Rather than a growth, why not have it do burst damage?
For example, it does not normally do damage, but it stores a charge with each "Pump." With each additional "Pump," the cannon has a chance to discharge, dealing, preferably, a large amount of damage.
That could work well. How does this sound:
"Weapon (Ranged): Deals damage based on psi.
Pump (reusable): Increase psi by 1, Lose half psi per turn."
Damage function could be something like:
damage(x) = 2 + 8*(.9*x)^4/(4 + (.9*x)^4) + .25*x
which gives:
- psi, damgage
- 0,2
- 1,4
- 2,9
- 3,11
- 4,11
- 5,12
- 6,12
- ...
- 9,13
- ...
- 13,14
- ...
- 62,26
At this cap, an OTK would indeed be possible, but would require 4 cards, 75
, and 7
(this+animate+ pump till 10
left+ sky-blitz+ parallel uni.). Thats gotta be harder to pull off than instosis due to the high quanta requirements.
This makes it much different than growth I think. It outpaces growth on quanta per damage point up to 5 quanta spent, but you have to keep inflating it every turn to maintain it or it rapidly drops back to the base 2pt damage.
Thematically, this seems to model an air gun fairly well I think. As long as you keep it pumped up, it does decent damage, but repeated uses will rapidly run it out of pressure.