Reducing the VRF Variance for Parcels

Hey frens, I wanted to create a standalone thread for the topic already mentioned below as well as in the Discord:

The VRF variance for Alchemica under the ground of parcels (0.2 - 1.8 of average) seems way too high to me and could lead to some people getting rekt big time. Stealing @eitri’s graphic he posted on Discord (feel free to cross-post the rest) to illustrate my point:

As you can see, a very unlucky spacious owner could get less alchemica than a lucky reasonable owner - which is imo absolutely insane, especially considering that it was communicated this wouldn’t be possible (at least that’s what I remember). Keep in mind that the first round (quarter) will distribute more Alchemica than the rest of them, so losing big in the first round could set someone back by a lot.

I want to propose lowering the variance to AT LEAST 0.5 - 1.5 if not even 0.75 - 1.25 for the first round. My issue with this insanely high variance is that people made financial decisions based on the average numbers published before the first auction, making people lose 50-80% of Alchemica value underneath the parcel is terrible UX to me.

A few things to keep in mind:

  • There are 9 rounds, so getting rekt in 1 doesn’t mean you’ll always get unlucky (even though you might!)
  • There is a VRF roll for every type of Alchemica (FUD, FOMO, ALPHA, KEK), so it’s likely you’ll get good rolls in one and bad rolls in others

Attaching a poll to see what the sentiment is, my choice would be 0.75 - 1.25 for round 1 and 0.5 - 1.5 for the rest of the rounds.

  • Keep the variance at 0.2 - 1.8
  • Lower it to 0.5 - 1.5 for all rounds
  • Lower it to 0.75 - 1.25 (round 1) & 0.5 - 1.5 for the rest
  • Lower it to something else

0 voters


Thanks Moon :slight_smile:

Here’s what the 0.2 - 1.8 range looks like, with min/avg/max plotted for each parcel size:

The Spacious range is really huge compared to the others.

Also, the ranges for different sizes overlap, i.e. it’s possible to roll a Spacious that has less alchemica than a Reasonable, or a Reasonable that has less alchemica than even an average Humble. Personally that feels wrong to me

I think it’s also interesting to look at the % that an unlucky minimum roll gets compared to the maximum - for 0.2 - 1.8 range, that’s 11%. So the unluckiest person is nearly 10x worse off than they could have been, which would be a horrible feeling.

The large Spacious range does benefit gamblers, with a much higher potential reward. This might be good if you equate whales = gamblers, but bad if someone has saved everything to get a single Spacious and then has to do an extremely risky roll.

Changing it to use the suggested 50 - 150%:

The ranges no longer overlap, and the min-compared-to-max becomes 33%. The Spacious range still looks huge!

In addition, here’s the 3rd option 0.75 - 1.25:


I think the graphs tell the story here. It’s really difficult to imagine a spacious parcel owner getting less of ANY resource than a reasonable parcel owner.

With the first round yielding significantly more alch than other rounds, I feel we have a responsibility to provide early land owners with reliable value – something we have not fully been able to accomplish with other in-game assets. I like the idea of lowering variance more significantly for round 1.

Even beyond the first round though, a larger parcel should ALWAYS yield more alchemica than a smaller parcel. Does this potentially prevent really funny and cool small parcels? Maybe, but it also provides some amount of security to people who are actually investing large sums into the gotchiverse.

0.5-1.5 feels like a sweet spot for most rounds. For round 1, I like the idea of going 0.75-1.25 to reward those of us who have held land and purchased it based on the shared averages during the auctions.

I can’t in good conscience vote to keep things as-is while voting against something like patch 0.1c (magnifying parcel boosts by 5x). Both are a departure from information that was shared when auctioneers parked their GHST.


Thank you, @eitri, for sharing this detailed analysis and charts to help put things into perspective. Seeing as how the initial distribution of alchemica for Round 1 of Act 1 is going to be significantly higher than future Rounds, I would vote to have the variance be limited to the 0.75-1.25 range.

Reason being, this feels like the first real gift the Team has given early adopters and everyone that owns a parcel should be able to benefit from it significantly. For future rounds, I think the 0.5-1.5 variance can be implemented since parcels will continue to get 4 VRF rolls after each Round (1 roll per alchemica type). So in the long run, things will even out closer to the average alchemica distribution as people will have more VRF rolls.

Lowering the variance makes the most sense to me and benefits all parcel holders, especially with the bonus alchemica for Round 1. Let’s allow the Devs to rewards us early adopters by giving every parcel owner a nice chunk of alchemica to start with and grow from!


I think it’s important for parcels to have the potential to vary a lot between parcels in order to not have everything feel samey. But there is definitely a tradeoff between this and having users not getting rekt. I think one way to improve the situation is to simply distribute the alchemica by a different formula.

One formula we can use is the binomial distribution.

With this distribution, we can have most people receive about the same amount of alchemica, but still leave the potential for large variations. As can be seen from the variations in this chart, it’s possible to make the lower tail more or less punishing depending on the parameters you feed into the distribution.

