Your math in the beginning of the video isn't quite correct... The limit of 4x+1 as x approaches infinity is infinity, not 4... The limit you are trying to take is the ratio "blocks exposed per block mined". The formula for this should be [number of blocks exposed, but not mined] / [number of blocks mined] = (4x+1)/x The limit of this as x approaches infinity is indeed 4. However, as others have pointed out, each block you mine can also be a diamond ore, meaning the number of blocks you actually expose should include the blocks you mine. therefore the limit should be 5x/x = 5 for the 1 block high tunnel. Edit: Okay, so I found another mistake in the end of the video, when you are comparing the efficiencies of tunnels with different spacing. The standard deviations of the mining efficiencies are too large in order for you to conclude anything about which spacing is most efficient. The sample size needs to be much larger.

Once you take efficiency 5 into account, 2x1 tunneling is actually faster because you're not slowed down by your crawling speed. Of course you could use speed potions to get rid of that but that's an extra expense.

In your "100% efficient" farm, the piston still blocks the growth for a few ticks. For the truly pointless true 100% you would have to use TNT or something else to harvest without blocking.

I looked for one last week for like 2 days best one o found was with a hopper and that makes it so slow, now you pop into my shorts thank you.

This was absolutely awesome. Absolutely awesome. I’m not an incredible math person and only took the first Calculus in college but you made it very accessible. Nice work👌

Amazing video. Time flyed and I didn’t realize how long it was because I was so engrossed

Something that might be important is that in a 1x1 tunnel, you'll be moving more slowly. This matters for the return trip, after you're done mining, and it would matter earlier if you could mine blocks faster than you could move to reach new ones

Fantastic! Thank you! Been looking for a deeper analysis and this hit the spot hahaha

You should try this in Java for even more accuracy

You just earned so much respect

Hey. You can't mine a 1x1 tunnel.

Damn, this looks pretty good!

I think that the shopping signal can break the farm since you are locking a repeater in the orange clock since if that repeater is on when you lock it the orange line will turn completely on a and there won't be a way to turn the farm on again without some rebuilding

something I would Love to see is this analysis but on iron instead of diamounds, I usually dont have a diamound shortage because am verry careful and not many things use them, but iron, Everything use iron and am Always on an iron shortage and I would actually be fine with strip mining just for iron when I Really need it

I used to strip mine back in the day because I was EXTREMLY terrifyied by mobs and caves where dark and had mobs so I did Everything to avoid them, tho now a decade later, I mine in caves because I find it faster and I like running and jumping around while am kinda sick of just digging like I used to do back a decade ago, also am not as scared by mobs as I used to be

Hi, i continue to explore your videos. This is realy nice one. Even though you do not use any classes for structuring your code came out realy neat. I think there is one more metric that would be helpfull. yield/plant/harvest(time) For thouse who want to get maximum kelp for given game lag.

I feel a little dumb asking, but how do you mine a 1x1 tunnel? Do you need an elytra?

I spent 2 hours mining ores in caves instead of strip mining. When caving with a nigh potion and elytra + magma block for caves with water, I got 5 stacks of diamond ore compared to 2 and a half stacks when strip mining in a 2x1. I would say it really depends on how lucky you are to find a cave that's easy to navigate so I wouldn't call those numbers a reliable metric, just putting it out there if anyone wonders how strip mining may compare to cave mining.

Amazing! Please do more of these for minecraft stuff!

I think in the newer versions Diamonds are less likely to generate next to air blocks in attempt to nerf the cave mining which got a huge vuff from the bigger caves. It is debatable though if the nerf was sufficient

I still prefer strip mining at y=-58. Within an hour I'll have more diamonds than I ever need in a game and it gets me a nice stash of deepslate. I love using deepslate, especially combined with dark oak.

