Oracle's inevitable criticals

Hi all, I'm relatively new to PoE! I'm currently trying to understand how the new inevitable crits work.

TL;DR: If my calculations are correct, you get the most bang for your buck out of this mechanic by keeping your crit chance just above 20% while maximizing your crit damage bonus, you need to get it to at least 300% for this mechanic to be worth it IMO.

I don't know how this mechanic interacts with other crit mechanics, but I'm definitely itching to try it with Tangletongue!

My current calculations are:

"

c = crit chance
b = crit bonus
f = 0.7 -- not sure if it should be 0.7 or 1 / 1.3 ≈ 0.77


Standard expected damage:

(1 - c) dmg + c dmg (1 + b)
= dmg (1 - c + c (1 + b))
= dmg (1 + c b)


Expected damage w/ inevitable crits:

dmg + dmg c b + dmg (1 - c) c f b + dmg (1 - c)^2 c f^2 b + ...
= dmg (1 + c b \sum_{k = 0}^\infty [(1 - c) f]^k)
= dmg (1 + c b / (1 - (1 - c) f))

In other words, it effectively replaces your crit chance with c / (0.3 + 0.7 c) - here's a Desmos plot for convenience: https://www.desmos.com/calculator/wugkee1hey

UPD: I took the ratio of the expected damage with and without inevitable crits and visualised it in Desmos: https://www.desmos.com/3d/mu2bexnlzc

Here, the axes are as follows:
- x: Crit chance (0 to 1, meaning 0% to 100%),
- y: Crit damage bonus (1 to 5, meaning +100% to +500%),
- z: The ratio of the expected damage with and without inevitable criticals.

The red surface is the ratio itself, as you can see it varies between 20% more and 40% more for realistic parameter values. The blue surface intersects the red surface at a curve that gives us the biggest improvement for each fixed value of the crit damage bonus. Its formula is c = (sqrt(30 b + 30) - 3)/(10 b + 7), I found it by plugging the ratio into Sage:

"

x, y = var('x,y')
dr = (1 + x * y / (0.3 + 0.7 * x)) / (1 + x * y)
solve(diff(dr, x) == 0, x)

Here is its graph, plotted separately for convenience: https://www.desmos.com/calculator/bd6bdqzg1j