57 Leaf Clover: the Actual Numbers

Overview

You might already know what the 57 Leaf Clover does. But chances are you don’t know how the numbers actually look. Want to know by how much your chances increase on each item but don’t want do do boring probability calculations? Then this is the guide for you.

Introduction

The 57 Leaf Clover is a Red (Legendary) item that makes you luckier.

All random effects are rolled +1 (+1 per stack) times for a favorable outcome.

Items effected:

Tri-Tip Dagger
Sticky Bomb
Stun Grenade
Ukulele
AtG Missile Mk. 1
Bandolier
Old War Stealthkit
Ghor’s Tome
Molten Perforator
Sentient Meat Hook
Happiest Mask
Brittle Crown
Spinel Tonic

Tougher Times isn’t effected as that would be a bit too overpowered.

Other things effected:

Critical Strike chance
Artificer’s chance to ignite with Flamethrower
drop chance for Monster Logs
Elite equipment drop chance

The 57 Leaf Clover doesn’t effect things like chest spawns/outcome, shrine chances/outcomes, chance for an Artifact Key to drop or the drop chance of items with Artifact of Sacrifice.

How it works

Whenever one of these random effects is rolled and you get an an unfavorable outcome, the 57 Leaf Clover will roll that effect again. This repeats for every 57 Leaf Clover you have.

The chance of activating something is calculated with the formula:

y = 1 – (1 – p)^(x + 1)

Where:

x = the number of clovers you have
p = the activation chance of the item
y = the new activation chance for the item with the clovers

So let’s say you’re using AtG Missiles and have one 57 Leaf Clover.
AtG Missiles have a 10% chance to activate.
p = 10% or 0.1 and x = 1
y = 1 – (1 – 0.1)^(1+1)
y = 0.19 or 19%

If the formula is a bit confusing then here is a simple probability tree for visualisation:
The AtG Missiles have a 1 in 10 chance of activation and 9 in 10 chance of not activating.

With a 57 Leaf Clover, if the item doesn’t activate the first time then we have another 1/10 chance of it activating.

There is a 1/10 chance of the item activating on the first attempt and a 9/10 * 1/10 chance of it activating on the second attempt.
1/10 + 9/10 * 1/10 = 19/100 or 0.19 or 19%

Adding a second clover would look like this:

1/10 + 9/10 * 1/10 + 9/10 * 9/10 * 1/10 = 271/1000 or 0.271 or 27.1%

Proc Coefficient

One last thing to keep in mind is Proc Coefficient.

If you don’t know what Proc Coefficient is, it’s essentially a multiplier (from 1 to 0) that gets applied to the chance of something activating.

Most attacks in the game have a Proc Coefficient of 1. This just means that they activate normally. If you’re using AtG Missiles, your attacks have 10% chance of activating the item. This 10% chance get’s multiplied by the Proc Coefficient of 1 and just stays the same.

But something like MUL-T’s nailgun has a Proc Coefficient of 0.6. Which means that the 10% chance of the AtG Missiles get’s multiplied by 0.6 and becomes 6%. MUL-T’s nailgun shoots really fast so it makes sense that it activates items a bit less often.

I’m not going to make a table for everything that has a different Proc Coefficient as that would just be a bit ridiculous.

To calculate the chance of something activating with different Proc Coefficient you need to simply account for the Proc Coefficient in the p variable of the formula representing the activation chance of an item (or proc chance).

y = 1 – (1 – p)^(x + 1)

p = 10% * 0.6 = 6% or 0.06
y = 1 – (1 – 0.06)^(1 + 1)
y = 0.1164 or 11.64%

If you want to know the Proc Coefficient for every single ability and item then check out the wiki page on Proc Coefficient[riskofrain2.fandom.com]

Tri-Tip Dagger

10% (+10% per stack) chance to bleed an enemy for 240% base damage.

(note: in the anniversary update the item got changed from 15% to 10%)

Tri-Tip Daggers are pretty self explanatory.

Their scaling is linear so the percentage per item just adds up.
1 Tri-Tip Dagger gives 10%, 2 give 20%, 3 give 30% etc.

Having 10 or more Tri-Tip Daggers gives you a 100% chance to activate the bleed provided you have a Proc Coefficient of 1. If you have 100% chance to activate the item then the 57 Leaf Clover(s) don’t really do anything.

Sticky Bomb

5% (+5% per stack) chance on hit to attach a bomb to an enemy, detonating for 180% TOTAL damage.

Sticky Bombs basically behave in the same way as Tri-Tip Daggers.

They also scale linearly.
1 Sticky Bomb gives 5%, 2 give 10%, etc.

Again, having 20 or more Sticky Bombs gives you a 100% chance to activate the item. which makes the 57 Leaf Clover(s) unnecessary.

Stun Grenade

5% (+5% on stack) chance on hit to stun enemies for 2 seconds.

With Stun Grenades things are a bit more complicated.

Their scaling is hyperbolic.
This essentially means that as you collect more the item adds less and less chance to stun.
This also means that you can’t get to a 100% activation chance.

The chance to activate with the amount of Stun Grenades is calculated by this formula:

1 – 1 / (1 + 0.05 * amount)

Due to how the chance is calculated even your first Stun Grenade will actually have a bit less than 5% chance to activate.

Ukulele

25% chance to fire chain lightning for 80% TOTAL damage on up to 3 (+2 per stack) targets within 20m (+2m per stack).

Ukulele is one of the most simple items to calculate.

No matter how many Ukuleles you have, the chance of activating them will always stay at 25%.
The only way to increase it is with 57 Leaf Clovers.

