Erfworld Forums • Gem Catalogue

Updated 2018-04-20 p.m.

Gem Size / Glow Probability Charts

Here are the updated probability charts for gems sizes and glows. Note, the odds are the same (size 1-10 odds = glow intensity 1-10 odds), and they are fairly run-of-the mill exponential. Special thanks to everyone who participated in this thread to provide the data we needed to come up with this. That end-of-month snapshot data removed the reporting bias that was skewing the original thread -- people were underreporting small gems and overreporting large gems.

tl;dr - these numbers are close enough to reality that you can use them as if they were reality - the error won't be measurable in the course of time we'll be mining gems

[close enough to canon that you will never know if it isn't without someone who knows the code telling you otherwise]

The odds of a small gem are slightly over 50% instead of being a nice tight flat 50%. Why?

Using the model alone, the numbers /would/ be a flat 50%, but that also adds other problems. Let me explain the reasons and assumptions that go into all this.

1) In a natural system, we might expect that sizes and glow intensities increase (effectively) infinitely. The mathematical model fit to the data -does- assume that. Looking at the total, and assuming the sizes and glows are capped as Titanic (size and glow category 10) we have 1/1024th (0.1%) as a fudge factor. Not ideal, but outside of collecting a lot more data, not something we can definitively assign.

a) We could force the #s to equal 100% by adjusting the entire system to cover that missing 0.1% but any method we chose will be arbitrary and not necessarily reflective of the underlying mechanics. In spite of that, and considering the error is the exact value of the odds of the Titanic size/glow gems, rather than count that as error or "fudge" in the system, we've chosen to use some meta (it is a created system) to assign it in what is a fair way (statistically as it's evenly distributed through the system) to force our otherwise boundless equation to fit to a 1-10 system instead of an infinite system (halving the odds of the next larger size/glow forever).

2) The gem size and glow probabilities are a man-made system, not a natural system. That means we have some tools at our disposal that don't exist in the real world. For instance, we can make some assumptions based on human behavior and the design of the grid for spins. You'll note there are 1024 spaces on the grid. That's classic binary / doubling / exponential math. The strict model numbers line up very well with that except for the missing 1/1024, literally the exact space of a single dot on the grid.

Think of it this way, if you want to break down the sizes into the same sort of space as the grid:

1024 total spaces on the grid.
Small - 512 spaces on the grid
Average - 256 spaces on the grid
Large - 128 spaces
Massive - 64 spaces
Enormous - 32 spaces
Gigantic - 16 spaces
Staggering - 8 spaces
Monumental - 4 spaces
Colossal - 2 spaces
Titanic - 1 space

See how neat and tidy that is? We get all ten known size/glow categories and can't halve the number anymore and keep it a whole number. Great!

But that adds up to 1023 spaces, not 1024...

This means we have to take our model and evenly distribute that missing 0.1% thoroughout the whole function, instead of just arbitrarily adding it into the odds for a given size/glow. That's very important, as while 0.1% wouldn't mean much to the odds of a small gem (50% vs 50.1%) it would /double/ the odds of a Titanic gem (0.1% to 0.2%). So each of the percentages are based on the above number / 1023 (instead of 1024).

Is that how it's handled in the code? No idea. Does that matter? No.

Why not? The differences are so small that, arguably, you will never be able to detect it and we probably can't even get a data set large enough to test and prove one way or another without mining for Erf for millenia. So we're not going to.

Given that minor adjustment, the final probabilities rounded to two decimals, in table form, follow:

If you are SUPER interested in the excel sheets and work behind fitting the data from here and getting the model, PM me, I can probably email you that. It's a headache to post and not of interest to most people so I'm not doing the necessary acrobatics.

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Classic Post based on individual data submissions below, for history.

Last Updated 2018-04-08 p.m.

Updates (TL;DR Version)
Total Observations: 226
Unique Color: 85

Glow 10 discovered - TITANIC!
Size 10 discovered - TITANIC!
New colors discovered: beige, midnight, sapphire, burgundy, sage, peacock, pumpkin

Established Point Max Gem: Colossal (81 pts) + Titanic glow (100 pts) = 181

Current Record Gem: 104 points (Average Titanic - mined by Linsaran 2018-Mar-4th)
Tie record holder: 104 points (Average Titanic - mined by JadedDragoon 2018-Mar)
Previous Record Gem: 82 points (Small Crown Jewel - mined by Tathar 2018-Feb)

Please Report All Gems - even those you don't think are exciting - to avoid skewing the data.

