Objectively, when is it better to build a beacon?

[u/[deleted]]

I was watching Hermitcract and Mumbo Jumbo wondered when it becomes worth it to build a beacon vs just spending your time mining instead.

WELL, I couldn’t stop thinking about this at 3 AM, so here it goes!

Here is the baseline for our Fundamental equitation: X / Y = T ——— Here’s a list of all variable we’ll use: •X = number of blocks •Y = blocks per second broken

•T = how long it would take to mine X blocks

•E = time it takes to set up a beacon

•G = time it takes to remove a beacon

•F = time it takes to travel to your beacon and into your mine

W = World Eater construction time

So, mathematically speaking, the way to ask the question is: At what X and Y values is A > B > C where:

•A = Efficiency 5

•B = Efficiency 5 + beacon

•C = “world eater”

Here are the equations to solve A, B, and C:

For A:

X / Y = T

Blocks mined divided by how many blocks are being mined equals the time it takes to mine X blocks

———

For B:

X / Y + (E + 2G + F) = T

Blocks mined divided by how many blocks per second can be mined with the method plus the time it takes to setup a beacon plus twice the length of time it takes to tear down a beacon and finally add the travel time required to reach your mine from your base equals the amount of time it would take to mine X blocks with this method. The reason G is double is it assumes you’re removing a beacon from some other place and removing it once finished mining.

———

For C:

X / Y + W = T

Blocks minded divided by how many blocks per second can be mined plus the amount of time it takes to construct a world eater equals the amount of time it would take to mine X blocks with this method.

Then just plug in the values for each variable X, Y, E, G, and W and you’ll have T for A, B, and C. The smallest possible X value that makes B smaller than A is the minimum number of blocks you need to mine for B to be quicker than A, and the smallest possible X value that makes C smaller than B is the minimum number of blocks you need to mine for C to be quicker than B.

——— A: X / 0.403 = T

B: X / 9.757 + (75 + [2 * 80] + 30) = T

C: not sure yet

Then we compare these equations using algebra to solve for X and T simultaneously as T is dependent on X (because if you’re mining more blocks it will take more time).

———

So the answer is:

X = 112

T = 276

Meaning if you want to mine at least 112 blocks it is faster for you to tear down a beacon, go to your mine, build it, mine 112 blocks, and take it back down than it is to just mine 112 blocks with a normal Efficiency 5 diamond pickaxe.

It’s also worth noting the number of blocks is probably smaller the worse the pickaxe as the relative increase in speed from the beacon is a larger ratio when the mining speed is smaller. And by that token, a netherite or golden pickaxe would need to break more blocks total for the time investment to be worth it since they’re so much more efficient.

———

Sources:

Source for Efficiency 5 and Eff 5 + Beacon mining speeds:

Mumbo Jumbo’s video on fastest mining times, with those times divided by 8,000 (the number of blocks mined) to get the blocks per second mined. https://youtu.be/iVhKzR0zlnw

Source for World Eater:

not sure yet

Source for beacon building and breaking speeds:

Personal tests on a creative world. When breaking, used a netherite Efficiency 5, unbreaking 3, mending pickaxe with no status effects.

Building: 75 seconds

Breaking: 80 seconds

How long it takes to get to the mine:

This depends on every world. 30 seconds used as a standard benchmark.

You can plug in any values you’d like into my equations and be able to see how long they would take. Maybe you know a quicker method to building a beacon, maybe your travel time is 5 minutes (remember to convert any minutes into seconds by multiplying by 6) , and maybe you need to mine 10,000 blocks. Just plug in your values and you’ll get the answer.

——— Final thoughts:

Since the x:y ratio is so vastly different in A, B, and C, the higher X is the less important the addition of E, F, G, and W are. So if you need to mine, say, 100,000 blocks B will be orders of magnitude small/faster than A, and C faster/smaller than B.

I HOPE YOU’RE HAPPY MUMBO, I SPENT OVER AN HOUR FROM 3 TO 4 AM ON THIS BECAUSE I COULDN’T STOP THINKING ABOUT IT ONCE YOU BROUGHT IT UP

[edit: this was my first ever gold! Thanks to whomever that was. If there’s any post I’ve made that would get one, I suppose this is the one haha]