3 EQUATIONS TO SOLVE HEARTHSTONE

Community Discussion
Hello,
I'm a physics student and for the last 3 years I developed a theoretical model for Hearthstone where I utilize the scientific method to arrive into equations that describe all elements within the game with great precision and accuracy.
The game can be divided in three major elements: Cards, Minions, and Hero Health. Each one of them have an equation to describe its value in the unit of Mana.

Equation 1, value in mana(V) of the effect of a card that costs (C):
V = 2(C+1)

Equation 2, value in mana(V) of a minions with attack (A) and Health (H):
V = Sqrt(5 * A' * H), Square root of 5 times the Health and the effective attack

The effective attack (A') is defined as:
A' = A , if A<4
A' = A - (A-3)²/12 , if 4<=A<9
A' = 6 , if A>=9

Equation 3, value in mana (V) of dealing (n) damage to the enemy Hero:
V = 12(ln(12)-ln(12-n))
12 times the diference betwen the natural logarithms (as result of a integral)

Variation of Equation 3, value in mana (V) of restoring(n) health to your Hero:
V = 12(ln(12+n)-ln(12))

I encourage anyone interested in this topic to test and question those results, to verify the consistency of this method in predicting the relative strength of cards. To do so you can quantify card effect (E) and divide by the value of a card with the same cost (V=2(C+1)) to get the efficiency of that card.
Efficiency = E/V

Example: Let's analize the card "Antique Healbot", a card that is considered above average and therefore has a efficiency above 100%
E = 3/3minion + Restore 8 Health
E = Sqrt(5 * 3 * 3) + 12(ln(20)-ln(12))
E = 12,84 Mana
V = 2(C+1) = 12 Mana
Efficiency = 107%

For anyone curious to know how I arrived into those equations, I have an article that describes with great detail the deduction of these and other formulas. To not break any rule in the Code of Conduct I will not leave the link in this post(I would like to hear from a moderator about this subject), but my article can be found in the Google sites domain by the name: "laws-of-hearthstone".
My objective is to share my findings with the Hearthstone community and eventually reach to the development team at Blizzard to improve future balance of cards. I would be very thankful to hear any idea or information to help me achieve this goal.
Well, that is pretty neat eh. Tip of the hat to you sir/madam.
I feel the must of giving you credit for the equations ... I study engineering and I know the amount of time and effort that kind of thing takes .. I'll study your model and test it in my free time ..
I do not study engineering and have no idea what it all means but am equally impressed! This is what i love about gamers & nerds <3
It seems good as far as it goes although I'm unsure what use anyone could make of it. It also suffers because it does not take account of Battlecry or Deathrattle, or of on-going effects (such as give other minions +2 attack), these things should surely affect the efficiency of a card.
02/10/2019 12:47 AMPosted by Clin1951
It seems good as far as it goes although I'm unsure what use anyone could make of it. It also suffers because it does not take account of Battlecry or Deathrattle, or of on-going effects (such as give other minions +2 attack), these things should surely affect the efficiency of a card.

Hi,
Those equations are just a small part of much bigger article, I think that you would enjoy reading it, there you can find how to quantify all of those effect that you're saying and have a detail demonstration on how to get to the equations.
I recommend taking a look
https://sites.google.com/view/laws-of-hearthstone

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