Probability of seeing a specific item drop from one of the new dungeons?

[xvshanevx]

Hi everyone,

So, I replied to someone on Reddit about how we as a community "choose" speed run dungeons, and possibly why we do so. And I was just think about the probability of getting just one, specific item from either of the new dungeons. Here is the post, and I think its near the bottom: https://www.reddit.com/r/ffxiv/comme...much_time_and/

I know some people do not read reddit, so here is the portion I wrote:

There are 2 new dungeons. These new dungeons have ilvl185 gear. Some players will use this to catch up in gear, while other will mainly use for glamour. Assuming the roles (Tank, Healer, MNK, BRD/MCH, BLM/SMN, DRG, and NIN), and also assuming that each boss has the loot table for all the ilvl 185 items, there are a total of 77 items in these dungeons (just an estimate) that can be dropped by each boss. Currently, each boss only drops 1 item. That is a 1 in 77 chance that one of the three bosses will drop the piece you are looking for. With 3 bosses, you have a 3/77 (4%) chance from the item to drop in 1 run that if "CHOSEN" would take 30-45 minutes to complete. So, if we CHOOSE to do these dungeons at the intended rate, it would take, on average, 600 minutes, 10 active hours, before a specific item drops. One item.

Pretty much 1/77 + 1/77 + 1/77 == 3/77 or 0.038. I rounded to 5% for simplicity of finding out the time it would take almost assuming that, after 20 runs (1/20 == 0.05), you would at least see the item. As mentioned, if my math is correct, which I am hoping is not, it would take someone near 10 hours before even seeing the item they are trying to get. this is also regarding active play and not including que wait times, deaths, duty abandon, losing the roll to someone else, etc.

I am posting this here so someone can say "no, your math is wrong, it is actually this..." But, if this is correct, or near to being correct, does this not seem a bit cruel?

[Sagittarian]

Your math is wrong but 10 hours is probably a decent estimate.

• I think there are only 70 i185 dungeon drops.
• The equipment can drop from more chests than just the boss chests. I think the arboretum has a total of 7 chests that can drop equipment.
• Not all equipment can drop from every chest.

Without really crunching the data, it looks like each piece of armor (not accessories) only drops from one boss but each boss chest only has a pool of ~14 items, so our chance of seeing a particular item is 1/14 or about 7%
The best way to calculate how many runs it will take you to get it is to look at how many runs you can do WITHOUT getting it.
Any given run has a 93% chance of NOT seeing this item.
The chance of 2 runs NOT seeing it is 0.93 * 0.93 ~= 0.86
After 5 runs we are at ~69%.
After 10 runs we are at ~47% - this is the tipping point where "most" people will have seen it.
After 20 runs we are at ~23%
After 30 runs we are at ~10.8% - this is where the chance of having seen it is ~89%
After 63 (!) runs we are at ~0.94% - this means that 99.06% of people will have seen it by this point.

So if you are looking for one particular item you will have "probably" seen it (>50%) after 10 runs. By 20 runs you have a higher than 75% likelihood you have seen it.

If you are looking for all 6 armor pieces you want the probability of having seen all 6 by a certain run. That is just the chance of having seen one particular item raised to the 6th power. So you will have "probably" (>50% chance) seen all of 6 particular items after 30 runs. This is a month of doing daily expert roulette. If not all items drop from each dungeon, then it is 2 months of daily expert roulette.

So yes it seems like a lot of time if you are just trying to get a particular item for glamour purposes but if you are doing regular runs anyway those should suffice in a few weeks.