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#155
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An experiment to study morale and luck rolls using a specific example (Problem No. 3 in Firaballa's reference guide) through practical means.

Goal of the experiment: to determine the pattern of morale and luck rolls when monsters deal a certain amount of damage.

Defining factor: For the experiment to be reliable, it is a mandatory condition that the actions of the player-controlled monsters are absolutely repeatable.

Concepts: Session (as applied to Heroes 1, first introduced by AlexSPl) – this is a complete restart of the executable file (heroes.exe), i.e., exiting the game to Windows and launching it again.
1 game round – actions performed by the player and the computer for each monster, once, or twice in the case of positive morale.
Note: a paralyzed, blinded, or low-morale monster automatically skips its turn.

Experiment: 10 sessions were conducted, with 10 battle rounds in each.

Description: This example examines 1 round of the aforementioned problem (see also the 8 explanatory images of the battle),

1) Riders - Berserk on gargoyles and Defense;
2) Swordsmen - move in front of the peasants;
3) Pikemen - move diagonally down and to the right from the swordsmen;
4) Peasants - strike the dragons diagonally.

Morale and luck rolls are recorded and entered into the corresponding column of the table below:

The following abbreviations are used in the tables:

рвс – upper wall destroyed;
рнс – lower wall destroyed;
нрвс – upper wall half-destroyed;
нрнс – lower wall half-destroyed;
У – luck;
М – morale.

Note: not a single case was recorded in any session where morale (and consequently luck), with such actions (specified above), rolled for the swordsmen or pikemen.

Let's examine this situation in more detail from the perspective of damage dealt by monsters in the first round:

Let's call this situation a full battle repeat (fbr), which is how we will indicate it in the table.

Damage received:
нрнс;
Archer tower on archers: 90 hp (-9 units);
Gargoyles on griffins – 30 hp (-1 unit);
Griffins in retaliation to gargoyles – 21 hp (-1 unit);
Griffins on archers – 26 hp (-2 units);
Archers in retaliation to griffins – 230 hp (-6 units, killed);
Dragons on archers – 958 hp (-74 units, killed);
Peasants with luck on dragons – 1795 hp (-8 units);
Dragons in retaliation to peasants – 578 hp (-578 units, 419 remaining).

All other situations that do not fall under fbr will be called "random battles" (rb) and will be detailed fully in the table.

Based on the results of the experiment (see table), we get:

Session 1 – fbr (90%);
Session 2 – fbr (90%);
Session 3 – fbr (60%);
Session 4 – fbr (90%);
Session 5 – fbr (90%);
Session 6 – fbr (90%);
Session 7 – fbr (90%);
Session 8 – fbr (90%);
Session 9 – fbr (90%);
Session 10 – fbr (70%);

During the experiment, it was established that under certain damage conditions dealt by the archer tower (90 hp to archers) and the catapult (нрнс), there is a full repeatability of battles regardless of the session; specifically, luck rolls for the peasants!

It is also clearly visible that each new session necessarily begins with a "random battle" (rb), after which a full battle repeat (fbr) cycle begins, and characteristically, the 8 rbs in the first attempt of each session are completely different (2 identical ones are marked in light green)!

Only in two sessions (3 and 10) did additional rb appear, which break the fbr pattern.

Of the 5 additional rb, 3 repeated (marked in dark green)!
Out of 10 sessions, in the first experience (attempt), 2 attempts repeated completely, and another 4 partially (marked in gray and light green).

Conclusions:

1) It is obvious that morale and luck in Heroes 1 are fixed given certain player actions, but unfortunately, there are "random battles" that prevent us from speaking of a 100% probability of battle repetition. Nevertheless, the probability of an fbr is very high, see table. Interestingly, in no session did an fbr occur on the first experience (attempt).

2) Morale and luck in Heroes 1 depend on the layout of the battle map rolled in a particular session. The battle map itself is fixed, and given certain human actions that determine this roll, it apparently remains unchanged until the end of the fight (determined by the Damage dealt and the actions leading to fbr). Morale and luck do not depend on time delays.

3) It also becomes clear that based on several damage values (in this case, the catapult and the archer tower!), one can tell which game map was rolled.

Note: In other battles, this can be observed via the damage dealt by monsters.

