The Futility of Geoclaiming

As described by the folks at the COIN App:

Geoclaiming

When you Geoclaim a tile, you are becoming an owner of the tile for the remainder of the campaign(Currently UTC Monday to UTC Sunday). Anyone that Geomines using the COIN app in your area will give you a chance, based on your Ownership percentage, to collect 10% of rewards.

An Owner with 100% ownership of a Geoclaimed Area will receive the 10% of rewards every time. 

An Owner with 50% ownership of a Geoclaimed Area will receive the 10% of rewards half of the time. 

An Owner with 25% ownership will receive the 10% of a miners reward a quarter of the time.

In theory, this is a way of earning that sweet, sweet COIN without having to actually, you know, go places.

In practice, it’s a lovely exercise in overestimation and accidentally returning COIN to the system.

But it doesn’t have to be, and my current goal is to figure out means of optimizing geoclaims.

The Basics

The amount you get out – your return – is proportional to your stake – i.e. the amount of the area that you control, or what the COIN folks call your ownership.

I’m using stake because in this context, ownership is a misleading term. Take a look at this screenshot:

Throughout this week, my ownership has never dropped below 10%, and has usually hovered in the 13-14% range.  Yet, my returns are well less than even 10% of the total 10,940 COIN held by this region.

That’s because you don’t own a fraction of the COIN held; you get a fraction of the COIN earned, as it gets mined.  And remember that geomines are random numbers, further dependent on whether that user happens to have a sentinel at the time.  It seems that my RNG luck this week was pretty crap, since the users I was earning from tended to have lower mines than average.  That, or a lot of users in my area have premium accounts, which prevents their mines from entering the pool.  Probably both.

The Point of No Return(s)

Say it with me: your earning potential is not unlimited.  It’s determined by your stake, and by the available earnings.  If we make the simplifying assumption that your stake is actually an ownership, then

the amount you pay into the geoclaim – your investment – must be less than your stake multiplied by the total COIN in the region.

Seems obvious, but you would be amazed how many people on Reddit get hyped about how much they dumped into their latest geoclaim without realizing this basic fact.  And, as discussed earlier, your expected return is actually significantly less.  (How much less? I’m working on a heuristic, but that’s another post.)

Consider the screenshot above: That 13% stake cost me 1905 COIN.  Even if I earned a full 13% of the available ~11k COIN, I’m still not going to recoup my investment.  (In this case, I saw that coming, but dumped the all the COIN in for other reasons.)

Good Money After Bad

But what if I just increased my stake until the math worked out?  There’s a possibility that would work, but it depends on two things:

First, the distribution of investments.  If it were linear, then doubling my investment would double my return.  But it’s not linear, it’s a Pareto distribution (more on that in a future post).  TL;DR: it’s like the American economy, where most of the stakes are taken up by a very small fraction of users.

It turns out that doubling your investment does indeed double your return.  The only thing that matters is how much has been invested total, below.

Second, there is a point of no return.  If the total investments ever exceed the available COINage, then nobody gets a positive return, no matter how much they put in.

The math is easy enough:  Again, pretending that your stake is an ownership – which, emphatically, it ain’t – we can say that your return is defined by

\(R = s \times A\)

where R is your return, s is your stake, and A is the total available COIN.  Your stake, meanwhile, is defined by the ratio of your investment to the total investment:

\(s=\frac{i}{I}\)

So, we end up with

\(R=\frac{i}{I} \times A\)

If we want a positive return, then

\(\frac{R}{i} > 1\)

meaning

\(\frac{A}{I}>1\)

or, the total available COIN must exceed the total investment.  If everybody tries to pump up their stake, then there comes a point where everybody loses.  Whoops.

So can Geoclaiming work?

It depends.  Specifically, it depends on the distribution of stakes, and a few other factors.  I’ll get back to you.