The battle formula does not work properly

[velhbxtyrj]

Please review the code in which the bonuses for the troops are summed up from the hero and from the Blacksmith and Armoury. According to my calculations, these bonuses are not taken into account.

There is a possibility that I made improvements through the admin panel. But it is unlikely that the problem arose because of this.

[Shadowss]

Works in combat simulator. Why you don`t give us a screen for an example :

Send 2000 Imperian with 20 level in Armoury to battle with 2000 Spearman with 20 level in Backsmith. Also send same 2000 Imperian level 0 in Armoury to battle with 2000 Spearman with level 10 in Blacksmith. And print us the screens.

[velhbxtyrj]

Most likely I was mistaken. But as for me, the formula does not work very well for calculating these bonuses.

[velhbxtyrj]

I understood what you meant

Here are some comparison attacks. And this happens in every report.

First Attack

Second Attack

[martinambrus]

calculations, calculations....... @AL-Kateb would you care to investigate this math as well perhaps? :)

[AL-Kateb]

I'm on it :)

[AL-Kateb]

Here are some comparison attacks. And this happens in every report.

I tested the bonus from blacksmith and armory, according to the code, and according to my testing it is working fine, I did not check the hero bonus yet, but as for these two, the battle report matched the simulation 100%, even though it was a little bit off compared to the regular T4 legends simulator, but that's a different story.

I think I know why your reports are different from the simulation, as I noticed you entered 2677 in the population, there is no village that can go that high in population, clearly you're assuming the population taken into account here is the account population, but this is inaccurate, the population used in calculation is the VILLAGE POPULATION not the account population, hence the real attack does not match the simulation.

As a side note, while I was at it, I was transferring troops from one village to another (Same account), and apparently there's something wrong with that code, something is wrong with returning the troops, after a few actions I was able to change the home for my troops from one village to another! Which is a big issue, players can exploit this to produce troops from one village and send them all (change their home) to another, it is not as straight forward as this, some condition needs to be met, I am gonna check how to replicate this and see how to fix it, then I will get back to you.

[velhbxtyrj]

The general population is taken into account (the entire account), since there is an additional bonus of protection for weak players (when attacking the strong on the weak), this exists from the very first travian.

I'll give an example: I'm top in the houses and the strongest player on the server. I have a village with a small population (in which all my main attacking troops) in order that the bonus in the attack is not taken into account. It will be stupid compared to players who started playing much later and much weaker than me.

Perhaps this is the problem of calculating battles. Because of the fact that only the population of the village is attacked.

Sorry for the bad english. I write through translator.

In English, I could not find descriptions where it was said that the general population was taken into account, I could only find it in Russian.

[AL-Kateb]

I completely understand your logic, and it makes perfect sense, but as far as I remember, I was in an argument with a friend of mine over this a couple of years ago, we tested the original Travian and we concluded that the population used here is the one of the village, not the entire account. Which as you said defeats the purpose of the bonus.

But regardless of how original Travian behaves, the code as it stands today calculates the population of the village, not the account.

I will do more research to check what population original Travian uses, and if it is the account's population, it is easy to edit the code to reflect that.

[velhbxtyrj]

I can give you a link to the Russian-language text, which describes completely how the simulator of strife works. You can read this through an interpreter. There is also an excellent resource where this calculator is available in an expanded form. It is recommended by a lot of people to use. There is an account of everything that is present in the game of travian. Also this calculator is available here. If you are interested in calculating, then I think you can ask Kirilloid himself what and how to count. I will also give a link to the calculation of formulas (also in Russian). If there are difficulties with the translation, I can help.

http://travian.kirilloid.ru/warsim2.php - Advanced battles calculator (excellent resource), pay attention to the population (when hovering on the field is written what kind of population) http://t4.answers.travian.ru/?view=answers&action=answer&aid=261 - How does the battle simulator work? (http://t4.answers.travian.com/index.php?aid=289 - I found this in English.)

