"Millions to one!" - but is it really?

Channel:
Coincident
Subscribers:
28,900
Published on ● Video Link: https://www.youtube.com/watch?v=OIHaSOBJC-U


Grim Dawn
Game:
Grim Dawn (2016)
Duration: 0:59
1,960 views
83

Full video: https://youtu.be/3kUQpaC_2yk

During one of my Grim Dawn loot reveals I came across two randomly generated items with exactly the same affixes. "Millions to one!" - I shouted. And even though the probability of 2 amulets being equal out of a set of 2 is actually 1.4 to a million, that number drastically changed due to the fact that I had many, MANY more than just 2 amulets...

In case you're interested, here are all the calculations:

Probability of 1 pair of consecutive equal amulets, out of 1 pair of amulets:
Chance of green amulet * chance of same prefix * chance of same suffix:
5556/10000 * 1/1000 * 1/397 = 5556/3970000000 (about 1.4 chance in 1 million)

Probability of 0 pairs of consecutive equal amulets, out of 1 pair of amulets:
100% - previous probability:
1 - 5556/3970000000 = 3969994444/3970000000 (about 99.99%)

Probability of 0 pairs of consecutive equal amulets, out of 359 pairs of amulets:
Previous probability to the power of 359:
(3969994444/3970000000)^359 ~= 0.9994977 (about 99.95%)

Probability of at least 1 pair of consecutive equal amulets, out of 359 pairs of amulets:
100% - previous probability:
1 - 0.9994977 ~= 0.0005023 (about 0.05%, or 1 chance in 2 thousand)

This happened on Grim Dawn v1.1.9.6

Grim Dawn on Steam: https://store.steampowered.com/app/219990/Grim_Dawn/
Grim Dawn on Xbox: https://www.xbox.com/en-US/games/store/grim-dawn-definitive-edition/9PNQ7KRWCRW3

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Grim Dawn Statistics For Coincident

Coincident currently has 78,344 views spread across 8 videos for Grim Dawn. The game makes up 2 hours of published video on his channel, making up less than 0.70% of the total overall content for Grim Dawn on Coincident's YouTube channel.