Short introduction; For almost one year I have been hardly working with decoding and coding the simulator algorithm, both for archer and non archer(classic) worlds (check my signature for more info).

Though, when I was working with the rams vs wall formulas I ended stuck, even with what seemed as a great thread by Cheesasaurus.

So, for all other people, being interested in getting the most out of your nukes(or defenses), or just knowing how some of the game mechanics works, here goes the true formulas:

Rams - A clooser look on how they work

Training time (in seconds) = 3200/[world speed] * 1.06^(-[workshop level])Bonus Wall

You might know that rams lower the wall, but did you know that they also negate the bonus your wall give to your troops while fighting?

At the beginning of the battle if your have level 20 wall, it will double the defense of your troops.(Giving a 2.07(207%) bonus)

This bonus can be calculated with following formula(the enemy havingfor the moment):0 rams

Formula 1

Note: Why 1.037? I have no idea :Pbonus = 1.037^[Wall]

But this bonus can be negligated if the attacker have rams.

Actually what happens is that the [Wall] level will be "downgraded", and out of this level, the bonus, as in the formula above, will be calculated. But the level to which the wall is downgraded isthe downgraded level at the end of the simulation. We will call this level(to which the wall is downgraded) thenotbonus_walllevel:

Formula 2

Note: Why 1.09 and 8? No idea neither :Pmax= [Attacking_rams] * [Attacking points of 1 ram at level 1] * [Attackers_Religion]/(8 * 1.09^[Wall])

Note for Religion: If the troops have beliefe, the religion is 1, if not it is 0.5. If world doesn't support church, religion is 1.

Note for attacking points of ram: Can either be 2(without ram paladin item) or 4(with ram paladin item)

Formula 3

So now we can write the Formula 1 yielding for Rams attacking too:bonus_wall= [Wall]-Round[max])

Formula 4

Example:bonus= 1.037^[bonus_wall]

Now there is anAttacker: 1000 axes, 100 Rams || Defender: 500 spears, level 15 Wall

Both with beliefe.

max = 100 * 2 * 1/(8 * 1,09^15) = 6.863451033

bonus_wall = 15-7 = 8

bonus = 1.037^8 = 1.33730372importantremark to do. The bonus_wallcan notbe smaller than the half of the wall level(or the forth in case of ram item). So;

Formula 5

and;min = Round(1/2(or 1/4) * [wall])

Example:If bonus_wall < min then bonus_wall = min)

Attacker: 1000 axes, 300 Rams, 1 Paladin|| Defender: 500 spears, level 19 Wall

Both with beliefe. Paladinwith ram item.

max = 300 *4* 1/(8 * 1,09^19) = 29.17345048

bonus_wall = 19-29 = -10

min = Round(1/4*19) = 5

bonus_wall < min , so --> bonus_wall = 5

bonus = 1.037^5 = 1.19920597Wall downgrade

Now, how many levels your wall is downgraded to in the end of the battle depends if the defender win or looses:

If Attacker wins:

Formula 6:

Wheredowngraded_level = [wall] - Round(max * (2 - Ratio))Ratio = attacking_units dead/ attacking_units totalfor archer worlds andRatio = (deffense points/ attack points)^1.5for non archer worlds.

If Defender wins:

Formula 7:

Wheredowngraded_level = [wall] - Round(max * Ratio)Ratio = defending_units dead/ defending_units totalfor archer worlds andRatio = (attack points/ defense points)^1.5for non archer worlds.

Now, how to find out the minimum of rams to use, and why the number 213 rams is floting around will soon be explained too, when I continue writing the guide.

As for now, I hope it was interesting;

-capi