows with an attack of 250 HP kill 1 angel and wound 1. And with their gaze, they stun another 200%, i.e., 2 enemies, regardless of how much health they have left - 1 HP or 200 HP. That is, the cows would not be able to take down even 1 archangel with an attack (he would receive less than 250 damage), but they would take down 2 archons with their gaze.:smile16:

Now, about the situation. 20 cows with a 250 HP attack kill 1 angel and wound another. And with their gaze, they can kill another 200%, i.e., 2 enemies.

What difference does it make how many they kill with a simple attack? It doesn't change anything. Where does the 200% figure come from? It feels like I'm wasting my time writing all these mathematical calculations. You try, you explain everything, and then someone tells you that 10 cows is 100%.

, and a stack of 10 cows has a 100% chance of doing that.

Where does 100% come from? They won't hit every time. If 100% and 87% are the same for you, then I suggest the following. Put 1 bullet in a revolver, spin it, and shoot yourself in the head. You'll have an 84% chance of survival. If that's the same as 100%, then you have nothing to fear.

Now, I'm quoting FizMiG:

When attacking, each of the attacking Gorgons, in addition to the direct damage, has a 10% chance to instantly kill one unit in the enemy stack.

I highlighted the key word in red! EACH!!! This means that the calculation is separate for each cow. I understand that this is difficult to grasp, so here's an example from real life:
Four people are standing with coins. Each has a 50% chance of catching an eagle when they flip a coin. This does not mean that the four of them together have a 200% chance of catching an eagle. There is still a chance that they will all flip tails.
If, even after this, 10 cows have a 100% chance, then I will not write or prove anything else.

I think I understand the idea. The more cows there are, the higher the chance of triggering the ability, and the damage from it is random, right? So, it can't be calculated in advance?

Is the damage from it random? Meaning, can it be predicted in advance?

Yes, it is random. But you can calculate the range of the randomness.

Sorry, Dirty, I wasn't paying close enough attention (or remembering correctly), which is why I came back to the question.
"87.8% chance to eliminate 1 to 3 creatures. That is:
29.26% chance to kill 1 creature,
29.26% chance to kill 2 creatures
29.26% chance to kill 3 creatures."
I was too hasty when I said 100% - it's less, but still much closer to 1 (100%) than to zero. But in battle, you don't calculate the probability of a particular amount of damage in detail on each turn - you just roughly estimate. That is, a 10% probability is a chance, and a 90% probability is almost a guarantee that you can rely on. That's why I figured that a stack of Gorgons would almost certainly destroy the enemy unit, and if we take into account your calculation (with an equal probability of 1, 2, or 3 units), then I could very well have relied on the average value - 2 units (1 unit - 100%). The actual range could be different - 3, 2, 1, or 0 units, which I also noted.
You're right to write out mathematical calculations. It's just that we have slightly different approaches to analyzing things. Everything complex often has a very simple explanation or solution. And I usually try to find that simple one. Because truth is born in debate. And sometimes it can be very interesting.
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P.S. In the previous post, I wrote for a stack of 10 Gorgons, "the stack may not eliminate anyone, it may eliminate 2 enemies, etc., but on average it will be 1." That is, the chance of each of the three options will be approximately 33%. I did the calculation using your formulas and got: 1 or 2 enemies - 65% / 2 = 32.5% each, none - 35%, in practice, this means equally likely. How did I manage to guess that?

- What are the chances of meeting an alien on the street?
- 50%
- ??????
- Either you will, or you won't! :D

It's a timeless topic – probability theory...

Quoting a post from five years ago on a neighboring forum (authors – Self-seeking, Jerky Fox):

***

The probability of at least one successful outcome in n events is equal to 1-(1-p)^n, where p is the probability of a successful outcome (in our case, p = 0.1).

Number --- Chance to kill an enemy with a gaze
Powerful Gorgons --- 1 unit -- 2 units -- 3 units -- 4 units.

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%

First, it should be noted that starting with 10 Powerful Gorgons, you have a 2 in 3 chance of killing at least one enemy with a gaze. Second, while 1 Powerful Gorgon has a 10% chance of killing 1 creature with a gaze, 11 Powerful Gorgons already have a 30% chance of killing 2 enemy units, 21 Powerful Gorgons – a 35% chance of killing 3 units, and 31 Powerful Gorgons – a 37.5% chance of taking down 4 creatures.

This leads to an obvious conclusion: THE MORE POWERFUL GORGONS YOU HAVE IN ONE STACK, THE HIGHER THEIR CHANCE OF KILLING THE MAXIMUM POSSIBLE NUMBER OF CREATURES! In other words, if you have 75 Powerful Gorgons, the chance of taking down 8 creatures is higher than the chance of taking down 3 creatures for 25 Powerful Gorgons. Second conclusion: accumulate Powerful Gorgons.

The second interesting question is: should you SPLIT Powerful Gorgons into 2 or more stacks? The first rule: NEVER SPLIT a group of Powerful Gorgons into quantities of 11, 21, 31, 41, etc. Any other number of Powerful Gorgons (in terms of probability) should be split into at least 2 stacks. Example: you have 2 Powerful Gorgons. When attacking, one stack can kill one enemy with a probability of 19%. If two stacks of 1 Powerful Gorgon each attack, you still have the same 19% chance for one opponent. But in reality, your chances of killing one opponent are 18%, while 1% is the chance of killing two at once.

