Targets
The blaze spawner split analysis in Blaze Bed or Zero Cycle? left a lot of unfinished work to do:
- For open spawners, we did not consider the case when blazes just drift away; For closed spawners, we did not consider the case that lava can be above the spawner.
- We did not consider the cases when we already have rods from strays entering the spawner, or how we may adjust our strategies after killing the blazes from the first spawn cycle.
- We always prioritize finishing all 25 seconds of spawner cleaning, but we might want to prioritize doing overlaps if we have a high rod count.
- (for ranked) An average time is not enough of a representative of win rate. For example, the difference between being 2 minutes ahead and 3 mimutes ahead is not nearly as affective as being 30 seconds ahead and 30 seconds behind. Most of the work is done for this and I will finish if and when I feel like it.
- (for rsg) An average time is also not enough of a representative of the probability of getting a pb/wr/sub 10/any other set goal. But that is way too complicated and requires proper modeling for every other part of the run so that is not going to be covered.
So I rewrote the spawner split simulator to take these factors into account, and it is also yielding a lot of other interesting results.
Approach
Leftover Details
Different Difficulty to Killing Blazes
This is only a problem if you blaze bed a open spawner. The best analytical approach I can think of will be something like this:
Because the blaze practice map does not recognize the actual hitbox of blocks, We will have to use
NoAI Blazes to block the spawn space to simulate the wasted spawns. But even if the blazes don’t fall off immediately upon spawn, they can still drift away if you don’t hit it careful enough, and that also costs extra time. So instead I manually killed ~100 blazes each for when there is nothing built out, only the back built out, the back and the left built out and fully built out. I also discarded results for blazes that take more than 7.5 seconds to kill, which is kind of an arbitrary cut off.
| Column 1 | None | Back | Back & Left | Full |
|---|---|---|---|---|
| discarded | 38 | 5 | 3 | 0 |
| spawned | 122 | 83 | 94 | 80 |
| average time to kill | 75.75 | 55.37 | 55.54 | 51.14 |
Note that I also applied Laplace Smoothing for the data, meaning I assume at the start there is 1 blaze discarded and 1 not. Using this data, the average time of a single blaze bed on an open spawner goes up by 2.9s to 1960.08±0.0620 ticks:
Side Note: You can see that there are many extreme points around early times, and there are very good reasons why that is the case. For example, in order to reach a spawner split time of
1087ticks, all you have to have the first and second spawn cycle spawn a total of 6 blazes and they all drop, and do all499ticks of spawner cleaning before the second cycle. That way, the remaining time before and after the second spawn cycle are fully used to do the300ticks of overlaps, adding up to48 * 6 + 499 + 300 = 1087. In this process, the biggest factor of randomness, the cooldown for the spawner is completely eliminated(so long as499 <= 20 + cd1 + cd2 <= 499 + 300), which is why so many results collide on this one tick. This also happens for the original results in Blaze Bed or Zero Cycle?, you can zoom in to see them.
Lava Spawner
I looked into the code for generating lava springs in the nether for 2 hours and gave up, according to what I found there are 3 different ways that a lava spring generates and its distribution across different y levels were all different and weirdly complicated and it would just be a complete nightmare to calculate it analytically and compare it to the distribution of spawners in fortresses, blaze bedding exploding which blocks, etc.
Instead I also just manually sampled 100 spawners, 15 of which had lava above it, though most of them can be quickly blocked if you react fast enough(which I modeled as a 5 second time waste), only 6 cannot be blocked fast and causes real problems(which I modeled as a 15 second time waste).
Side Note: The same Laplace Smoothing was also applied. I implemented the time waste here as the clean progress halts at when the bed was triggered and further time spent not registering before the time waste was met.
With that, the average time of a single blaze bed on a closed spawner goes up by 0.5s to 1994.06±0.0644 ticks:
New Features
Resample
In previous versions I made the spawn rate after same cleaning time the exact same, but I decided to include the information from the raw data how much the spawn rate deviates by including a random truncated normal distribution of 0.5σ deviation of spawn rate. This changed the average results by around max 3 ticks.
