Another 3oC Theory

My apologies if I'm late to the conclusion. I don't have as much time to scrub through all of the similar threads before I try to post something to related.

Like many other guardians, I struggle with the blessing of RNGesus. Specifically, when it comes to 3oC farming, I fail to hit the 1-in-5 number that so many others seem to boast (even with waiting 10 minutes between boss kills). In fact, it seems more recently that my past few attempts have been 1-in-12 or 1-in-13.

Here is where my theory starts.

Assuming that you have a natural chance of 1% to drop an exotic from an ultra character, consuming a 3oC prior to beating the ultra grants, what I believe to be is, a 3% increase in exotic drop chance. This makes your total chance for an exotic when beating a boss a whopping 4%.

When no exotic is awarded as a result of the 3oC consumption and defeating the boss, another 3oC is consumed, then another 3% is tacked on to your chance; now at a total of 7% chance.

After the wash-rinse-repeat of 3oC-bosskill, some guardians are finding success around the 5th 3oC consumed. These guardians are finding success at the 16% chance. How is it that seemingly most people find success around the 16% chance marker?

With the above theory in mind, I put my crude programming skills to the test and I whipped up a simulator, complete with counters and output, which might help me pin point the patterns which I was seeing within the 3oC farming. I bumped up the number of iterations and 3oC stretches in order to see how the data would normalize. What I found through my own experiences, the experiences of my friends, and the output of the data is this:

20 3oC Consumed : Longest stretch of use without a drop is 8. Received a total of 3 exotics. Success rate is 15%. 3oC to Exotic ratio is 6.666.

100 3oC Consumed : Longest stretch of use without a drop is 11. Received a total of 14 exotics. Success rate is 14%. 3oC to Exotic ratio is 7.142.

• 3 coins: (2)
• 4 coins: (1)
• 6 coins: (2)
• 7 coins: (2)
• 8 coins: (2)
• 9 coins: (3)
• 10 coins: (1)
• 12 coins: (1)

100 3oC Consumed over 10 iterations, then averaged : Longest stretch of use without a drop is 17. Received a total of 16 exotics. Success rate is 16.2%. 3oC to Exotic ratio is 6.25.

• 1 coin: (8)
• 2 coins: (16)
• 3 coins: (21)
• 4 coins: (15)
• 5 coins: (20)
• 6 coins: (19)
• 7 coins: (13)
• 8 coins: (9)
• 9 coins: (10)
• 10 coins: (10)
• 11 coins: (7)
• 12 coins: (6)
• 13 coins: (2)
• 14 coins: (1)
• 15 coins: (2)
• 16 coins: (1)
• 17+ coins: (1)

100,000 3oC consumed : Longest stretch of use without a drop is 20. Received a total of 15008 exotics. Success rate is 15%. 3oC to Exotic ratio is 6.663.

• 1 coin: (584)
• 2 coins: (999)
• 3 coins: (1286)
• 4 coins: (1593)
• 5 coins: (1677)
• 6 coins: (1689)
• 7 coins: (1574)
• 8 coins: (1340)
• 9 coins: (1230)
• 10 coins: (932)
• 11 coins: (740)
• 12 coins: (477)
• 13 coins: (349)
• 14 coins: (245)
• 15 coins: (140)
• 16 coins: (71)
• 17+ coins: (36)

100,000 3oC Consumed, 100 iterations and averaged : Longest stretch of use without a drop is 22. Received a total of 1509 exotics. Success rate is 15.09%. 3oC to Exotic ratio is 6.626.

• 1 coin: (5913)
• 2 coins: (10213)
• 3 coins: (13628)
• 4 coins: (15851)
• 5 coins: (16947)
• 6 coins: (16804)
• 7 coins: (15728)
• 8 coins: (13919)
• 9 coins: (11766)
• 10 coins: (9508)
• 11 coins: (7069)
• 12 coins: (5013)
• 13 coins: (3428)
• 14 coins: (2219)
• 15 coins: (1365)
• 16 coins: (774)
• 17+ coins: (423)

By the time I was done fiddling with the numbers, I found that within this theory, the average success rate is about a flat 15%, with the average exotic appearing every 6.5 3oC. Also, it is not uncommon to go 12 or 13 3oC without a drop, but that doesn't make it not suck. And furthermore, it seems the peak of success is around 5 coins.

Though, after everything was done, I never found a stretch of 23 coins or more where an exotic was not awarded. Speaking to probability, it should be possible, but highly unlikely.

Using this template, I was interested on what the buff increase would be to achieve the true 1-in-5 chance for exotic drops. I found this was awarded at a stacking 5%, instead of a stacking 3%. However, within this algorithm, the chance of going 12 or 13 3oC in a row without a drop was near impossible (~140 out of 100k). And considering I now, have had back to back 12 and 13 3oC runs, I would like to think my experience supports the 3% stacking scale, rather than me having the worst luck in the world.

TL;DR version: I made a simulator to test 3oC drops. On a large scale, I found average drop rate is 15%, resulting in 6.5 3oC consumed for every exotic engram.

I'm curious on your thoughts.