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  1. 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 hasp0 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)t 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) +p0 * @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
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