My only question is, considering you'll be returning periodically to the surface from your mining journey (to empty your inventory, craft new tools, etc), how long can you mine a 1-block shaft for before the time it takes to go back to nullify the gains in relation to other methods?

dam

Really neat stuff, hope your channel reaches the algorithm and you get more attention for your work. Your wizards chess recreation is awesome btw

The abuse of the limit notation is so painful

But how do you make a 1x1 tunnel if the player is 2 blocks tall

4:10 Did you consider that for the layers in the middle you're exposing triple the amount of blocks? (if you go for 2x1 or 1x1, but the others have similar ratios) you could triple the amount of diamonds in the middle layers and then scale everything down

One thing you didn't account for is the return to base time, when you mine one long tunnel you'll take longer to return, would be nice to see if it ends up changing the results

This is so cool! any chanche we can loon at your code? id love to see in depth how youre simulating all of this in python

cave mining isnt as efficient since air exposed veins are usually smaller, this was a countermeasure implemented against the new bigger caves to make them less OP

Yesterday I used a simple TNT duping quarry for about an hour and a half and got 2 stacks of diamond ore, with fortune III it ended up giving me 426 diamonds. It also only took about 10 minutes to build the machine

i think what you should calculate each method for different pickaxe and their enchantments. and maybe beacon effects I have feeling what mining with effectivity 5 netherite pickaxe with 1x1 tunnel method would be more slower compare to 2x1 tunnel just because you move very slow wile crawling

this fps is making me sick

Oh look, another person that uses Excel to play Minecraft. Friend of mine uses it to design farms

Обожаю статистику! Спасибо за видео. Очень интересные подходы к сбору данных. Если бы я решал подобную задачу, возможно, я бы попытался автоматизировать процесс. Возможно написать программу для эмуляции генерации руды в майнкрафт. К сожалению, я считаю, что данных мало чтобы утверждать что твои результаты статистически значимы. Если что, могу и на английском ответить, просто с большими текстами мне бывает трудно выражать свои мысли на англиском.

I love how you brought in a calculus limit. I was thinking the same thing!

Mfs get a PhD in statistics and CompSci and immediately use it for Minecraft. This community is so good

Ok, but I always do 1x1 1 gap spiral mining and I've felt proud of how unique and efficient I was being. Could you run the math behind that one too? (my way of doing it is by mining 3 blocks left and 3 forward extra before turning right and mining until I see the 3 mined blocks to the right and then turn right after 3 more. The logic behind that method is that I have some sort of OCD that makes me think of the left behind and unmined diamonds and without doing any math, I've "proven" to myself that this is the best way to do it. I'd LOVE to see some numbers behind that method too!

What about the time it’ll take to get back to your base? As when you are crawling you are very slow vs sprinting in the 2x1 vs head hitting in the 2x1?

Awesome analysis and testing! Mad respect, SeaJay!!

Doing gods work for the community ❤

fundamentally, exposed blocks per block mined are still ordered the same whether you count the block mined or not, it's just adding or subtracting one from every ratio at the end of the day

One thing I was hoping you'd test is the spacing with the side tunnels. Like should the offshoots be 3 blocks apart, or 4 or 5 perhaps? I think that would make a larger difference than the spacing between the tunnels themselves given that they're quite wide compared to the no offshoots tunnels. Very nice vid tho

You should do sweetberries, their mechanics are quite interesting.

Gotta love tech minecraft. Keep it up bro

Love the “Only survival friendly of you hate yourself” 😂

By the way, the randomness of redstone should hopefully be fixed in the latest snapshot if you turn on the experimental redstone feature, since thats basically what they changed - before that there are some undefined states in which basically some stuff like hashes in the backgrounds or chunks or stuff like that determine the outcome instead of a true random number generator, creating location based behaviour sometimes.

Since diamonds generate a certain amount per chunk it might be good to align ur mining tunnel between 2- 4chunks

I think the more interesting discussion when it comes to "most efficient" bamboo farms is bonemeal based farms. How does it compare especially in terms of area efficiency and resource cost? Both with and without factoring in the necessary bonemeal farms

you’re so smart holy shit