I calcaulated exactly how much crit chance does lucky give you

So I did it all in my head because I was born a math genius and my head enable laser accuracy and took me 30 secs instaed of several hours.

but you can mimic my head if you wanna see it yourself by using a method I developed for you:

use a random number generator to generate 10 attacks 10 times so in total it will be 100 attacks without lucky.

10 none unique numbers from 1 to 100 if crit is 20% then any number between range of 1-20 is a crit. so you should get by average 2 points between 1-20 10 times so total crits should be 20 crits out of 100 random numbers.

If that is not the case then change RNG website/softwear until you find a decent one.

now to simulate a lucky(for example:20% crit chance) you would generate 10 numbers from 1 to 100 then if you somehow get 4 crits out of 10 then you generate 6 numbers from 1 to 100 and any number falls from 1 to 20 is a lucky crit so if its 1 number then you 4 plus 1 equals 5 crits in total

you do this 10 times simulating 100 attacks with lucky.

if your RNG generator is perfect you should get 20 crits and 16 lucky crits if your results are no where near that then either try again or faulty RNG. if its always identical 20 crit 16 lucky crit then you must be using a quantum computer because that means you are using a true RNG.

use a number sorter to quickly coun the crits. a number sorter will also reduce human error

anyway my head is true RNG and simulated maybe thousands of attacks in mere secs with pen and paper it would take several hours

Here is argumentative proof for 20% plus lucky equals 36% crit chance: if your chance to crit is 20% it means 10 attacks will give you 2 crits and 8 none crits on average. lucky will activate 8 times. and 20% of 80% is 16% so total crit is 36%


Now I will do from 0% to 100% ten percent at a time:

0% lucky doubles crit chance lucky is at maximim potency total crit 0%

10% lucky gives 9% total 19%

20% lucky 16% total 36%

30% lucky 21% tpta; 51%

40% lucky 24% total 64%

50% lucky 25% total 75% (lucky increases crit chance by 50%)(maxumum efficiency of lucky is this point, boynd this point lucky starts to lose efficiency)

60% lucky 24% total 84% (around this point you reach maximum effiency of crit chance you need 10% crit chance to gain 7% and 20% crit is needed to gain 12%)

70% lucky 21% total 91%

80% lucky 16% total 96%

90% lucky 9% total 99%

100% lucky 0% total 100%

now I have also discovered that 91% with lucky is more dps than 99% with lucky LOL

91% lucky 8.1% total 99.1% (so if you increase crit by 1% (from 90% to 91% you lose crit chance due to lucky factor and only increase by 0.1%)

99% lucky 0.99% total 99.99

99.1% lucky 0.8919% total 99.9919% (0.1% crit is actually 00.0019% crit chance incrase)

85% lucky 12.75% total 97.75%

75% lucky 18.75% total 93.75%

So in conclusion assuming 100% crit chance is achievable its waste of passive skills and gear its better you get crit dmg increase. The best crit chance with lucky is either 50% when lucky is efficient or 59% where crit chance plus lucky is most effienct or somewhere in between, but this is speculative I have never played a crit build.

spark crit builds who insta nuke bosses could you elaborate which crit chance is most effient? you guys experimented

I was wrong about lucky I baselessly assumed it is better than double crit chance that its magically so powerful and the more crit chance the more powerful it becomes.


after doing the math, mathmatically impossible to give you more than double crit(only achievable at 0% crit chance)

it grows more powerful as you increase crit chance until you reach 50% crit chance it peaks at 50% where it is at maximum potential then it losses its potency as you go beyond 50% either way (less or more than 50%)

It don't take a genius to understand how "lucky" works. You also don't really have to do any calculations, and even if you do, they'll be wrong. because it don't give you flat percentage.

Even if you have 99% chance and chance is lucky, it will not be 100%. You will still end up missing that missing 1%.

Sorry to debunk your geniusness, but even the math don't add up.


1. Misunderstanding of “Lucky”
In games like Path of Exile, “Lucky” doesn't add extra crit chance — it means:
You roll twice and take the better outcome.

2. Wrong math in later examples
You claim things like:
“50% lucky = 25% crit”
That's not how lucky works. The formula is:
Plucky=1−(1−p)^2

3. Simulation misunderstanding
You describe:
Generating 100 random numbers between 1–100
Calling anything ≤20 a crit (20% chance)
Doing that 10× and counting results

That's fine in principle. But:
The result won’t always be exactly 20, even with perfect RNG — it's probability, not certainty
Blaming “faulty RNG” if your test doesn't give 20% exactly every time is incorrect — randomness includes variance

4. Table of lucky values is off
Your table suggests weird things like:
“60% lucky gives 84% total”
But:
Plucky=1−(1−0.6)^2=1−0.16=0.84

I simplifify it in my head as "lucky roll on X% means: X% will succeed on their own, X% of failed rolls change to succeed due to follow up lucky roll."

with 90% chance, 90% succeed + 9% succeed from luck (90% of 10)
with 50% chance, 50% succeed + 25% succeed from luck (50% of 50)
with 10% chance, 10% succeed + 9% succeed from luck (10% of 90)

It's really not genius level math

I've always had an issue with this "lucky" crap. Now, I'm actually on the nerd side, so it's fun deciphering this, but after you get over the hee hee fun of deciphering it all becomes kind of tedious, and everyone just wants it simplified.

POB for builds exemplifies this. All this mumbo jumbo, can u tell me how much more dmg/ehp on avg? And ppl who use the simplification have a great advantage because it's digestible and can make intuitive changes.

Like here's how I mentally categorize new ascendancies.
Forgemaster = elemental dmg can't hurt you, easy gearing
Lich = great damage and defence if you use uniques to avoid downsides
Ritualist = if you have gg rings, late game only
Amazon = more accuracy rating on gear is more damage.

Tactician = I don't know because POE streamers haven't really figured it all out yet.

All this, so at the very end = can i one shot bosses?