4) There is likely a certain cycle for rolling the number of battle maps per session, and moreover, the number of such maps is limited!

5) I believe that specifically in the first attempt of each new session, luck or morale can be triggered for virtually any monster, but only in the first (except for those who by definition do not roll these components)! This first attempt seems almost like a cheat.
Note – I don't know if this is a glitch or my inattentiveness in determining the archer tower damage, but as seen in the table, in 1 out of 100 cases during fbr, luck did not roll for the peasants (marked in yellow)!

Such are the ambiguous results and thoughts.

Respectfully, VDV_forever
Единый справочник по Героям Меча и Магии

ТУРНИРЫ ПО ГЕРОЯМ 1!:smile13:
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#156
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AlexSpl
2VDV_forever: I will try to anticipate the results of your tests:
1) The first battle of a session can be anything (any damage, any morale and luck for anyone);
2) In all other battles, the damage will be fixed (the same from battle to battle), and luck will only come to the peasants at the end of the first round.

I suspect that you and I are conducting tests in approximately the same way: we look at who will have luck/morale (in particular, we expect luck for the peasants), and then, at the beginning of the second round, we run away and reload again. By doing this, we will always catch the luck of the peasants, starting from the second battle of any session! The game really saves(!) R after running away!

It's very good that we are independently coming to practically the same results and conclusions!:smile03:

Indeed, I actually always ran away after the peasants got a lucky hit!, i.e., at the beginning of the next 2nd round!
And when I was lazy:o, i.e., I understood that they would get a semi-lucky hit, I ran away before their turn, and this can explain the phenomenon of "random battles" in my table, after the first round!!:smile03: !
Great AlexSPl! It seems the problem is solved!
Respect!

AlexSpl

For the sake of a clean experiment, I recommend starting a new session each time or, at least, not running away during the cavalry's turn. Then the probability of luck coming to the peasants should decrease sharply. And with the current approach, it will be 100%, starting from the second battle of any session.

I will definitely try! Testing continues, although this battle is already a little tiring:smile40:
AlexSpl

I also found the upper limit of the number of possible battle maps with fixed player actions - 1000.
How? :smile11:

P.S. Today I was testing for about 5 hours....:smile33:

Sincerely, VDV_forever
Единый справочник по Героям Меча и Магии

ТУРНИРЫ ПО ГЕРОЯМ 1!:smile13:
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#157
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Therefore, it is indeed possible to identify a battle map by looking at the damage dealt by two or three (sometimes, of course, more) pre-determined monsters (such as an archer tower). For example, if an archer deals 90 hp of damage, and the damage of a pair of gargoyle-griffons is 30-21 hp, then with a high degree of probability (possibly even 100%), it can be asserted that this is a peasant-peasant-berserker (PPB) map, and luck favors the peasants. Also, based on just a couple of damage values, it is possible to predict the magnitude of all other damage values in the current battle. Unfortunately, the probability of a PPB map will decrease significantly if the cavalry is not allowed to move while attacking.
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#158
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AlexSpl
Thus, it is indeed possible to identify a battle map by the damage dealt by two or three (sometimes, of course, more may be required) pre-determined monsters (e.g., an archer tower). For example, if an archer deals 90 HP of damage, and the damage of a pair of gargoyle-griffons is 30-21 HP, then with a high degree of probability (possibly even 100% probability), we can assert that we are dealing with a "perfect peasant bonus" (PPB) and that luck will favor the peasants. Also, based on just a couple of damage values, it is possible to predict the magnitude of all other damage values in the current battle.

Exactly!:smile03:
AlexSpl

Unfortunately, the probability of a PPB will decrease significantly if you don't move the cavalry while retreating.

However, I believe that if you consistently retreat with a different monster in every battle, say with swordsmen on the second turn, while performing absolutely the same actions, the repeatability should also be 100%:)! It should be checked!:smile03:
Although the chronology of events will be different, the PPB will be 100% starting from the second attempt! Super!