Difference with Rod Count After First Spawn Cycle
In reality, we only have to decide whether to blaze bed or not after killing the first batch of blazes. We can also calculate how much a rod is worth at a certain point and decide whether or not to go for a stray blaze.
Side Note: That is, if you would have to go to a spawner at all.
The solution is simple: Make the rod count and blazes killed in the first spawn cycle a parameter, and instead of having the cooldown 20 ticks, let the cooldown be a random cooldown left after killing that amount of blazes.
Adjusting Strategy Based on Rod Count, Spawner Cleaned and Overlaps Done
This is really the heart of the issue. The solution I ended up with is to calculate for every rod count spawner cleaned and overlap done combination, how much time we should spend further clearing the spawner before switching to doing overlaps (the precision of time is lowered to second to save computational resource, which lowered the time for solving a spawner from 21 days to 1.3 hours). You can check on the details its implemented in the code, basically it is a slightly optimized version of running a simulation for every possible strategy, so the strategy solved might not necessarily the best strategy, but based on the iterations of simulations I used every decision cannot be more than ~2 ticks worse than the optimal one.
Comparing a strategy to another
This means the drop rates, spawn cycle cooldowns and spawn position have to be standardized. Rates and cooldowns are easy to standardize, but the available spawning space % does not include the information for where exactly the spawns are blocked. So for that I made that if both spawner are at a state before floorCleaned(that is, explosives being triggered in a spawner), 80% of the time the spawn check share the same rng(the spots that fails spawns are highly overlapping); whereas if either of the spawner reached floorCleaned, only 20% of the time the spawn check share the same rng(the spots that fails spawns are very much independent, random fire, blocks uncleaned, etc.).
Note: If both spawners are fully cleaned, the number should have been 100%, but I claim that at that point probability of spawn failing is low and it would not have a drastic effect.
Note: this only affects the distribution of the time gain/loss graph, and not average.
Results
With all that details out of the way, let’s see some results!
Strategies
blaze 1 bed open remade solved.txt
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7 17 19 22 16 22 22 20 22 20 22 21 20 20 22 20 20 22 21 20 20 18 19 19 20 17
2 21 21 22 23 23 21 21 23 23 23 21 21 21 21 22 21 22 21 21 21 20 20 21 14 14
8 13 22 21 24 20 22 24 23 24 22 22 24 24 22 22 23 22 22 22 22 22 21 21 22 15
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5 12 6 11 11 11 12 11 11 13 11 11 12 10 12 12 11 11 13 11 13 11 13 11 11 11
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8 13 10 16 16 14 16 15 14 14 15 16 15 14 14 14 16 14 16 16 16 16 15 14 14 14
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10 16 16 19 16 18 19 19 18 19 19 19 19 19 19 19 19 18 19 19 19 18 19 17 17 17
5 11 20 18 20 20 18 20 18 20 18 20 20 18 18 20 18 20 19 18 18 18 19 18 20 18
13 13 19 18 19 20 21 20 21 21 21 19 19 19 21 19 21 21 19 19 21 19 20 21 21 21
18 18 22 22 20 22 21 22 22 21 19 22 20 22 20 20 20 20 20 20 20 22 21 21 20 22
21 16 21 22 21 23 23 23 23 23 23 21 21 23 21 23 23 21 21 22 21 21 23 21 21 21