A more obvious example: 30 Powerful Gorgons (probabilities are shown in the table). Let's split them into 2 stacks of 15 Powerful Gorgons each. Suddenly, there is a 20% chance of killing 4 enemies with a gaze at once! You didn't have this chance when all 30 Powerful Gorgons were in one stack. And this is despite the fact that the minimum chances have not worsened. It doesn't matter how exactly you split the Powerful Gorgons, but it is obviously not necessary to create large discrepancies, say, 20:10.

Of course, splitting one stack of Powerful Gorgons also has disadvantages. If the resulting stacks are too small, they can be easily defeated even by low-level enemy troops. Advice: DO NOT SPLIT Powerful Gorgons UNTIL YOU HAVE ACCUMULATED THEM, AT LEAST 32 OF THEM.

With such an amazing feature, the main goal of Powerful Gorgons is level 7 monsters. Don't even worry about taking them down with your other troops. Powerful Gorgons can withstand a decent amount of damage. If the enemy has 13 Archangels, and you have 48 Powerful Gorgons (by the time the enemy accumulates 13 Archangels, you may already have more Powerful Gorgons) – don't despair. The Archangels may not know it, but they are already dead. With their first attack, the Powerful Gorgons will most likely kill 4 Archangels. In a retaliatory strike, the Archangels will not kill more than 9 Powerful Gorgons. After 2 more attacks, 2 or 3 Archangels and 15-20 Powerful Gorgons will remain. It should be noted that such hero parameters as Defense and/or the Armor skill GREATLY shift the advantage in favor of the Powerful Gorgons. Attacking level 6 and lower monsters makes sense only if there are no stronger ones. DO NOT WASTE GORGONS ATTACKING A LARGE STACK OF WEAK UNITS. This is the task of Hydras.

The only unpleasant thing is that DEATH RAY DOES NOT WORK ON THE DEAD. Therefore, in a confrontation with Necropolis, you cannot rely on Powerful Gorgons as much.

2AmberSoler It's strange that in your post, 10 Gargoyles can't kill two units, but 20 can kill three. :confused: According to the formula, the maximum number should be (n/10)+1. Or am I mistaken? But I think 10 Gargoyles definitely kill two. And regarding the number and percentages, isn't it also an interesting point? Doesn't a random number get chosen from a certain range? :confused:

I quoted an old post, as I mentioned above. I didn't provide a critical analysis of the numbers, I admit. )) This question requires a slight clarification and, possibly, a correction...

It’s unbelievable, but it’s a fact. When Vasily bites, stone golems turn into stone! The same happens with gargoyles...

Let me explain...
There's a formula, again from mathematics. :cool:

An 87.8% chance to take out 1 to 3 creatures. That is:
29.26% to kill 1 creature,
29.26% to kill 2 creatures,
29.26% to kill 3 creatures.
I hope I explained it clearly? :)

Hmm... Even the character from Bulgakov's unforgettable novel was aware of Newton's binomial... And the binomial distribution is taught in school. (It is assumed that each cow breathes independently). The expected value is 0.1N, the variance is 0.09N... With large N, it can be estimated using a Gaussian distribution.

For ten, the probabilities are approximately: [0.349 0.387 0.194 0.057 0.011 0.001 0. 0. 0. 0. 0. 0.] (to "breathe" 0, 1...; theoretically, it can be 10, but it is extremely unlikely)

Accordingly, no less than 1.2... [0.651 0.264 0.07 0.013 0.002 0. 0. 0. 0. 0. 0.]

You can check it in your Excel. (I can post a one-liner in Python)

Added after 12 minutes

THE MORE POWERFUL GORGONS YOU HAVE IN ONE STACK, THE HIGHER THEIR CHANCE OF KILLING THE MAXIMUM POSSIBLE NUMBER OF CREATURES!

The numbers are correct, and then something fantastic... The trials (breaths, in this case) are independent, so the probability distribution for a large stack is the same as for its components... That is, whether 10 attack, then 5, and then again 5.

And where does the magical one come from?)

For a probability of ten, it would be approximately: [0.349 0.387 0.194 0.057 0.011 0.001 0. 0. 0. 0. 0. 0.] (breathe 0, 1..; theoretically, it could be 10, but it's extremely unlikely).

I disagree. I claim that 10 cows cannot kill 3 creatures. There is a limit from 1 to N/10+1. I won't claim that 1 or 2 numbers are equally likely to appear, although it seemed that way to me. :rolleyes:

...

In general, it would be more ethical to confirm your calculations yourself, rather than simply stating that you have calculated something and asking others to disprove it. I tested it. The test was as follows:
The attacking hero has 6 stacks of 5 Rust Dragons each. The defending hero has 6 stacks of 10 Cows each. Battle order: all Dragons fly in, Cows attack; after 1 round, restart. Results: With 10 Cows, only 1 Dragon always died, or the gaze attack did not trigger (this is for those who thought that 10 Cows give 100%). Two deaths were not recorded. Then, I set 11 Cows. The number of deaths was strictly 0, 1, or 2. I couldn't tell the percentage ratio between 1 and 2 by eye; for this, I would have to record the results and conduct 1000 experiments. But the following is obvious:
1. 10 Cows can kill a maximum of 1 unit with their gaze.
2. 11 Cows can kill 1 or a maximum of 2 units.
3. Most likely, the numbers provided by AmberSoler are correct.

Number --- Chance to kill an opponent with a gaze
Gorgons ---1 unit--2 units--3 units--4 units

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%

4. The formula for the maximum number of units killed, n/10+1, is incorrect or requires some adjustment.
5. My hypothesis that the number of units killed is chosen randomly from the possible range is not confirmed, but also not refuted. For this, the results need to be recorded in writing.