AtG Missile Mk. 1

10% chance to fire a missile that deals 300% (+300% per stack) TOTAL damage.

AtG Missiles are also easy to calculate.

Similar to Ukuleles, the activation chance for AtG Missiles will always be 10% no matter how many you have and the only way to increase this is with 57 Leaf Clovers.

Bandolier

18% (+10% per stack) chance on kill to drop an ammo pack that resets all skill cooldowns.

Okay so the Bandolier is a bit weird.

First one gives you 18% and each Bandolier after that gives you +10% right?
Well… the wiki says that this is calculated by the formula:

1 – 1 / (1 + amount) ^ 0.33

But if that’s the case then the first Bandolier actually gives you 20.45% not 18%.
Having 2 will give you will give you 30.41% which is close to a 10% increase but 3 Bandoliers give you 36.71%.

So… ehm… what?

I’m going to stick to the formula because if that’s how it’s calculated in the code then those are the right numbers but if anyone understands this heresy please explain.

Old War Stealthkit (outdated)

Falling below 25% health causes you to gain 40% movement speed and invisibility for 5s. Recharges every 30 seconds (-50% per stack).

The item got changed in the Anniversary Update.

It used to have a chance of activating depending on how much damage you took.
Now it activates when falling below 25% health and is no longer effected by luck.

Ghor’s Tome

4% (+4% on stack) chance on kill to drop a treasure worth $25. Scales over time.

Similar to Tri-Tip Daggers and Sticky Bombs, Ghor’s Tome stacks linearly.

Having 25 or more will give you a 100% chance to drop gold on kill.
This again makes the 57 Leaf Clover(s) unnecessary because they won’t really do anything.

Molten Perforator

10% chance on hit to call forth 3 magma balls from an enemy, dealing 300% (+300% per stack) damage each.

Molten Perforators also always have a 10% chance to activate no matter how many you have.

So it’s literally just like AtG Missiles.

Charged Perforator

10% chance on hit to down a lightning strike, dealing 500% (+500% per stack) damage.

This is just an alternate version of the Molten Perforator added in the Anniversary Update.

In terms of activation chance, it’s the same.

Sentient Meat Hook

20% (+20% per stack) chance on hit to fire homing hooks at up to 10 (+5 per stack) enemies for 100% TOTAL damage.

The Sentient Meat Hook is another item that has a hyperbolic scaling.

The chance to activate it is determined by this formula:

1 – 1 / (1 + 0.2 * amount)

And yes, this does also mean that your first Sentient Meat Hook actually gives you 16.67% and not 20%.

Happiest Mask

Killing enemies has a 7% chance to spawn a ghost of the killed enemy with 1500% damage. Lasts 30s (+30s per stack).

The Happiest Mask will stay at 7% no matter how many you have just like Ukuleles, AtG Missiles and Molten Perforators.

Brittle Crown

30% chance on hit to gain 2 (+2 per stack) gold. Scales over time.

The Brittle Crown also stays at a 30% chance no matter how many you have.

Spinel Tonic

Gain a massive boost to ALL stats. Chance to gain an affliction that reduces ALL stats.

Drink the Tonic, gaining a boost for 20 seconds. Increases damage by +100%. Increases attack speed by +70%. Increases armor by +20. Increases maximum health by +50%. Increases passive health regeneration by +300%. Increases movespeed by +30%. When the Tonic wears off, you have a 20% chance to gain a Tonic Affliction, reducing all of your stats by -5% (-5% per stack).

With the Spinel Tonic things are a bit different.

When the Tonic wears off, you have a 20% chance to gain a Tonic Affliction.
This is a negative effect but the 57 Leaf Clover re-rolls random effects for a favorable outcome.

You can think about this as having 80% chance to get the good outcome.
To calculate the chance of getting an Affliction you just need to calculate the chance of not getting it and then subtract it from 1 or 100%.

Formula for Spinel Tonic:

y = 1 – (1 – (1 – 0.8)^(x + 1))

Critical Strike chance

Your attacks have a 10% (+10% per stack) chance to ‘Critically Strike’, dealing double damage.

Gain 5% critical chance. Critical strikes heal for 8 (+4 per stack) health.

Gain 5% critical chance. Critical strikes increase attack speed by 12%. Maximum cap of 36% (+24% per stack) attack speed.

Gain 5% critical chance. Critical Strikes bleed enemies for 240% base damage. Bleeding enemies explode on death for 400% (+400% per stack) damage, plus an additional 15% (+15% per stack) of their maximum health.

Critical Strike chance is also something effected by 57 Leaf Clovers.

All Survivors have a base of 1% critical strike chance.
Lens-Maker’s Glasses give you +10% Critical Strike chance per stack while Harvester’s Scythes, Predatory Instincts and Shatterspleens only give you 5% which doesn’t increase with more items.

Flamethrower

And finally Flamethrower.

Every tick of the Flamethrower simply has a 50% chance to ignite enemies.

It deals damage 22 times so overall increasing the chance for each tick isn’t as important.

Thank you!

Thank you for checking out this guide.

If you see any mistakes in any of my calculations please let me know so I can correct them.
I had to make a lot of tables for this and something somewhere could have easily gone wrong.

I hope this was at least a bit helpful or interesting and I wish you plenty of 57 Leaf Clovers during your runs.

Purity Guide

So ehm… this guide blew up a bit more than I expected.

Thanks everyone for all the support and feedback!

I thought that since I made a guide about the Clover, I should probably also research the opposite item now.

And well… here’s the sequel to this guide I guess:
[link]

Risk of Rain 2 Guide