An important factor is the total population of the attacker and defender (not just of the village, but the total pop of the account across all villages).

http://travian.wikia.com/wiki/Combat_simulator - on this site speak about Kirilloid https://github.com/kirilloid/travian - from Kirilloid for travian

[AL-Kateb]

I just tested on Travian, even though the result was not exactly as the simulator it was closer to the one where I put the whole population instead of just the village population, so you're right.

I will modify the code accordingly

[velhbxtyrj]

http://t4.answers.travian.ru/index.php?aid=345 - it's in Russian, I could not find it on the English site (The battle system: formulas) I'll try to find it in English, but it's unlikely.

[martinambrus]

A very nice debate guys, I appreciate the time you took to look into this :)

[velhbxtyrj]

@AL-Kateb you have not forgotten about this problem? :)

[velhbxtyrj]

@iopietro Please pay attention to this problem, it is very serious for the game process.

[iopietro]

Fixed in c3e2bae.

@velhbxtyrj Let me know if i can close this issue.

[velhbxtyrj]

With the game calculator this perfectly matches. But a little different from that of another calculator :)

[iopietro]

Which calculator do you use? I've tried kirilloid and it works fine. (without walls, palace/residence and blacksmith/armoury)

[velhbxtyrj]

I only know the kirilloid calculator and I've been making attacks with improvements. Perhaps the situation is in bonuses from forges and walls. Here is my result of the attack:

[iopietro]

Yeah, you're right, with no forges/walls our battles are equal to kirilloid battles, but with forges/walls they're slightly differtents.

[iopietro]

Ok, it should be finally fixed in 5f9186b . Blacksmith and armoury upgrades are now counted correctly:

[velhbxtyrj]

This is an almost perfect battle :) You make the final decision :)

[iopietro]

I think that our formula has a very little differences than the kirilloid's formula. So, considering that the two battles are very very similar to each other, this issue is finally resolved :) (the battle formula can't be better than this, unless kirilloid gives us his formula).

[velhbxtyrj]

@iopietro I wrote a letter to Kirilloid. Let's wait can help :)

[kirilloid]

Attack/defense points for units are rounded to 4 decimals places after upgrades. So values for units in the bottom table are EXACT: http://travian.kirilloid.ru/troops.php#s=1.36 52.4048 means 52.4048000000...

Wall bonus is rounded to 3 decimal places or 1 place if percents are used. Again, these are exact values: http://travian.kirilloid.ru/build.php#b=31&s=1.36 80.6% means 80.6000000...%

[kirilloid]

Total attack/defense points are rounded to the nearest integer. Also notice there’s a slight difference between upgrade formulas in T3 and T4/T5. The formula is correct with the latest commit—just pay attention, which version do you use in my site, everyone.

Formula guide in English: https://wbb.forum.travian.com/thread/75248-combat-system-formulas/

[iopietro]

@kirilloid, Thanks a lot! Tomorrow i'll look into these formulas.

[iopietro]

@kirilloid I've looked at our formulas, and they seem equal to your formulas.

For example:

I think that the different results (with no wall bonus, no residence/palace bonus, no morale bonus, no unit upgrades bonus, etc.) are because of a wrong approximation in our formulas.

This is how our battle system works (without any kind of bonus):

For example: The attacker has 10k of Legionnaires and 90k of imperians (for a total of 100k of attacking troops). The defender has 50k of Phalanxes.

1) Calculate the total cavalry and infantry defensive points for the defender:

50k 40 = 2 Millions of infantry defensive points. 50k 50 = 2,5 Millions of cavalry defensive points. (useless in this case, because the attacker has no cavalry)

Involved troops in the attack= 50k.

2) Caltulate the total cavalry and infantry attacking points for the attacker:

10k 40 = 400k (Leggionaires) 90k 70 = 6,3 Millions (Imperians) For a total of 6,7 Millions of infantry attacking points and 0 cavalry attacking points.

Involved troops in the attack = 50k+100k, for a total of 150k troops.

3) Calculate the total attacking points:

Total attacking points = 6,7 Millions (because the attacker has no bonus in this case).

