MMO high roller hits triple legendary drop so rare that people are struggling to even calculate the odds

It is 10:54am on a Monday morning and I've had to do a ton of math that I am frankly not qualified for, all because of an unbelievably lucky Old School Runescape player who bagged three ultra-rare drops in a true feat of MMO RNG. 

I honestly don't know where to begin, so let's start with this tweet from OSRS diehard Bazilijus, who recently obtained three mega-rare items from Old School's clue scrolls in a single day, with the Twitch clips to back it up. 

You may remember Bazilijus as the first player to get every single boss drop in an enormous grind after 22,000 total hours played. The point of that boss grind, and now this clue scroll grind, is to complete Old School Runescape's daunting collection log, which essentially tracks all the rare drops that you've obtained. This incredible clue scroll high roll has brought Bazilijus considerably closer to the (still far-off) finish line, and like many players, I'm struggling to calculate the odds because there are so many variables in play. 

Bazilijus managed to save up 600 of the reward caskets that you get from hard clue scrolls, with each clue taking around five minutes to complete (judging from his final run). That's approximately 50 hours of grinding, and he was going to cash in the payoff in a matter of minutes.

By his 426th casket, Bazilijus had obtained three pieces of the ultra-rare 3rd Age armor which is often seen as the pinnacle clue reward. I am a bit of a math nerd but I am not a mathematician, so I'm just going to do my best to explain why my gast is so flabbered.

There are 13 3rd Age items on the hard clue drop table, and the Old School Runescape wiki confirms that the odds of getting a specific piece from a reward roll on a hard clue are about 1/211,250. However, the odds of getting any piece are only 1/16,250. And because you get multiple rewards per clue, the total odds of a hard casket dropping any 3rd Age item are 1/3,250, as OSRS developer Jagex affirmed in a blog post last year. 

The thing is, Bazilijus wasn't after any 3rd Age piece. They're trying to fill out the collection log, after all, so they wanted unique 3rd Age items – pieces they'd never obtained before. The collection log hiscores show that they only had two 3rd Age items logged before this mind-boggling chain of events, which means they had successive 11/13, 10/13, and 9/13 odds of getting a unique 3rd Age item after hitting the 1/3,250 drop table. And yes, this does mean that the ultra-rare clue hunt gets considerably harder over time. 

This shrinking pool changes the odds of each of these three drops – Bazilijus's third, fourth, and fifth 3rd Age items – being unique. Here's my best estimation:

• First roll: 1/3,840
• Second roll: 1/4,225
• Third roll: 1/4,694

The good news is that the average rate of hitting a unique 3rd Age piece in this data set, 1/4,253, lines up pretty cleanly with how many reward caskets Bazilijus opened. 

The vast majority of Old School Runescape players will never see a single 3rd Age drop in their lifetime, and now one person has gone 10 times the unique drop rate three times in one sitting. One 3rd Age piece would've been extremely lucky here, but three? I admit I don't know the net odds of getting that result within this many attempts, but I don't need to be a mathematician to know that Bazilijus should buy a lottery ticket next. 

In an even more extreme display of grinding, one player blew 8 years of banked experience maxing out a single OSRS skill in just seconds.