To be specific, with the binomial distribution with parameters (n, p):

  • Increasing n will decrease the variance of the results, but also provide more possible outcome values
  • Increasing p makes the lower tail more punishing. p also doubles as the average value of the random number

One of the beauties about this distribution is that it’s fairly trivial to implement. We simply generate n random numbers between 0 and 1, and count up how many are greater than p. Divide by n, and you have a new random number between 0 and 1 but distributed according to the distribution. We can then plug this new random number into any transformation we want.

Here’s a concrete example:
We want an alchemica pull to range from 1000-11000 with an average of 3000.
We’ll use binomial(20, 0.2) to create a random number between 0 and 1 with average 0.2
Then the alchemica pull = binomial(20, 0.2) * 10000 + 1000

This achieves an average pull of 3000, a floor of 1000, and a ceiling of 11000 (extremely rare)

Here’s a Binomial Calculator to play around with


Making the VRF calculation for Alchemica rates on land less degen is something I can get behind.


Very elegant way to solve that problem, love your idea.

Another distribution model we could look into would be a Weibull distribution.
For an average of 1000, minimum could be 800, median 950, maximum 2000.

Could be fun although i’m not sure it is really worth to make it more complicated (and have 50%+ owners earning a bit less than expected). Could be a nice sink for us degens (ex: pay xx GLMR or FRENS to reroll)


Starting with the assumption that:
the narrower the variance, the less interesting the dynamics of Laand Parcel price discovery…
I ask myself, if this would entail a smaller price-discovery-space for parameters like location, neighborhood, road/wall/monument-proximity etc….

Or conversely:
that if the expected Alchemica-content would be more „predictable“, even more fantasy around other parameters would ensue.

I agree with @Moon, that a spacious should in no case turn out with less Alchemica than a reasonable.

Like @Mori, I think that „sameyness“ should be prevented.

I like the idea by @letsgobankless of limiting the downside, while leaving the upside similar to the 0.2-1.8 variance: I would be especially interested about the outcome of a vote about that.

Another vote-outcome I would be thrilled to see (although I dont think, that it would be desirable/feasable) would be about the possibility to be able to choose the variance when „opening the parcel“.

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So we basically need a balance between “stable outcome” and also “RNG”.
BTW I love that I can learn a lot of statistical maths from all of you guys.


I think its good how it is.

The spacious parcels are for degens, and I promise you there will be people who sit there continuloally buying unsurveyed spacious and reselling them, hoping for the godparcel.

The reasonable parcel is the reasonable choice, and a pile of humbles is the reliable choice. Do as ye will.

This is my vote. You’re brilliant as always. This afford a chance at a super-producer while protecting the downside.

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I’ve been working on a slightly modified version of the method I talked about, which I think produces pretty good results.

There are two key changes I make here:

  1. The prize scales exponentially based on the number of successful rolls
  2. I use a low p and cut off a big portion of the tail

This results in an average pull of 100, a minimum pull of 60, and a maximum pull of ~800. There is a fairly reasonable chance of winning this top prize, with ~0.02% of parcels being able to achieve this. The median is ~83% of the average in this model.

Potential Alchemica Distribution Table - Google Sheets and here is the spreadsheet I am using to generate these models. Model 2 is what I’m demonstrating here.


The long tail makes it so much fun while the low end is protected. I really support this model. The possibility of surveying a super-producer will add value to unsurveyed lands and support investors who have been holding onto land for months.


Also take into account that most of the parcels was bought without knowing about the variance beforehand, this could make people feel worse.

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Nice, I actually really like this model! I’m undecided between #1 & #2 but here’s the proposal:


I despise the idea of changing the rules after we’ve had two of three land releases, but this is the best way to do this bad idea. Definitely go with raising the floor a bit(-50% to +180% is pretty nice, uif you pay for it by making the average be about 90% of what it is now), but keeping the insanely high potential. This crowd has clearly shown they love to gamble, so taking away the high roll is not a good plan.

I also like the idea of letting people spend lots of GLMR for a reroll, as the more sinks there are for GLMR, the more people will be willing to stake large sums to get it.


Thanks for your input! Allowing people to pay for rerolls would make predicting overall alchemica output close to impossible. This is problematic because the amount of alchemica is capped, and targeting a certain number of alchemica being released per phase would be made difficult under those circumstances. Maybe it’s doable if we limit the number of rerolls available.

I like this a lot too! I dragged my husband in to plot these as graphs (as he does a lot more data science work than me):

Note that the graph on the left has a logarithmic axis for easier comparison between the parcel sizes, and the one on the right is the same data with a linear scale. The Y axis is amount of FUD, and the x-axis percentages represent the number of parcels which roll that amount of FUD, though the precise % values aren’t important, they’re just for plotting the graph.

The long tail causes overlap between parcel sizes, but at a very small likelihood (<1% of draws).

Here’s the spreadsheet, which also includes the other models with flat-probability (all values equally likely).


interesting work! Thanks to your husband for giving such a great visual aid. I wonder if we can consider the overlap a desirable characteristic? I think it could be pretty exciting to have a reasonable have the opportunity to outroll a spacious. This likely will not ever happen for all four elements, and I don’t think it’s too extreme or unrealistic for a lower tier to very rarely outroll a higher tier.


I really think people are undervaluing the 4 rolls thing. The odds of 4 low rolls are impossibly small. The odds of getting one roll so good you spend the round just mining that one are pretty high.