4) Calculate the total defensive points:

Total defensive points = Infantry defensive points * (Total infantry attacking points/Total attacking points)+0 (0 because there are no cavarly units).

Total defensive points = 2,0 Millions * (6,7 Millions/6,7 Millions) = 2,0 Millions.

5) And the winner is?

Total attacking points > Total defensive points, the attacker won.

6) Calculate the "K" factor: Involved troops >= 1000, so we have to calculate the K factor.

round(2*(1.8592 - Total involved units^0,015)) rounded at the nearest integer (or float), for a maximum of 4 decimal digits.

2 * (1.8592 - 150000^0,015)) = 1,3269 --> K = 1,3269

7) Calculate the result of the battle:

Attacker result (winner) = round((Total defensive points / Total attacking points)^K) rounded at the nearest integer (or float), for a maximum of 8 decimal digits.

Attacker result = (2000010 / 6,7 Millions)^1,3269 = 0,20105780 = 0,2010578

Defender result (loser) = round((Total attacking points / Total defensive points)^K) rounded at the nearest integer (or float), for a maximum of 8 decimal digits.

Defender result = (6,7 Millions / 2000010)^1,3269 = A number greater than 1. Defender result = 1.

8) Calculate the attacker losses:

10k 0,2010578 = 2010,578 = 2011 Leggionaires (rounded at the nearest integer/float number). 90k 0,2010578 = 18095,202 = 18095 Imperians

9) Calculate the defender losses:

50k * 1 = 50k Phalanxes, all defender's units are dead.

So, i don't know what approximation is wrong.

P.S: Sorry for the wall of text, lol.

[kirilloid]

Step 6: rounds to the nearest multiple of 0.0002, the formula should be

2 * round(1.8592 - pow($total_units, 0.015), 4); // 1.3268946071185956

K = 1.3268

[iopietro]

Ok, I modified the formula from:

round(2*(1.8592-pow($involve,0.015)),4);

To:

2*round((1.8592-pow($involve,0.015)),4);

($involve = total units)

But there's still a very little difference (without bonuses):

Infantry attacking points = 1635870 Cavalry attacking points = 628080

Infantry defensive points = 805660 Cavalry defensive points = 2275410

Total attack points = 2263950 Total defensive points = (Infantry defensive points (Infantry attacking points/Total attacking points)) + (Cavalry defensive points (Cavalry attacking points/Total Attacking points)) + 10 = 1213417,7771152

K = 1,3634

Attacker final result = round((Total defensive points/Total attacking points)^K),8) = 0.42728169 Defender final result = 1

Attacker losses: 19293 0,42728169 = 8243,54564517 = 8244 Leggionaires 12345 0,42728169 = 5274,79246305 = 5275 Imperians 5234 * 0,42728169 = 2236,39236546 = 2236 Equites Imperatoris

Defender losses: all troops are dead.

[iopietro]

I changed that formula with your formula and it seems to work great:

 $rdp = round($cap/$rap, 4)*($cdp) + round($ap/$rap, 4)*($dp) + 10;

1) $rdp = Defender result points 2) $cap = Cavalry attacking points 3) $ap = Infantry attacking points 4) $cdp = Cavalry defending points 5) $dp = Defensive points

[kirilloid]

Yes, wanted to say about the mix of infantry and cavalry, should be round to 4 decimal places. Total defensive points would be 1213418 rather than 1213417,7771152, total points are rounded to the nearest integer (that's obviously important for small values). Attacker final result no need to rounded with round(... , 8) Doesn't really matter, though.

[iopietro]

Ok, thanks, i modified it and now it works great, with all kinds of bonus (walls, residence/palace + base defense, troops upgrades) except for the morale bonus, i don't know how it should be approximated (i tried 3 decimal digits):

If Total attacking points < Total defending points

$moralbonus = round(min(1.5, pow($attpop / $defpop, 0.2 * ($rap / $rdp))), 3);

else

$moralbonus = round(min(1.5, pow($attpop / $defpop, 0.2)), 3);

But it's slightly different than your simulator.