Sincerely, VDV_forever
Единый справочник по Героям Меча и Магии

ТУРНИРЫ ПО ГЕРОЯМ 1!:smile13:
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#159
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2VDV_forever: The number 1000 is taken from the executable file. At the beginning of the battle, the game generates a number from 1 to 1000, which is used as a "seed." Thus, the number of possible battle outcomes is limited to one thousand. But, I suspect that 1000 is just an upper limit, and in reality, the number of possible battle outcomes is much smaller(?). I will try to study the pseudo-random number generation algorithm in this game more closely. Perhaps I will find cases where a player, without any additional tools, can predict the outcome of morale and luck based on the damage dealt.

Added 7 minutes later
When I was talking about the morale of pikemen, I meant the following: Fireball provided a description of the probability. Of course, it was easy to repeat it because of the interesting property that the number R remains fixed if you quickly move a specific unit. But what about descriptions where the player's victory involves repeating the battle outcome? What is the probability that the organizer will repeat this battle?
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#160
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AlexSpl
2VDV_forever: The number 1000 is taken from the executable file. At the beginning of the battle, the game generates a number from 1 to 1000, which is used as a "seed." Thus, the number of possible battle outcomes is limited to one thousand. But, I suspect that 1000 is just an upper limit, and in reality, the number of possible battle outcomes is much smaller(?).

I will try to get to know the pseudo-random number generation algorithm in this game better. Maybe I will find cases where a player, without any additional tools, can predict the outcome of morale and luck based on the damage dealt.

:smile20:
AlexSpl

When I was talking about the morale of spearmen, I meant the following:
Fireball provided a description of the probability. Of course, it was easy to repeat it because of the interesting property that the number R remains fixed if you run away with a specific unit. But what about descriptions where the player's victory involves repeating the battle outcome? What is the probability that the organizer will repeat this battle?

Indeed, if victory is achieved through a specific battle outcome, it will be problematic to repeat it! I agree!
But, the probability that it will be achieved by a player (such an important victory) on the very first attempt of the session is virtually impossible, unless that player deliberately uses this obviously cheating (as it has become clear) 1 attempt in each session.
Again, it is possible to introduce a rule in the tournament regulations that strictly limits the use of such a tactic when playing in offline tournaments!
We need to think about this...

Do you even understand what we have done today (although we started working on this problem not today)? A discovery!!! Many thanks, dear AlexSpl! :smile20:

Sincerely, VDV_forever
Единый справочник по Героям Меча и Магии

ТУРНИРЫ ПО ГЕРОЯМ 1!:smile13:
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#161
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I tested the mechanic a bit more, but this time in a battle against neutral creatures. No repetition was observed after the first attempt. So, before drawing any conclusions, we need to find the conditions under which this repetition occurs.

It would be cool if the repetition only occurs in a task from Fireball :smile05:
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#162
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AlexSpl
I tested the mechanism a bit more, but this time in a battle against neutral creatures. No repeatability was found after the first attempt. So, before drawing any conclusions, we need to find the conditions under which this repeatability occurs.

It would be cool if the repeatability is only achieved in a task from Fireball :smile05:

We need to find a suitable battle with neutral creatures and test it there. I suggest testing on the same battle; is that an option?

So, are you saying that my theory might be correct?
VDV_forever

Unlike battles with neutral monsters, the algorithm for determining luck and morale in a battle with AI heroes is different and depends on the damage dealt by a specific monster. Therefore, in one way or another, the battle with AI heroes can be repeated! That is, for the same battle, with repeated playthroughs using load/save, the number R0 remains constant and unchanged!

I was indeed too quick to draw conclusions; we need to continue digging in the same direction and find 100% certain conditions :) Whew, it's all so difficult...

Sincerely, VDV_forever
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ТУРНИРЫ ПО ГЕРОЯМ 1!:smile13:
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#163
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So, are you saying that my theory might be correct?
It seems so. We need to check:
a) battles with neutral creatures;
b) battles with heroes in an open field;
c) castle siege.
I suggest testing on the same battle; is that an option?
I don't think it's that important. On the contrary, by testing different battles, we are more likely to get a reliable result.

