# Strategy game math

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I've been searching around to try to find good articles that discuss the math behind a strategy game. I'm not talking about visual math, but more about how do stats like ATK and DEF react to each other? While it seems like this tends to be more difficult to make generic due to the massive amount of differences in each strategy game, I get the sense that there are some common elements between these games that can create some base algorithms for calculations.

The core example I'm trying to figure out is, given an Attack Strength for an attacker and a Defense Strength for a defender, what would be the actual damage caused by the attacker? I'm hoping to find a solution that will prevent a certain DEF from overpowering an ATK, but should be more appropriately based on their differences, and ideally won't be based on random chance (though it could be included for a CRITICAL type of modifer). This wouldn't take into account the actual attack speed, since that would determine the rate at which this algorithm runs.

Some articles I have found thus far:
http://na.leagueofle...5201&highlight=
http://serenesforest.../fe10/calc.html
http://en.wikipedia....ing_mathematics

TL;DR - Does anyone have any thoughts as to some simple algorithms that can take statistics of Attack and Defense and calculate the damage that would be done by an attacker? Any suggested reading is welcomed as well!

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You could make atk a number and def a %of damaged blocked, that way at least a little damage would always go through.

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There are a lot of ways to do it. It depends on what kind of relationship you want between the 2 values. They also come with border cases which break the whole system, so you need to take this into account too. You should figure out the higher level relationship between the units before deciding of a damage formula. This should let you know if you need some extra parameters. For example, Starcraft has damage and armor types to create a circular counter system that wouldn't be possible with a simpler damage formula.

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I like the super straight forward models like the ones in Starcraft. If something has 10 "attack" then it does... well 10 damage, duh. Then there is armor that reduces damage by the armor value. So an attacker with 10 damage that attacks a 2 armor defender deals 8 damage... Combine that with attack speed and you get an already very versatile and easy to understand system. An attacker with huge damage but low attack speed will almost ignore armor but overkill small targets. On the other hand with low damage and high attack speed you get more "economic" killing of small stuff but also have a harder time against armor.

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Great ideas! I think the "percentage block" makes the most sense, since it is a more direct relationship that ends up adjusting if the statistics increase or decrease. On the basic level, this type of algorithm is the driver. Then bringing in the armor types and weapon types (like Tiblanc mentioned) as well as other modifiers such as breakable armor or critical hits will give your equations a higher meaning. I was noticing how this compares to Pokemon, at least in the Blue version, where each creature has a series of values including ATK and DEF, that power it through each battle. These are obviously modified by the type of creature and the weakness/strength of the enemy, but the idea rings true.

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The formulas depend on the desired game balance. For example, in Pokemon fights having the right moves and choosing the right type of Pokemon is expected to be normally more important than grinding upwards the stats and level of one's Pokemon: accordingly, attacker vs defender type combinations affect the "bottom line" (double or half damage, almost guaranteed success or failure of special afflictions) drastically, moves form very effective combos, while stats are usually close in value between opponents and less useful.

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