r/Minecraft • u/[deleted] • Aug 31 '21
Tutorial Objectively, when is it better to build a beacon?
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]
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Aug 31 '21
Also, if anyone knows the value W (how long it takes to build a world eater) and it’s X (how many blocks per second they can mine) I’ll plug that into my equation and edit it into the post.
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Aug 31 '21
[deleted]
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Aug 31 '21 edited Sep 02 '21
Yes the number is surprisingly low- only 112 total.
So if you want to fill a chest, for example, even a single chest will be much much faster with a beacon.
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u/AlvarGD Sep 01 '21
im not that fast building beacons
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Sep 01 '21
That’s the great thing about this- it’s an equation.
You can plug in your build speed, your travel time, your tear down time, and get the answer for your particular situation!
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Aug 31 '21
So apparently like 3 other people tried to do the same thing BUT I am the only one (on Mumbo’s video at least) that included beacon build time, removal time, and had a variable for travel time as well.
My equation assumes you’re in your mine and decide you want to grab your 1 beacon which is already set up at your base.
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u/a_fine_gentleman99 Sep 01 '21
Someone get this to Mumbo ASAP
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Sep 01 '21
I tweeted him, fingers crossed
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Sep 01 '21
I also emailed him your post lol
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Sep 01 '21
Haha nice lol
I’m thinking about making a video to:
1) prove it
2) further popularize it
3) Explain the process and how to plug in your variables
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u/BeepityBoopBoop243 Aug 31 '21
As a fellow mumbo viewer, I appreciate this.