The actual rarest thing that can happen in Terraria.

The actual rarest thing that can happen in Terraria: a luck-turbocharged Pirate Corsair
Much thanks for @damnthisisabadname's collaboration efforts.

Chapters:
0:00 Intro
0:15 What is a single "event"?
0:45 My hypothesized event
1:25 The Pirate Corsair's massive drop pool: item drop rates
2:09 How luck works, and how it allows for extremely unlikely scenarios/journeys
4:41 Extra chances like modifiers, coin drops, crits and weapon probabilities
7:04 The final summary
7:58 Conclusion

Music:
Stardew Valley - Mines (Marimba of Bone)
Vanilla Calamity Mod Music - "Nearing the Inferno" - Theme of the Caverns by Heart Plus Up!
Vanilla Calamity Mod Music - "Chambers of the Tyrant" - Theme of The Dungeon

Mods, Shaders, Pack:
DragonLens (Cheat Mod) -
Stanberry Font (Pack) -
Stormdark UI (Pack) -
Lights And Shadow (Mod) -

#terraria

The actual rarest thing that can happen in Terraria: a luck-turbocharged Pirate Corsair

[Terraw]

Hopefully I didn't fat-finger some numbers here. Chances are high given how much there are...
even if I did, the range of around 10^500 should be accurate no matter what. Does it even matter at this point?

Some people have mentioned possible inconsistencies involving the Mech boss summon calculations which might affect the numbers a bit.
(Mechanical summons may only drop 1 at a time, not all 3.)
I also may have forgot about Lucky Coin extra-coin chances. Oops!

Also, credit to filipssh for the reduced gap design for the hypothetical logic gate thingy.

[spookyjailopossum]

this is pretty crazy, but i still feel like the daedalus stormbow is just a bit rarer

[xsinam]

My friend casually just getting this chance 3 times in a row while I'm farming for a rod of discord

[damnthisisabadname]

Fun fact:

The odds of the whole chained faulty gate thing happening is roughly one in 2.466239346 * 10^27966 (this number will have 27996 digits)

[lucky]

Sadly all 3 mech summon isnt possible : for every enemy killed, it roll a 1/2500 for destroyer summon. ONLY if it fails then it roll for the twins and skeletron in order try using a max luck mod to see

[unArthodoxDR]

Oh my, it's that day again where Terrasteel throws an absurd amount of math at our favorite video game!
_I'm not complaining though, keep it coming!_

[sboogbloog]

I'd be interested in the rarest "observable" event too, for example the player can't know anything about their luck or crit chance rolls except by the damage indicator number.

[tpeter]

Now we need the most common occurrence in Terraria.

[Shyguymask]

Dream would be able to get that drop if he speedruns Terraria.

[Nottwitte]

If anyone watching is interested in other ways luck plays a part in Terraria, I recommend Wand of Sparking's Dream luck playthrough. He goes through many different situations that you might not think luck plays a part in, with a lot of number crunching to boot!

[hiimapop]

I'm always fascinated with stupidly large numbers and rare chances and events, so this video tickled all the right spots for my monke gamer brain. Please don't stop making these useless but fascinating videos, I never get tired watching them. :)

[Murpler]

As a cookie clicker player, I have seen many large numbers, some I can’t even pronounce properly. But this number tops it without question. I had thought centillion was the largest number with a name, but you leave me gobsmacked.
The hell is a septenseptuagintacentillion.

[_Suitable]

I have never even heard of terraria before and this is my first introduction? I love it already!

[WomanSlayer]

In order to visualize such a drop rate, it is rarer than an event where if you picked a random atom in the observable universe and imagine each atom as its own universe, then pick an atom from that universe and imagining each atom in that universe to contain its own universe, and so on and so forth, and repeating the cycle three more times before picking an atom from that imaginary universe, then I pick an atom at random and imagine each atom as its universe and so on and so forth with the exact same method as you did, and we manage to pick the same atom in the exact same imaginary universe by random chance.

[EagleScoutGamer]

And that is less rare than your chances of getting a girlfriend.

edit: and that includes myself as well

[AveryTheHorror]

you cant have a hybrid evil + hallow biome, which led you to correctly exclude the hallow key from the biome keys list, yet soul of light is still in the drop list.

[purplehaze]

This is one of the most convoluted videos I've ever seen.

[chronology.]

If there is a Bloodmoon, would that not also include the chance to get the KO-cannon (0.1% base drop chance from all hardmode enemies during a bloodmoon)? Meaning you can make this even rarer?
Or does that event overwrite some of the other biomes/events you want to happen?

[maddiestratus]

Honestly, i feel confident in saying that this is one of, if not the rarest thing that could happen in any game, period.

[leandrolima]

Still more common than the merchant selling what I want. Got this video results two times before it happened!