RECENT NEWS
CONFIRMED! Size 7 gem FOUND!
Added visual size probability chart (based on 2018-Feb-25th model)!
Prediction of Glow 9 Confirmed via Discovery! - Crown Jewel glow

Extended Version
Hi there!

I didn't see a specific thread for this yet, so I'm starting one.

Please respond with what gems you've found. I'll add and tally them here and we can try to get a count as to their frequency and maybe be able to derive a commonality (and value) from that.

Include, for each gem (and my first gem for example):
Size: Massive
Glow: none
Color: Strawberry

Also - first spin or mined. I don't expect a difference but it's worth tracking.

NOTE: You can't direct link to a gem (such as https://login.erfworld.com/gem?id=7856) as you cannot see a gem unless you're the current owner (presumably). Images can be shared, of course.

Good mining to you!

The end-of-March data capture was a huge success. I have it on good information that we captured a large portion of the total gems mined for the month. Considering we're most certainly getting underreporting of smaller gem sizes and over-reporting of larger/shinier gems, I'm going to stop tabulating and refining the model against the individual gem data reported in this thread.

I'll post a summary of the results of the end-of-March post here once it's complete.

Updated 2018-04-08 p.m.

Okay! Here are the latest stats from the thread and last to be added specifically based on the data in this thread, ending with my update post on page eleven. Yes, that's right: ours go to eleven.

Sizes
We're up to 226 reported gems so far, and the expected power curve is holding by and large (smaller = more common) and firming up. We had a second report of the size 7 class, called Staggering. Very exciting and validating that it finally was seen and shared.

We're inferring a size 10 gem based on the appearance of a glow 10 (meaning 10^2 = 100 points, not html code values). It may or may not exist, but if it does, it's predicted to occur at a roughly 0.098% (~1 in 1024) pop rate when a gem is mined. The hunt is on!

Spoiler: show

I'll update the visual scale and the percentages after a) size 10 shows it's lovely, ginormous face, or b) early next month after I get a clean data set from people's March mining results pages.

We also have enough clean images to have built a visual size comparison scale, based on the stock display orientation and distance.

Spoiler: show

Also, there's now enough data that I'm comfortable in the model. Sufficiently so to make a nice visual key to give people a good idea of a given gem being a given size:

Spoiler: show

Glows
Glows and no-glows have been trending away from the initial 50/50 seen. I'm concerned that we're adding some reporting bias here over time as people may be less likely to report "boring", non-glowing gems.

UPDATE: we are definitely underreporting no glows. The end-of-march data supports a very clean 50% chance of a gem having a glow.

The Titan of the glows has been mined! All hail the 100-point (level 10) glow of the Titanic!

Glows function in the same fasion as size, increasing glow intensity increasing the point value in a power scale fashion.

It's notable that the current glow distribution now follows the expected trends given the point values. Yay for a larger data set! Earlier it didn't when the set was small and made figuring out the glow-related points more challenging. Remember data doesn't always play nice boys and girls; get a bigger sample size (to a point) - yay randomness!

Spoiler: show

Colors
New gems brought new colors!
New colors added: beige, midnight, sapphire, burgundy, sage, peacock, pumpkin!

historical note: we've lost one color - Turquiose (now turquoise). Retconjured / RIP!

Gem Names
Gem names are not permanent - you can rename them, even if you didn't mine them up or initially name them. (thank you Valareos for verifying)

Raw Data

Spoiler: show

Archive
I'm moving a few parts of this document down here. They're interesting history that make people aware of the challenges posed initially in figuring some of this out that are no longer the case, like:

Did you know gem points weren't available information outside of the leaderboard?

Spoiler: show

Thank you everyone who's been participating in this thread! We've learned a lot and wouldn't have without your involvement!

Now that we have established the size/glow probabilities within a reasonable margin of error, I will likely be updating the main post at a much lower frequency. I intend to revamp the front end here to be more informative piece than it is now, and move a lot of the history into a Spoiler-blocked Archive of sorts.

If there were a single thread and post I'd ask that you make sure to enter, it's the end-of-the-month screengrab of all the gems you've mined for the month. That's a huge data dump and easier to process. Right now, for instance, this thread has collected over 225 unique gems, while the end-of-March data dump thread acquired over 400!

Again, thank you all for the input!

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