The answer is: 49253 ticks, with the efficiency 36.006436594099256 sugarcane per tick for 1 million sugarcane Or, 2462.65 seconds / 41 minutes and 2.65 seconds (Explanation in comment reply) Here is the python code that I used: from scipy.stats import binom def efficiency(cycle_length): n = 2 for i in range(0, 16): n -= 2 * binom.pmf(i, cycle_length, 3/4096) for i in range(16, 32): n -= binom.pmf(i, cycle_length, 3/4096) return n * 1000000 / cycle_length for i in range(49240, 49260): print(i, efficiency(i)) Here is the output: 49240 36.00642974585812 49241 36.0064307260955 49242 36.0064316307466 49243 36.00643245981445 49244 36.0064332133022 49245 36.00643389121294 49246 36.00643449354977 49247 36.0064350203158 49248 36.00643547151411 49249 36.00643584714785 49250 36.00643614722013 49251 36.00643637173403 49252 36.0064365206927 49253 36.006436594099256 49254 36.00643659195679 49255 36.00643651426848 49256 36.00643636103739 49257 36.00643613226671 49258 36.00643582795952 49259 36.00643544811894

When ilmango says “that would be a bit to advanced for me to calculate” We know we are screwed.

i love anti-clickbait. putting the answer in the thumbnail just makes me want to watch the video even more to find out how you arrived to that answer.

Shame it's not 42. So close to finding out the meaning of life was efficiently growing sugarcane

I am a big fan of ilmango's "I am right and here is exactly why" videos

Gotta love the thumbnail hahah😂 *"THE ANSWER IS 41"* Brilliant :')

A year ago I was curious about the same thing and I wrote a simulation in Python based on info I found on the wiki about sugarcane and got the similar results. The best seemed to lie within 40-43 minutes.

I will still do 42 no matter the answer!

41? Sacrilege! everyone knows that if you're this close to 42, you fudge the numbers.

I love all of his videos. They never fail to impress!

Sugar cane takes, on average, 21845.333 ticks to grow one block taller. The average time for sugar cane to grow from 1 to 3 blocks tall is 43690.667 ticks, or 36 minutes, 24 seconds, and 10.667 ticks. The reason is that a sub-chunk has a volume of 4096 blocks. A random tick speed of 3 means that each piece of sugar cane gains, on average, 3/4096 of a stage per tick. Since a sugar cane needs 32 stages to fully grow, you multiply the denominator, 4096, by the number of stages, 32, so you get 131072. Divide the numerator 3 from that and you get 43690.667 ticks. I assume the reason the optimal time is 41 minutes and some amount of seconds is because, if you harvest when roughly half of the sugar cane are fully grown, a large percentage would only be 1 or 2 stages from being fully grown, but would be harvested before being able to do so. The extra 4-5 minutes gives the sugar cane almost done growing time to do so whilst not wasting too much time not harvesting the rest that is already grown.

ilmango does it again! Another amazingly interesting redstone video. I absolutely love these.

I would love to see separate videos for the other extra farms you mentioned at the end. I find it's really helpful to have explicit videos for partially niche topics covered somehwere in a standalone video as it makes it a lot easier to find in the future.

Small correction around 2:45: a linear process would indeed reach zero, but that'd mean there's a finite clock setting at which the harvest yields no items, which of course doesn't make sense.

now I want Mojang to slightly adjust the growth rate so the answer is 42, not 41

Very interesting! I love the testing videos you've been doing, like the hopper locking and redstone lag stuff.

…. I had to test this for 400 hours to get some good numbers…. This guy is awesome

I really enjoyed this video. Honestly it's kind of like when you did the crystal math, it's just barely useful minecraft math. I love it.

