The Rarest Item in the Game?

General
1

Hi everyone.

I have gotten pointed out that you can indeed easily acquire Fractured Crown, thus making this post kind of void lmao

I was digging around doing some research on Last Epoch Tools, and I came across the unique item Fractured Crown. It’s a helmet that can only be obtained by using a Rune of Ascendance.

Given that there are 20 unique helmets and 7 set helmets, that would give it a 1/27 aka 3.7% (full numbers in the math section) drop chance.
On Last Epoch Tools, they also have the percentage for the Legendary Potential chance, and it shows that there is a 0.00024% chance for the helmet to be LP 4. So I was wondering what the full drop chance would be to not only get the Fractured Crown, but also for it to have LP 4.

3.7% for the helmet, and 0.00025% for the LP4 means that you have a 0.000000000888888888% chance of getting a Legendary Potential 4 Fractured Crown whenever you use a Rune of Ascendance on a helmet.

In other words, you statistically have to spend 1.125 BILLION Runes of Ascendance to get a LP 4 Fractured Crown. I am not kidding. The full number is 1,125,000,001.13 runes.

I believe this to be the rarest item in the game. I can’t even think of a lower droprate of an item in any game I have played. It’s going to be very interesting to see who the first person to acquire the LP4 item is.

As an extra fun little way to put it in perspective:
If the current 185k online players all tried to get the item. It would statistically take every person 6081 tries before one player got it.

I hope you enjoyed my little breakdown. This sure led me down a rabbit hole.

Boring math section for those interested. Feel free to double check my calculations.

P(ID) = Probability of the item dropping
P(LP) = Probability of Legendary Potential

Fractured Crown Ascendance Chance = 3.7037037%
Calculation:
P(ID)
= 1/27
= 0.037037037
= 3.7037037%

Fractured Crown LP 1 Ascendance Chance = 0.9296296287%
Calculation:
P(ID) × P(LP)
0.037037037 × 0.251
= 0.009296296287
= 0.9296296287%

Fractured Crown LP 2 Ascendance Chance = 0.00001103703703%
P(ID) × P(LP)
= 0.037037037 × 0.0298
= 0.0011037037026
= 0.00001103703703%

Fractured Crown LP 3 Ascendance Chance = 0.000000407407407
P(ID) × P(LP)
= 0.037037037 × 0.0011
= 4.07407407E-5
= 0.0000407407407
= 0.000000407407407%

Fractured Crown LP 4 Ascendance Chance = 0.000000000888888888%
P(ID) × P(LP)
= 0.037037037 × 0.0000024
= 8.88888888E-8
= 0.0000000888888888
= 0.000000000888888888%

You made it to the bottom. You found the hidden Duckie :duck:

1 Like
2

Thanks for Duckie!

But every time you complete the ritual, namely …

Using Rune of Ascendance on Runed Visage that has Mana and Damage Dealt to Mana Before Health prefixes with 21+ total affix tiers

… you get Fractured Crown. So the other helms existing does not matter.
Now what’s the chance of getting the input items for the ritual and not running out of FP, that’s another topic.

1 Like
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As Iceberg pointed out - Fractured Crown is one of the most targetable uniques :wink:

On tunklab we can see it has an LPL of 56 which 1 in 291,579 will be an LP4.

Compared to something like a Ravenous Void which has a 1 in 9.56 Trillion odds of hitting LP4… There’s definitely rarer items.

Still - thanks for making the post! Always fun to think about :slight_smile:

1 Like
4

yes thanjks

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5

Ah, thank you for the correction! That does make the most of the calculations not matter at all. I am happy that it does not in fact take over a billion runes to get the LP4 item lmao

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6

Sometimes a single detail can change the entire story. Time to go down the Ravenous Void rabbit hole

7

Because I’ll feel bad if you do this thing again, here’s the rarest item in the game for 4LP:

Also, it’s a boss-only drop.

Now if you really want to send your sanity to the shadow realm, check this site:

Since Ravenous Void is both a boss drop and a world drop you can account for the reroll chance of all uniques to get the exact percentage for its relative 4LP rarity.
But please don’t.

1 Like
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Thank you. Sometimes my excitement for numbers takes over. I have had enough math for this week, but I will definitely save that website

9

One of the column’s in that link (TunkLab Unique Items) is Legendary Potential Level (LPL).

You can use that value here to see your odds of a 1, 2, 3, or 4 LP drop: