Data from 1,000 Tujen rerolls
Hey everyone. I recently used 1,000 Exotic Coins in order to record data on a few things.
1) Expected returns per refresh window/coin.
2) Appearance rate of "T1" currencies (Exalt, Annul, and Divine).
3) Appearance Rate of Divines specifically.
4) Mirror shard appearance rate? (lol)
Method was to simply haggle for "worthwhile" items. This meant we did not take Blacksmith Whetstones, Armourer's Scraps, Orbs of Transmutation, Quality gems (although you can view them as GCP shards). There were other items that were not worthwhile to take, non-Deception/non-priceless Heist contracts, Jewels, Breach Rings. Some of these can be incredibly good, Jewels being the first that springs to mind, but hard to sell at this point in the league, and I would rather err on the side of caution and understate our returns than the opposite.
I counted occurrences of all Annuls, Divines, Exalts and Prime Chaotic Resonators. I also counted backwards, as I had the coins in my inventory, so when I hit a T1 currency, after the first 14 rolls, it would be noted as roll 986.
Results were as follows:
Divines - 28 (24)
Annulments - 11
Exalts - 10
Prime Chaotic Resonators - 5
Mirror Shards - F
There is a bracket for Divines there because on roll 986, only 14 rolls in we were offered a stack of 5 Divines. So we were offered 24 stacks on different occasions. We received 28 Divines in total.
Divines - 986,938,921,921,870,774,773,765,678,665,647,656,609,569,548,388,358,311,298,210,181,75,41,9
Annuls - 967,846,840,802,779,360,283,281,210,177,45
Exalts - 792,721,625,547,473,458,327,207,177,15
Prime Chaotic Resonators - 981,744,519,247,215
From this data it appears that you have a ~4.5% chance to be offered a T1 currency in any given window. Longest Divine Dry Streak was 160 windows, between 548 and 388.
Around the 700th window I started to note down what kind of artifacts each item cost, and how many items there were, and created a mental model of how I think the Tujen window is populated. There are 4 reward slot types in the window, those that cost Exceptional, Grand, Greater and Lesser Artifacts.
Model: The server rolls a 4 sided dice, and adds 12 to it. This gives a number between 13 and 16. I have never seen more or less items in Tujens window. This gives the total number of reward slots.
The server then rolls a 2 sided dice, and subtracts 1 from the result. This gives the number of Exceptional Rewards. It then rolls a 5 sided dice and subtracts 1. This gives the number of Grand Rewards.
The other two reward types, Greater and Lesser, fill out the remainder of the reward slots in the window.
Costs/Returns - I also kept everything I haggled from Tujen in 5 quad tabs. It costs slightly less than 9c for an Exotic Coin. In bulk they are 29 for a Divine. A price that is relatively stable the whole league.
1,000 Coins cost around 34.5 Divines, or 9450c. Exilence Next reports that our 5 quad tabs are worth 106.5 Divines, or 29,171c. Our returns are therefore around 29c per window, with a profit of 20c per window.
What made up the bulk of the currency? I have a screenshot of the data here: https://imgur.com/a/qMIYYbP
Shout-out to Orbs of Augmentation for there being 10,940 of them.
I have made a video presentation of this data, it can be found here. https://www.youtube.com/watch?v=1UGQr5LfkkU
Happy to answer questions if you have any. I think I pre-empted a lot of them in the video, but happy to reiterate here.