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22 21 25 25 22 24 25 25 24 25 22 25 23 23 24 23 25 23 23 23 25 25 23 23 23 23
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1 4 2 1 0 4 2 2 4 2 4 4 4 3 4 4 4 4 4 4 4 4 3 4 4 4
3 0 3 5 2 5 5 5 3 5 4 4 5 3 3 5 5 5 5 5 3 5 5 5 5 5
2 3 6 3 6 3 4 5 5 6 6 5 6 4 6 6 6 4 5 6 4 6 6 6 4 6
0 5 4 6 7 6 5 7 6 7 7 7 7 7 6 7 7 7 7 7 7 7 7 7 7 7
0 4 6 7 5 8 8 6 8 6 6 6 6 6 6 8 8 8 8 6 8 8 8 8 8 8
6 6 7 6 9 7 7 8 7 9 7 9 9 9 9 7 7 9 9 7 9 9 7 7 9 9
0 10 8 8 8 7 10 10 10 10 10 10 10 10 10 10 10 10 8 10 8 10 10 8 10 10
0 11 6 11 11 11 10 10 8 10 11 11 11 11 10 11 11 11 11 11 11 11 11 11 11 11
3 10 9 11 11 9 12 11 12 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
13 3 7 11 10 12 11 13 13 13 13 11 11 13 11 11 13 13 11 13 13 13 13 13 13 13
10 7 14 14 14 13 13 12 12 12 14 14 14 14 12 14 12 14 12 14 14 12 14 14 12 14
13 13 14 15 15 13 14 13 15 13 13 15 15 15 15 13 15 15 15 15 13 15 15 15 13 13
9 11 14 13 13 15 16 16 14 16 14 16 14 16 16 16 16 16 16 16 16 14 16 14 14 16
7 15 16 17 15 17 16 16 17 17 15 17 17 17 16 17 17 17 17 17 17 17 17 16 17 17
6 9 17 17 16 16 17 16 18 18 18 18 17 17 18 18 18 18 18 18 18 18 18 18 18 18
15 16 15 19 19 19 17 19 18 18 19 19 19 19 19 19 19 19 18 19 19 19 18 18 19 19
13 17 20 18 17 19 20 20 19 20 18 20 20 18 20 20 20 18 20 20 18 20 20 18 18 18
13 18 21 19 19 21 21 20 19 21 21 21 21 19 21 21 20 20 21 19 21 21 21 21 19 21
7 22 21 18 19 22 20 20 22 22 22 22 22 22 22 20 22 22 22 20 22 22 20 20 22 20
12 13 23 23 20 23 21 21 22 22 23 22 21 22 23 23 23 22 23 22 22 21 21 23 21 22
11 24 24 22 22 24 23 24 24 24 22 24 22 24 22 24 24 24 24 22 23 24 22 22 24 24
20 20 22 25 25 24 25 25 23 25 25 24 23 25 25 23 23 24 25 23 24 23 23 22 23 25
The 8 squares correspond to the case of having 7, 6, 5, ..., 0 rods; the 26 rows each correspond to having the spawner cleaned 25, 24, 23, ..., 0 seconds and the 26 columns correspond to having 0, 1, 2, ..., 25 seconds of overlaps left to do. As a quick refresh, the numbers denote how much time by seconds we should spend further clearing the spawner before switching to doing overlaps.
For example, you can see for open single blaze bed, even if you need 25 seconds to finish overlaps, if after killing blazes from the first spawn cycle you have 4 rods, you should still blaze bed instead of doing nothing to the spawner, and build out only the back of the spawner before moving on to doing overlaps(spend 15 seconds clearing). This is still true for 3 rods, but for 2 rods you should do overlaps around the time after building the back and the left of the spawner(spend 20 seconds clearing). But if you can do your overlaps in 15 seconds(used in Blaze Bed or Zero Cycle?), you should instead spend 22 seconds clearing, meaning you should fully build out both sides of the spawner but not bother to break extra blocks.
You can come up with other logical conclusions like that. As for whether you should remember all 4*7*26*26=18928 numbers for actual speedrunning, I will leave it for you to decide.
The first column denotes how much time you should spend clearing the spawner if there is 0 seconds left to clean, in such case I just make it so that you keep cleaning the spawner, so it doesn’t matter and is fully random. In theory, the numbers should go down as we go from left to right, but for the said reasons there may be some deviency because the chosen strategy is not worse enough than the optimal one.
