1/128 item on a first try. What are the odds?

#1SmokedChiliPosted 5/12/2014 9:11:40 AM
Who here has been so ridiculously lucky that you got one of those freakin' near-impossible-to-get 1/128 items the moment you defeated the first enemy to yield it?

This happened to me with a Ghost of Starman. It was literally the first enemy I encountered in invaded Onett. I was only planning to use that fight for Rock Candy abuse, but when I defeated that guy, BAM! Goddess Ribbon, f*** yeah!

Anyone else who was this lucky?
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#2Cpt_CalamityPosted 5/12/2014 11:35:01 PM
You literally typed out the odds and then asked what the odds were.

Anyways, best luck I ever had was getting the Sword of Kings against the second Starman Super that I fought. Ironically it happened during my no Equipment run so it pissed me off more than anything lol
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#3thecartoonheroPosted 5/12/2014 11:37:46 PM
best luck i had was third try for sword of kings (also, it's the only rare thing i go after).
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#4outsider90909Posted 5/14/2014 7:48:22 AM
A 1/128 item? I've probably gotten that lucky once. Now, a GOOD 1/128 item, on the other hand, ...
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#5LvthnPosted 5/14/2014 8:13:35 AM
7/128 assuming you kill one of each, and not adjusting for minutae like additional enemies.

In fact that means that about 1 in 20 playthroughs should get a rare item on the first try.
#6CrazyIvanPosted 5/20/2014 6:14:52 PM
Lvthn posted...
7/128 assuming you kill one of each, and not adjusting for minutae like additional enemies.

In fact that means that about 1 in 20 playthroughs should get a rare item on the first try.


This is not how probability works. While that makes sense intuitively, it's not mathematically correct. To find the probability you will get at least one 1/128 item, you actually need to find the probability that you will get -no- 1/128 items, and then subtract that from 100%.

Mathematically that works out to 1 - (127/128)^7, which yields:

1 - (0.9928775)^7 = 1 - .9466 = ~5.34%

7/128 yields 5.47%; I realize that's not a huge difference given the low sample set, but consider how the odds change if you take 64 attempts. 64/128 tells you that's a 50% chance you'll have at least one 1/128 item, whereas the proper expansion tells you the odds of finding one are actually ~37.5%. Going even higher, 96 attempts actually gives you ~52.9% odds to find one, whereas simply taking 96/128 gives you 75%.

Now you know. And knowing is half the battle!
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#7BLAHMASTERPosted 5/21/2014 4:33:13 AM
If you kill 16 enemies, your odds are 11.8% that you'll get one.
If you kill 32 enemies, your odds are 22.2% that you'll get one.
If you kill 64 enemies, your odds are 39.5% that you'll get one.
If you kill 128 enemies, your odds are 63.4% that you'll get one.
If you kill 256 enemies, your odds are 86.6% that you'll get one.
If you kill 512 enemies, your odds are 98.2% that you'll get one.
If you kill 969 enemies, your odds are 99.9% that you'll get one.

Get Kraken. Bionically I mean.
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#8LvthnPosted 5/21/2014 11:35:29 AM
CrazyIvan posted...
Lvthn posted...
7/128 assuming you kill one of each, and not adjusting for minutae like additional enemies.

In fact that means that about 1 in 20 playthroughs should get a rare item on the first try.


This is not how probability works. While that makes sense intuitively, it's not mathematically correct. To find the probability you will get at least one 1/128 item, you actually need to find the probability that you will get -no- 1/128 items, and then subtract that from 100%.

Mathematically that works out to 1 - (127/128)^7, which yields:

1 - (0.9928775)^7 = 1 - .9466 = ~5.34%

7/128 yields 5.47%; I realize that's not a huge difference given the low sample set, but consider how the odds change if you take 64 attempts. 64/128 tells you that's a 50% chance you'll have at least one 1/128 item, whereas the proper expansion tells you the odds of finding one are actually ~37.5%. Going even higher, 96 attempts actually gives you ~52.9% odds to find one, whereas simply taking 96/128 gives you 75%.

Now you know. And knowing is half the battle!


Good explanation!

I kept it in simpler notation, though, since other factors create a margin of error of a few percent, all of it against the odds of getting a drop. All I really wanted to do was point out that there are multiple opportunities for "a 1/128 on the first try" in a single playthrough, and since most people's perception will simply take the narrow view of "what are the odds of getting this on the first try?" Getting the SoK on the first try is quite rare, but getting any 1/128 item on the first try is surprisingly not that uncommon. If you do multiple playthroughs you have a decent chance of seeing it happen, despite the fact that it should seem like a very rare event.

I did get very lucky once: on my very first playthrough I got SoK on the second Starman Super I ever killed. Getting it on the first would have been epic but this was certainly nice. By now I'm pretty sure the starmen have a billion dollar bounty on my head as a war criminal guilty of genocide.
#9Starman_SuperPosted 5/22/2014 8:15:29 AM
It was you!
You killed my brother!
#10empblmmmsdPosted 6/9/2014 3:52:09 PM
I never got a 1/128 item on my first try.
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