I love your content ilmango, you're always the first one i look to when i need Minecraft expertise, but as an amateur videos like this make me consider searching elsewhere from now on. After 10 minutes, i understand why 41 minutes is the optimal time, but you didn't say *anything* as to how I reach that. I've been googling, rewatching and scrolling through comments and STILL have no idea how I am supposed to reach a 41 minute clock. I have the exact build you used for your clocks in this video, an item count next to the minutes would've been helpful for those of us who don't want to go through the process of joining your discord just to ask someone else something which is apparently so trivial it didnt need to be included.

I am really impressed for several reasons: One the science is crazy Two you actually put the answer in the thumbnail (no clickbait)

thanks for doing all these tech videos, always fun to learn new stuff in an old game. I have always used a daylight detector set to trigger right before a player are able to get into bed so the sugarcane gets a full day of growth before harvest each day. maybe time to reconsider and run it bidaily... :)

I've been thinking about what would be the perfect time for quite some time and this video was just absolutely perfect. Good job 👌

That was really interesting. I didn't think of all the growth stages and always just harvested mine every minecraft day using a daylight sensor. But it is nice to know that there is an optimum!

Amazing video. For me it began with a pumpkin farm which "mined" each pumpkin instantly, and I needed a clock that has a chance close to 100% to collect the pumpkin items before they despawned, for which I came up with connecting it to bamboo and making it harvest everytime the bamboo grew 2 blocks. After that I made my first sugar cane farm, and just used the same bamboo clock as earlier, so my sugar cane farm harvests every couple of minutes. Never really thought that there would be another local maximum in efficiency vs time besides the one close to instant harvesting. Might consider delaying my clock to this more lag-friendly alternative as a service to my friends playing on the same server XD. Already irritated them by accidentally making an automatic chicken farm exponentially blow up in amount of chickens while I was away that day. They had to massacre them with a bucket of lava in order to play normally again.

Massive props for putting the answer right up front

This would probably be a dofferent answer if you included the flying machine since the flying machine blocks potential growth while it flies. Maybe negligible but I would like it to be included in the experiment.

Priceless! Just put a 41 minute clock on my farm! Thank you for doing such awesome research!

Really love these kind of videos. Please make a Minecraft optimisation series/playlist. It will be super interesting for the community to try and reverse engineer the mathematics behind all these algorithms, or even come up with empirical answers.

Love the time and dedication you put in your video!

Hu, this is giving me flashbacks to the cactus mayhem we had back then. So I suppose the next couple of videos will be about more and more efficient sugar cane farms too? ;) I wonder if someone will actually present the forumla for the perfect harvesting time

i did figure this out before!, but never did any testing, so 41 sounds good. your logic for that makes total sense

Thanks! This was a question I’ve had in my mind for some time

I’ve been doing it at thirty for a while. Now I know! Thanks Mango! :D

This is interesting because on my single player world I built a small sugar cane farm of the type where the cane is broken by a bar of slime blocks pushed by a piston, and I spent some time testing and found that if you only let the sugar cane grow 2 high and harvested every 5 minutes you got more cane than if you let it grow 3 high for much longer. Of course, with such a small farm I wasn't concerned with the lag as I just needed a small regular supply growing in spawn chunks. This is also convenient because it it very easy to make a 5 minute timer with an item despawn timer.

there's also a consideration for how many potential growths are interrupted by the harvesting device being in the way. this matters most for very short collection cycles, but if your flying machine (or whatever) is where the crop would grow to, it can't grow. in fact, I think you've discussed this issue, maybe in the context of pumpkin/melon farms before.

Wait...the answer is not 42???

Very good video! Tips: you can easily make your graph more informative by putting the duration of the simulation in the title.

Reminds me of how you pulled up a spread sheet of Possion distribution when you calculated the optimal harvest interval for amethyst shards.

Stellar thumbnail. I wasn't even interested in the answer, but I watched, thumbed up and commented just for that thumbnail.

Amazing description

So cool, I had no idea about this.

Great video! What about bamboo and kelp tho?