Spawner Splits
With the optimal strategy, we only manage to save a mere
~6 ticks from always fully clearing out the spawner. That is because in most cases, blazes from the first spawn cycle only drop 0~2 rods and in that case building out the spawner isn’t that much of a worse strategy anyway. But let’s say we have rods from strays, so that after killing the first 2 blazes we have 4 rods:
In this specific case, doing the optimal strategy saves 2.2 seconds.
To see how much time a rod is worth, let’s work out the numbers for all rod count after killing 2 blazes:
| Rod | Avg Time | ΔTime/ΔRod | ΔTime/ΔBlaze | ΔTime(s)/ΔBlaze |
|---|---|---|---|---|
| 0 | 2132.38 | / | / | / |
| 1 | 1846.57 | 285.81 | 142.91 | 7.15 |
| 2 | 1566.17 | 280.40 | 140.20 | 7.01 |
| 3 | 1308.85 | 257.32 | 128.66 | 6.43 |
| 4 | 1036.24 | 272.61 | 136.31 | 6.82 |
| 5 | 741.82 | 294.42 | 147.21 | 7.36 |
| 6 | 375.18 | *366.64 | *183.32 | *9.17 |
| 7 | 300.00 | *75.18 | *37.59 | *1.88 |
*The last rods, more specifically the last two rods are worth much more than that since you might not need to go to the spawner at all.
This means that each stray blaze is worth roughly 7 seconds if you would always do single blaze bed at an open spawner.
Comparing Strats
Blaze Bed vs Iron Pick
Open
at 4 rods after killing a 2 spawn spawn cycle:
The average being positive means that the latter takes more time, in this case blaze bedding saves
103.9528±0.0352 ticks or 5.20s on average. (the historgram kinda looks like a cat)
at 5 rods after killing a 2 spawn spawn cycle:
Interestingly, at
5 rods the optimal strategy solved for both blaze bed and mining out with iron pick are do overlaps first, so what it is really saying is that if you ignore the value for the extra bed for consistency, the optimal strategy at 5 rods is do all your overlaps, and if they are all done then you should do single blaze bed, saving 0.3s on average. Who would have thought?
For reference, if we make it so that we still always finish 25 seconds of blaze bed cleaning before doing overlaps, then mining out with iron pick saves 5.32s on average.
overall:
Blaze bedding saves 20.54s on average.
Closed
at 4 rods after killing a 2 spawn spawn cycle:
Blaze bedding saves 4.87s on average.
at 5 rods after killing a 2 spawn spawn cycle:
Blaze bedding saves 0.78s on average.
overall:
Blaze bedding saves 19.54s on average.
For now I still only have data for single blaze bed vs mining out with iron pick, but this can also be nice for double blaze bed, blaze 1/2/3/4 lifted/4 donut tnt, left & right vs front & back blaze bed, iron pick vs gold pick, etc.
But I am burnt out from data collection, so I am officially accepting data donation. If you believe you are fast enough to collect data, you simply need to go into the Mescht’s Blaze Practice Map, turn off Blaze Spawning, run the following command
/scoreboard players set 500 c 500
and put this command into a repeat command block
execute if score timer timer <= 500 c run tellraw @a [{"score":{"name":"timer","objective":"timer"}}, " ", {"score":{"name":"available_per","objective":"spawns"}}]
do many many spawner cleaning sessions with the method you wish to collect data for(ideally as fast as possible, for every session wait until no more data shows up in the chat before resetting, remove in the log or at least leave a note on sessions that you messed up on to get them discarded), then send me the log(you can remove the irrelevent parts).
Data and code used in all the analysis can be found in
SpawnerSplitAnalysis,
But may you be warned that I did not clean up the code and the project as a whole is a mess and you would likely spend half the time I spent on the project to understand what is going on.
