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• 100% 1x T2 module
• 100% 1x red circuit, with 25% 1x extra red circuit
• 100% 1x blue circuit, with 25% 1x extra blue circuit
• 100% 0x tungsten carbide, with 25% 1x extra tungsten carbide

• T3Q1 & T3Q2 speed modules as input (with a customly-selected ratio of 3:1)
• T3Q3 quality modules in recyclers (+16% quality)
• Q4 & Q5 are not unlocked

Copy blueprint

Rseding91 wrote: ↑Sun Nov 10, 2024 7:23 pm Thanks for the report however random is random. It's entirely possible that you get zero of one result and all of another with an ever increasingly small chance.

Flouid wrote: ↑Wed Nov 13, 2024 2:37 am I just want to add onto this that I've spent a considerable amount of time working on a blue circuit recycling plant and I've created half a dozen design iterations. It's not at 300% productivity yet so an input of normal circuits is toggled only when the belts inside the build start running low... I've had to manually clear the system of uncommon green circuits about a dozen times, and they keep backing up and clogging everything. It's never reds that fill in excess, but green circuits do appear to be returned more than the ratio would imply. Are you sure there is not a rounding issue? When I added logic to remove some uncommon green circuits when the belts were near backing up and no reds were present, the problem fixed itself. Only now it spits out some extra uncommon green circuits from time to time with no apparent reason. I think something is up.

Edit: A few hours later, this build has produced 6000 excess uncommon green circuits, and the problem is beginning to manifest at rare quality level... Something is wrong.

Flouid wrote: ↑Sun Nov 17, 2024 3:56 pm So I've ran this for quite a few hours now and I'm starting to conclude that in the long run, it is balanced. I've had to add what are pretty much "overflow valves" for green circuits at every quality, and even ones for red circuits at common and uncommon. I think random variance over very large numbers of crafts can swing pretty far in favor of green circuits if you get unlucky with reds for long enough, and then letting some out inevitably means that when variance catches up you'll have slightly too many reds. A ring of belts like in my build is not large enough to buffer these swings, so it looks like it's imbalanced. My bot builds with chests for supercapacitors do not suffer from this problem. I think Rseding was right after all.

Stringweasel wrote: ↑Mon Nov 18, 2024 10:42 am Just a note: for these tests make sure to count actual items. The production statistics still has a few oddities as mentioned in 120132

Hares wrote: ↑Mon Nov 18, 2024 12:59 am

Flouid wrote: ↑Sun Nov 17, 2024 3:56 pm So I've ran this for quite a few hours now and I'm starting to conclude that in the long run, it is balanced. I've had to add what are pretty much "overflow valves" for green circuits at every quality, and even ones for red circuits at common and uncommon. I think random variance over very large numbers of crafts can swing pretty far in favor of green circuits if you get unlucky with reds for long enough, and then letting some out inevitably means that when variance catches up you'll have slightly too many reds. A ring of belts like in my build is not large enough to buffer these swings, so it looks like it's imbalanced. My bot builds with chests for supercapacitors do not suffer from this problem. I think Rseding was right after all.

It looks for me that it is balanced on the very long run -- more than 50 hours, and is unbalanced on runs ~10h. Maybe the RNG method has linear distribution when speaking strictly on the infinite time but on the finite time it's not. In other words, the cumulative distribution function itself is a function of time rather than straight line (which should be for a random value from 0 to 1).

I can't make a strict proof of that... yet -- I'm still considering options/methods to do so.

To answer the question of how many times will a random walk cross a boundary line if permitted to continue walking forever, a simple random walk on Z will cross every point an infinite number of times.

In one dimension, the trajectory is simply all points between the minimum height and the maximum height the walk achieved (both are, on average, on the order of √n.