I'm never this early. But early or not I'd never miss a video from Mango

It would be really nice to know the timings for other kinds of farms

The perfect timer for a bamboo farm was the first thing that came to mind!

Nice hitchhikers guide reference

I feel like the answer to all farms is "check out ilmango's vid on it"

"...see you in the next video!" My programming to switch the video in the last 10 seconds is always thwarted by your Recklass outro music.

Thank you ilmango, you're much better at farm math.

Hmm. What about stacking. Harvesting less frequently yields larger harvests. But is the farm lossless. Items that land in unrecoverable locations pose a threat to grab other items that otherwise may be collectable. I also anticipate this poses a lag concern as I imagine despawn timers are reset and larger stacks probably also pose a trivial amount of more lag. Additionally the third layer of cane could very well be more likely to be catapulted out of the collection system

So long, and thanks for all the fish

The cactus farm gave me an idea, what if you used allays to catch cactus blocks before they land on the cactus underneath? Maybe that would increase the efficiency of the farm.

I would really like to have seen a comparison with a constantly running flying machine. I don't play on a server, and my computer is more than capable of handling the lag I create, so I don't bother with a clock at all. You're also almost never losing growth stages.

i like how after someone proved to him how 41 minutes was slightly better than 40 minutes he quickly changed the thumbnail

I use the observer on each side detecting when most of it is already about 2 blocks high and i place it at the three block mark its not really efficient but its something i also use it for the bamboo farm or i call the fuel farm.

Yield per second, rounded down: 5min 6845/s 10min 3068/s 15min 1878/s 20min 1519/s 25min 1145/s 30min 910/s 35min 831/s 40min 764/s 45min 664/s 50min 556/s 55min 466/s 60min 392/s so in the same space, you can get up to 1746% more crops if you harvest 12 times more often I know it isnt that scientific, but I like some numbers

I love that new farms are being made for blocks that have existed since time and memorial.

I love the thumbnail

i wanted so badly for it to be 42 minutes. universal number

Maybe create a public google sheet with perferct timings for things, with applicable versions and so on (proof videos, items required in hopper clock, other notes)

Ilmango's a hitchhiker. Where's his towel?

wow! this is super insightful! how many *planted* sugarcane were there in a single slice?

Maybe a flying machine cactus farm would be really good, as you can increase density significantly. And yield should also be higher.

Using some basic statistical analysis in Excel VBA, I fit a 2nd order polynomial curve to the data, and I got 41 minutes and 2.8 seconds as the ideal harvest time based on the data shown on screen around 7:40

Does a random tick counter (like Doc uses for his amethyst farm, S9:13 around 11min) have the chance to increase the efficiency even more, keeping the long time between harvests?

Love the anti click bait thumbnail. I hope this becomes the new meta.

oh since you brought this up how about you do a " perfect clock for piston based amethyst farm " ive been strugling to know whats the best time to harvest amethyst ..

Can you put the last videos you mentioned at the end in the description please? Thank you

Deep thought says 42 is "the" answer

Good video 👍🏻

I sort of want to run a regression on this and give a really exact number. I would probably do a multiple regression to express farm size, because I wouldn't be surprised if that affects the numbers as well. Hmmmmm

Oh that's a pretty interesting math problem. You ideally want to harvest exactly when the sugarcane hits 3 high, right after that 32nd random tick. With a random tick probability of 3/4096 = 0.000732421875, so that would be 36.41 minutes. But, at 36.41m we get the 50%-point of the binomial bell curve, where half of the sugarcane has hit h=3. At 41m, that's 77.1% at a height of 3. Now the hard part would be to find where the percentage gains of waiting longer, stops outweighing the gained growth on a fresh field.

I wish it was 42 😂

Oman, the answer was so close to the right one! We all know it's 42, of course.

Well I'm not sure if anyone asked about the same but looking on your video about that new sugarcane farm and how lag friendly it is I'm getting a bit curious in similar designe for bamboo and perfect timer for that.

