Vault: Difference between revisions

==== Pyramid slopes ====

Pyramid have historically been designed to maximize the time needed to break them while minimizing the amount of resources (i.e: diamond) needed to build them.

This is especially important because the cost of a pyramid is <code>C(N) = 2*N³ + N</code> <ref>https://oeis.org/A005900</ref>, N being the height of the pyramid and therefore the number of blocks that will have to be broken in order to access to the chest at the center.

Adding an extra layer costs <code>Ca(N) = 2L(N+1)+1 </code> <ref>https://oeis.org/A001844</ref>

{| class="wikitable"

|-

! Height !! Additional Blocks !! Total Blocks

|-

| 1 || 1 || 1

|-

| 2 || 5 || 6

|-

| 3 || 13 || 19

|-

| 4 || 25 || 44

|-

| 5 || 41 || 85

|-

| 6 || 61 || 146

|-

| 7 || 85 || 231

|-

| 8 || 113 || 344

|-

| 9 || 145 || 489

|-

| 10 || 181 || 670

|}

It is however possible to reduce the overall cost while keeping the same break time.

The first method is to build the vault on the world border. This divides the total cost by 2 as players can not go past the border and will be teleported back.

Another classic method to lower the cost was to optimize the slope. A steeper slope than 1:1 could indeed be more efficient as players were not able to fit in 1 block tall gaps and would have had to break more blocks if they were breaking a 1:1 pyramid from the side. [https://www.youtube.com/watch?v=xY548SXhI44 Video explanation about vault pyramids]

Nowadays, most vault pyramids are 1:1. The main reason is that most of the time spent during a vault break will be breaking bastions rather than breaking the pyramid. Moreover, by the time attackers reach the pyramid, the vault will be virtually lost and afking the pyramid break is not as risky as it used to be.

Furthermore, players can now crawl and fit in 1 block tall gaps. Therefore, old break paths might not optimal anymore.