Let's try to put it all together now. We're going to continue to ignore the time spent casting the spells that are burning mana. We're going to assume that as long as you have health to burn, you'll be canni-dancing the manna robe. Once you've burned through the health you have to burn, you'll canni-dance to match your passive health regen. We'll write equations in terms of ticks, and calculate how many ticks until you run out of mana. Mana burn will be guestimated at 500 mana/minute or 50 mana/tick. For explanatory purposes we'll assume 3500 mana and 2000 health to burn - meaning that after you've burned through 2000 health you're at 20% or whatever safe minimum threshold you've chosen. For now we won't worry about the casting time of the spells that burn mana; it's just a constant 50 mana/tick drain.
At the end of this post we'll have equations for mana burn rate and health burn rate before and after you've burned through all extra health. In the next post we'll take those equations, solve for the time until zero mana, and answer the question initially asked:
If you want to add hp or mana to extend the time until out of mana, what's the relative exchange rate between the two?
We have a couple of equations to juggle:
h(t) is current health after t ticks have passed
m(t) is current mana after t ticks have passed
Balimor explains the regen options here:
https://wiki.project1999.com/Kurrat%...f_the_universe, but we'll just assume 29 hp/tick from regrowth, z-heart, phantom armor, and standing regen. Since manna robe costs 60 health, that means the steady state after we've burned all the health we can is one click every other tick. Since two ticks regens 58 health we're close enough.
In the first phase, we'll canni-dance the manna robe until we run out of health:
each tick, you'll burn 60 hp, regen 29, and start at 2000 hp, so:
h(t) = 2000 - 60t + 29t = 2000 - 31t
And each tick we're assuming a mana burn of 50, while a manna robe click each tick gets us 20 mana for an adjusted burn rate of 30 mana per tick - note that this isn't accounting for medding mana regen yet.
m(t) = 3500 - 50t + 20t = 3500 - 30t
total ticks in the first phase:
h(t) = 0 = 2000 - 31t
t = 2000/31 = 64.5 ticks
If you graph h(t) you'll see a straight line with a value of 2000 at ticks=0, and a value of 0 at ticks=64.5
If you graph m(t) you'll see a straight line with a value of 3500 at t=0, and a value of 1565 at t=64.5
In the second phase you'll click manna robe every other tick
h(t) = starting health + 29t - 30t = starting health -1t ; we're just not going to worry about losing one health per tick
m(t) = starting mana - 50t + 10t = starting mana - 40t