42 is the answer to everything after all.

it was so close. and yet so far.

Not 42 ???? Heresy !

If you make a flying based cactus farm using the same flying machine of the sugar cane farm, could this be more compact than the instant one. Because you could fit more cacti in the same area, the problem is that you lose vertical space in order for the cactus to grom 3 tall. i dont know, maybe the amount of cactus you place in one layer will make a difference. really great video Mango as always

I may have missed it but did Ilmango mention the rates for bamboo?

I always used lightsensor with binary counter o if I afked it harvested every 2 ingame days.

I do something different with my sugar cane farms. I dont use a clock with my sugarcane farm. What I do instead is have a line of 15 observers wait for a third layer of sugar cane to grow in front one of them. The observers triggers a flying machine. Because of this the harvesting occures at a variable rate. Can a plant timed sugar cane farm offer similar efficiency compared to a farm 41 minute fixed timer farm?

*Brings popcorn*

Lag and efficiency, these are what MC players really crave. I think you used to do lots of these, but not recently. Ps thanks for deep dive as always

So i know that it used to be a thing that the top (3rd) sugarcane block grew faster than the 2nd block because growth triggers from either lower block could stack upward for a new block, so how does a test about only the top block harvest only style short tick design work?

What about the clock times dor a flying-machine based farmfor kelp, twisting vine or weeping wine? There's even more variation, cause they can grow much larger

This makes me curious though. If you had a system that harvested immediately would it be more efficient to harvest just the top part of 2 high plants, the middle and top parts, or just the middle part without letting it get to the top growth stage?

How many items in the hopper would make it a 5min delay? I have roughly an hour before all my friends log on in a morning so i could run it at max efficiency for one hour, for the rest of my time online i wouldnt be able to spend much time near the farm for 41 mins to make a single harvest

I usually sync flying machine farms to the day cycle, is good enough

So the question all along was "what's the optimal time interval in minutes you need to wait for maximum sugar cane in Minecraft?'

i have an odd question/thought about lagg, ive seen that chests cause lag , but do double chests cause less or more lag, or would it be the same?

I usually build my sugar cane farms with an observer observing one sugar cane in the corner until it fully grows to 3 block height, which starts the flying machine. I wonder if the clock based farm is more effective.

As a Hitchhiker's Guide fan, the thumbnail pains me.

If i may suggest, perhaps including a pastebin of commands used in command blocks and such?

Daft question incoming: how many items would you need in the hopper clock for it to fire every 41 minutes? Might have missed a separate video where this was demonstrated/

Are you able to test the sugar cane count in intervals smaller than 1 minute? If so, I think it would be as simple as calculating the intervals between 40 minutes and 42 minutes, as a peak lies somewhere in-between those to values. I can see their being 3 scenarios: a peak before 41 minutes, at 41 minutes or after 41 minutes. If you aren't able to test it, the only way I can think of to predict which interval has the best return in sugar cane would require someone to fit your data to a function and then check for the absolute maximum between 40 and 42 minutes. I'm not sure which equation would best fit the sugar cane drops, so I'm not sure how to predict that, but I'm someone might know.

Wouldn't the harvesting mechanism effect the results? I think the actual results for lower times would be worse, as there's (a lot) more time a flying machine will be above the sugar canes when they are being random ticked, preventing the growth stage to increase. Also, pure speculation: won't the growth stage reset to 0 when a sugarcane is random ticked and it can't grow because of a block above it? That would make frequent harvests a lot worse.

What if you send it continuously at 1 block higer? So the grow stages won't get removed. Or is it exactly like the 5 min clock?

We should fiele a Buck Report. Random Ticks are definitivly slighty to fast because we all know the answer has to be 42

How does cutting 2nd and 3rd block compare to cutting only 3rd? How would the growth stage act? You'd have two blocks that can be random-ticked, so the plant growth stage should grow twice as fast. Definitetly not lag friendly because harvesting must be frequent.