Have a great weekend! ;)
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#164
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2VDV_forever: Unfortunately, the battle we are discussing is more of an exception than the rule.
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#165
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AlexSpl
2VDV_forever: Unfortunately, the battle we're discussing is more of an exception :(

Well, I'm sure there's some kind of dependency with the heroes, the main thing is to always retreat at the same time and perform the same actions. :p

With the neutrals, it seems to be completely random.:(

I'll be testing it thoroughly next week and will post the results here;

P.S. How is it possible in the program that there are exceptions in the form of PPB (probability per battle) in certain battles? I.e., in one battle, the program remembers this value (R), but in another, it doesn't?:smile07: There should be a specific algorithm, we just can't understand it (hopefully not yet), because it's not that simple and straightforward.

Sincerely, VDV_forever
Единый справочник по Героям Меча и Магии

ТУРНИРЫ ПО ГЕРОЯМ 1!:smile13:
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#166
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I conducted a small test on the initial stages of a siege, using a recent online tournament (OT) as an example. Out of 30 attempts, the wall was breached approximately an equal number of times at points 2 and 4 where units were stacked. The wall was never completely breached in any of the attempts. In one case, lightning spells had no effect on the defending dwarves. This suggests that each event is considered separately and occurs with a set of probabilities. Therefore, it would be very difficult for the tournament organizer to reproduce a complex battle where luck played a role 2-3 times in an official tournament, even after a very large number of attempts.
With best regards, Ergon.
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#167
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Ergon
I conducted a small test on the beginning of a siege, using a recent replay as an example. Out of 30 attempts, the wall was weakened approximately equally at locations 2 and 4. It was never possible to completely break through the wall. In one case, the lightning spell had no effect on the defending dwarves. This suggests that each event is considered separately and occurs with a set of probabilities. Therefore, it will be very difficult to reproduce a complex battle, where luck played a role 2-3 times in an official tournament, and this brought victory, even with a very large number of attempts.
With best regards, Ergon.

Good day!

Regarding the walls:;
http://handbookhmm1.narod.ru/10.html

In the case of the dwarves, this is indeed a probabilistic event, and the probability is 25%.
http://handbookhmm1.narod.ru/7.html

You need to test the battle itself, focusing on the chance of morale and luck, which directly depend on the damage dealt in combat (Damage) during certain actions. Using magic will change the nature of the battle, and consequently, the outcome of these factors may also change. However, morale and luck do not directly depend on the use of magic!

Sincerely, VDV_forever
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ТУРНИРЫ ПО ГЕРОЯМ 1!:smile13:
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#168
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P.S. How is it possible for the program to have exceptions in the form of repeatable battles on certain maps? That is, in one battle, the program remembers this value (R), but in another, it doesn't? There must be a specific algorithm, we just can't understand it (hopefully not yet), because it's not that simple and straightforward.

As our tests have shown, in some cases, a 100% repeatable battle is possible after fleeing. A prime example: the task from Fireball. In these cases, the first battle of any session can be anything, but starting with the second, the battle map repeats again and again and does not depend on the session number!

So, your Hero has left the battlefield, and you have reloaded. What are the conditions for the battle to repeat 100% after reloading?

It turns out that it is both simple and strange at the same time:

If the enemy hero gains one or more experience levels in the battle from which your hero fled, then all battles, starting with the second, will become constantly repeating battles (repeatable battles, VDV_forever).

So, in the task we are considering, Agar has level 8 (10000 xp). If he doesn't manage to kill 1000 xp to reach level 9, then there will be no repeatable battle! If he does manage to reach level 9, then the repeatable battle will be 100%! Moreover, the type of repeatable battle depends on how many levels the enemy hero gains in the battle.

Therefore, any battle with a hero can be divided into several parts:
1) the enemy hero did not kill enough creatures to reach the next level;
there will be no repeatable battle.

2) the enemy hero killed enough creatures to reach the next level;
the repeatable battle will be 100%.

3) the enemy hero killed enough creatures to gain several levels at once;
the repeatable battle will be 100%, although its type will depend on the number of levels gained.

In a battle with neutrals, obviously, there can be no question of a repeatable battle.

That's the way it is.
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#169
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I apologize, but let me describe a situation. Our hero has 10 gargoyles left, while the opponent has 30 peasants. The opponent's hero needs to kill one more gargoyle to level up. The first time, we let the gargoyle attack his peasants; he kills one, and we retreat. The second time, we simply eliminate his 30 peasants. What will happen the third time? There won't be a repeated battle (I assumed this was a constantly repeating battle; if not, I apologize).