# guide Battleforge Math

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So here I'd like to work out any math problems people may have about Battleforge! Send me your questions and I'll try to answer them.

For starters, here is a mathematical model of your power pool and an explanation of why t4 is a terrible idea in PvP 1v1.

• time t is measured in 2 second increments (because that's how the game adds power)
• v(t) is the power in the void pool as a function of time t.
• p(t) is the power in the power pool as a function of time t.
• w is the number of power wells  a player has
• p0 is the power at the start (i.e. p(t0)=p0)

Your void pool returns 1/50 of its power to the power pool. If we modeled a differential equation, dv/dt=-1/50v. Solving for v, v=v0e-t/50. This is perhaps a little complicated, so I'll show you another way that is more intuitive.

Let's develop the model by inspection.

v(t1)=(49/50)v(t0) because at 2 seconds [that's v(t1)], the void has lost 1/50 of the void at 0 seconds [that's v(t0), or v0].

v(t2)=(49/50)v(t1) for the same reason as above. Since v(t1)=(49/50)v0, v(t2)=(49/50)(49/50)v0. In other words, v(t2)=(49/50)2(v0).

v(t3)=(49/50)v(t2) which equals (49/50)3(v0) and I think you can get the pattern. The void pool can then be calculated as

v(t)=v0(49/50)with t measured in 2 second increments (so t=4 means 8 seconds).

This way is actually a bit more accurate (since the method with a first order linear homogeneous differential equation is compounded continuously and it's actually compounded every 2 seconds) so we will go from here.

This model describes the void pool at any given time (assuming that nothing else is added to it). So to find the amount of power that the void pool injects into the power pool, it will be v0-v0(49/50)t. Or in other words: v0(1-(49/50)t).

We furthermore know that the power in the power pool increases by 1 power every 2 seconds from every well. Thus,

p(t)=wt +v0(1-(49/50)t) +p

* @Hirooo commented that the portion v0(1-49/50)t maxes out at 20. So if your void goes above 1000, you will get a steady +20 from the void every 2 seconds until the pool goes below 1000, when you'll gain like normal.

If you plug this into a graphing calculator, you can easily see what a difference in void power makes. For instance, type p=wt+v(1-(49/50)^t) +C into https://www.desmos.com/calculator and make sure to use sliders for w, v, and C (you can use any letters). This will model any power if you assume that nothing gets added to the void pool and no wells drop or get added.

I'll illustrate how to use this model to explain why t4 is bad for power. Sometimes people ask "since enlightenment is 260 power, why isn't it just better to use t4 for an extra 40 power, and then you can play t4 cards whenever." Here is why.

Suppose you've graphed that function in desmos. C&P so there's two and then change the variables w,v, and p for random constants (if you want a ballpark estimate, w=4, v=600, p=100). Those constants don't really matter for this though, so you can even make anything that doesn't change 0 if you want. That's what I will do for this comparison. Since we want to see what happens if I spend 260 power (234 void)  for enlightenment vs 300 power (0 void) for a monument.

The equation for using enlightenment looks like p=234(1-(49/50)^t) +40 because w=0 (it doesn't matter if we assume both players have the same wells) and C=40 because enlightenment is 40 power less than a monument.

The other player has p=0 because w=0, v=0, and C=0. Note that you can put whatever numbers you want here as long as the first equation has C=40 higher than the second equation's C, v=234 higher than the second equation's v, and w is equal.

The difference between these two functions tells us how much more power the player who used enlightenment has. After 10 seconds (t=5), the player who used enlightenment has 62 more power than the other. After 30 seconds (when the monument gets built) the player with enlightenment has 101 power more than the other. As time goes on, the player who used enlightenment will eventually get 273 power more than the other.

Hope this model was useful! Feel free to ask any questions or propose more math subjects!

I have also created a supplementary video: https://www.youtube.com/watch?v=zhqUuZMUb0Q

Edited by Eirias
LEBOVIN likes this
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Maybe I did not read carefully enough in that case i apologize but shouldnt the voidpower gain limit of 20 be mentioned?

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Doesn't this really say that you shouldn't got T4 in PvP because you actually BIND power you are not going to get back fi you destroy it? If using enlightenment to summon T4 you instantly put a lot of it in the void, and by constructing T4 that power is gone for good.

(Don't worry I do find numbers interesting:D)

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Maybe I did not read carefully enough in that case i apologize but shouldnt the voidpower gain limit of 20 be mentioned?

I didn't actually know there was a limit of 20. I don't think it really makes much difference though, because if you are getting 19 void every 2 seconds vs 21 every 2 seconds, the guy with t4 is going to win. Power doesn't really matter at that point. The power will come back eventually, but there will just be a flat line until it naturally starts going below 20. I'll add your comment though.

@Chimerae Yes, that's the point. It graphs exactly how much power difference you have if you bind power instead of "wasting" it. You can basically just use the calculation to see any difference between player void and how that power comes back.

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Germanwings likes this
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?

he wants me to participate in this forum but i dont think its wort tha affort i mena u created a graph for the void energy  decrease wich is technicly 1%/sec capped at 20 power

but i dont know why we need to discuss this mathemaicly Edited by Anonymos
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the reason why t4 is not wort its bound power is more simple:

first of all the hp of orbs and monuments in bafo do not scale into the game this is really important vbecause destroying them is the way to win

after realizing this the second step is to realize that the unitpower/energy quotioent increases over the tiers (a t1 unit has worse attack and hp/ energy than a t2 or t3 unit does)

a long time ago i approximated the energy wich u have to play in t2 to pay out the 150 orb cost to ~200 power. I dont really know if this is mathematicly correct (if someone has to much time he could check it :D)  but it genereally means a t2 unit doubles a t1 unit in  combat power. u need to keep this in mind when rushing a t2 since u havet to pressure the enemy to spend energy inefficient in order to keep up with the raw power t2 units bring into the field.

well the unit power / unit cost  quotient scales way harder when comparing t2 to t3, meaning when a t2 unit is much stronger than a t1 unit a t3 unit is way way much more stronger than a t2 unit .

this means if u want to stay t2 vs t3 u pretty much have to kill a orb or multiple wells to stay in a game xD.

in addition t3 provides a lot of finishing options (jugger, sandstorm, tremors, cultmaster/ anti sepll aura (forgot its name))  wich where really hard to defend (i´n gneral!!! everyone knows timelessone but whatever). One of many parts is the 2k hp of wells /3k hp of orb wich i mentioned earlyer.

while in t1 a well attacked by 100 power lives like 25  secs in t3 a well attacked by 100 power lives like 8 secs? this means as soon as u loose the tempo fight on the battlefield by spending 300 energy to build a t4 u will get crushed u will not have the time to spend ur energy in t4 long enought to make it worth

Edited by Anonymos
Germanwings likes this
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• 2 weeks later...

the reason why t4 is not wort its bound power is more simple:

first of all the hp of orbs and monuments in bafo do not scale into the game this is really important vbecause destroying them is the way to win

This is the most important thing here. Orb's and power well's hp doesn't scale with game time. Which means you can hardly go to a "late game". Which would be when you can play out all your T4 cards. The other reason for no late game cards is the limited deck size so people don't really use them in pvp.

It would be interesting to see a game mode with bigger deck size and scaling orb and power wells. But that would require more power wells on the map Edited by Azta

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