[kirilloid]

Yes. I use a single expression with min function, but the logic is the same. The trick is inverse value should be rounded. You might think about it as a handicap for attacker rather than moralebonus.

// here it's still a bonus, you multipy it the same way in all other parts of code.
$moralebonus = 1 / round(max(0.667, pow($defpop / $attpop, 0.2 * min(1, $rap / $rdp))), 3);

Also I don't see from the code your shown, whether there's a check that moralebonus cannot be less than 1.

[iopietro]

Nice, it works perfectly :)! Yes, it's a huge handicap in certain cases. Yeah, there's a control which decides if it should apply or not the formula, this is the whole code:

        if($attpop > $defpop) {
            $moralbonus = 1 / round(max(0.667, pow($defpop / $attpop, 0.2 * min(1, $rap / $rdp))), 3);  
        }else{
            $moralbonus = 1.0;
        }

[iopietro]

I've another question, what is the formula which determines the new level of a building partially demolished by catapults/rams (I can't find it in your guide)?

For example (with no bonuses, no defenses, no losses):

10 catapults will bring a building from level 20 to level 18, how can i know that the new level must be 18?

[kirilloid]

https://wbb.forum.travian.com/thread/75248-combat-system-formulas/ See 3.a Catapults Target level N. For every level k find amount of catapults enough to demolish building completely. Find minimum k such that (amount of catapults to demolish N) minus (amount of catapults to demolish level k), that would be final level.

Actually I don't know why do you need super-precise calculations. My research is not ideal anyway. There are problems with stonemason or/and artifact. Formula gives big error for lower level buildings.

[iopietro]

Thanks! Yeah, I saw that chapter, but I haven't thought about that formula. Because your combat system simulator is the best external tool for simulating travian battles :)! It could give errors for lower level buildings and stonemason/artifact, but it's much better than our previous formula (not the actual one that I've made, that works pretty good) that used to calculate square roots of negative numbers, lol (resulting in an error, obviously).

[Shadowss]

Can be closed ?

[iopietro]

Not yet, there's still a discrepancy with the battle formula, when you attack a village with a wall and you damage/destroy it, the whole battle is recalculated, but battle results are a lot different than the original travian.

[Shadowss]

Ahh ok

[Shadowss]

I wanna ask if is counted in battle formula next attributes :

• Earth wall (teutons) is harder to destroy then other walls (roman and gauls walls)
• City wall (romans) is the easyest wall to destroy
• Palisade (gauls) is the half between romans and teutos walls

[kirilloid]

Maybe, create a separate issue for rams? For me “combat formulas” seems more like an epic, rather than one issue. But it’s up to you.

Walls durability coefficients are:

• city wall: 1
• palisade: 2
• earth wall: 5

[kirilloid]

Also you might be interested in https://github.com/kirilloid/travian/commit/4a78db0d614e58a97dd03facf0581220665d3330

[iopietro]

@shadowss, Yes, they're already implemented.

@kirilloid, The only wrong formula is the one that recalculates the battle after the destruction/damaging of the walls, while the formulas that calculate how much a building have to be damaged (for rams and catapults) are slightly different than yours.

[iopietro]

@kirilloid Sorry in advance for the distrubance, but I would ask you some questions:

1. I implemented your exact formula ("demolishPoints" in kirilloid/travian@4a78db0), but I don't know the exact point of it in which I can divide or multiply the catapults morale bonus.
2. In a forum thread, you talked about this: How can this "virtual intermediate level" be calculated?

Thanks for the help!

[kirilloid]

Technically now I have a solution, but it is incorrect with low wall levels and artefacts. Let me play with new simulator on PTR and I'll return back to you.

[iopietro]

Ok, thanks again :).

[kirilloid]

In new simulator rams works just incorrectly

[iopietro]

Lol, nice, did you report it to the Travian's devs?

[kirilloid]

Yes, I reported and they accepted it. I'm in the process of updating code, rams weren't added yet, but you might be interested in other aspects, illustrated with tests: https://github.com/kirilloid/travian/commit/26b27f0a9a98dda196c9154faf1545dbd9ac5066