What's the chance a solo miner gets a block?

I'm aware this might be a long shot, but I'm wondering how often a solo miner actually manages to solve a block. It’s probably not something someone would openly share since they're trying to stay private. So, I did a little bit of quick math and wow, the odds are really against you. Let’s say there’s around 170 million TH/s currently available. If you were using 5 overclocked newpac usb sticks at 100GH/s each, you’d have 0.5 TH/s. Dividing 170 million by 0.5 gives you 340 million blocks before you’d theoretically find one. If you break that down by the 144 blocks mined each day, it works out to about 2.3 million days, or roughly 6500 years. But hey, just because the math says that doesn’t mean it’s impossible. You could hit a block on your first attempt, get lucky with a bunch in a row, or maybe never hit any at all. I've heard that big mining pools like slushpool account for about 15% of all bitcoin mined per pool. But really, how often do you think a solo miner actually manages to solve a block on their own? Anyone got interesting stories or thoughts on this?

no such thing as solo mining.. that disapeared in like 2014 with the invention of asics if you mean farmed blocks. where a pool is owned fully by one owner and he has warehouses of asics.. well that can happen but a home user with USB sticks in his pc.. or a couple asics in their basement working alone. forget it

No serious person would solo mine Bitcoin, it's a waste of electricity, you would most likely die before you see even 1 block. It's simply uneconomical to waste electricity if you could instead join a pool and make steady profit if you have decent hardware. And outdated hardware like those USB miners are not going to be profitable ever, the electricity needed to find 1 block would cost you more than the block reward. You'll have better chances going to some crypto casino, as they offer 1% house edge or even less, that's much better odds than wasting energy on solo mining Bitcoin or buying lottery tickets.

So what have you heard, how many of these people are out there?

bitmain.. aka antpool. is a big mining farm. they actually manufacture asics and run them in their warehouses. things like slushpool are just random people linked to a syndicate(pool) so not a farm

As the OP said, it's all random luck. Remember, no matter what the size of your farm, only 1 machine in the world finds a block. We can only hope that it is one of ours. I've been on KanoPool since late 2014 and to-date have found 10 blocks for the pool. The last one (block #608428) was found on 2019‑12‑16 by one of my A841's in a 60THs cluster, one before that (#570025) found on 2019‑04‑03 by a M10 and another (#566019) found on 2019‑03‑07 by a 8-9THs R4. That same R4 also found a block (#543875) on 2018‑10‑01. Point is that individual miners CAN and DO find blocks. Yes I would have LOVED to have hit those running solo but knowing how the Fates can work I prefer to think it would not have happened...

it depends on you luck and your hashrate  if you have mining farm with Exahash Scale could be mine 1 or two in single day

You could but the odds are not the same at all. Think of it as a lottery, if you buy one ticket you only have 1 chance and your odds are low. If you buy 10, 10000, ... then you increase your odds. Considering the fact that mining is not a competition for find only one block, but it is a competition to find every block every day of every month in every year the long duration makes it so that the odds of finding the block is proportional to the amount of hashrate you have compared to total hashrate.

It depends on what you mean by a "solo" miner. Strictly speaking a solo miner is person or company that hasn't joined a pool. For example, Bitfury is a solo miner. They have been doing large-scale mining since the beginning. They don't advertise in the blocks that they find, but I'm sure that they find a significant fraction. In fact, the miners that find about 30% of the blocks are unknown. I'm sure that there are many solo miners in that group, though they are probably all large-scale operations. Anyway the math is simple. During the current difficulty period, one S19 at 110 TH/s will find a block on average once every 2.06x1013 * 232 / 110x1012 = 8.04x108 seconds = 25 years. Note that this is the same whether you mine solo or in a pool. If you want to average 1 block a year, you will need 25 S19s.

Solo mining is almost impossible because most miners are professional and industrial managed. A normal person, even if he has huge coding skills, will only find a block very luckily, because hashrate is relevant for finding a block. Normal devices have not enough power for a considerably high hashrate to find a block.

Does the number of inbound and outbound network connections to your blockchain play any role in who is awarded the block?  For example, if a solo miner solves a block and then say 1 second later a large pool solves the same block before all the nodes record the block in the blockchain?  Who wins?

That's called an Orphan race. Which found block is confirmed first wins. So yes, connections matter but not how exactly many you have but rather how fast of a connection they have to the Bitcoin network so their found block is available to be confirmed and have the next block built on it.

To easily calculate your chances use this website > http://solochance.com/. This is the last block solved on CKsolo The miner was lucky to solve a block with 77.7th being his 7d average, of course, we don't know for how long it was, but he most certainly earned more than we could ever earn mining on a pool. But not everyone is lucky enough, solo mining should be done for fun (I do it for fun on Cksolo), but your main hash power should be pointed towards a pool if you want to make some profit.

If by "confirmed" you mean another block follows it, then yes. The block that is first to have the next block built on top of it wins. Of course, the earlier block has a head start, but it is not guaranteed because the chain follows the longest branch, and the later branch could get lucky. And, if the next blocks are produced at about the same time, then it is the next block that determines the winning branch. And so on ...

I am solo mining with my own blockchain and wallet hosted by me, I have opened the firewall to allow inbound connections, not just outbound, I figured it may be relevant in the off chance of success.

To answer your original question about connections, you want as many connections as possible. Also, getting on a relay network will help. You want to be mining on the latest block as soon as possible and you want the major miners to start mining your block immediately. Read this: https://galaxsis.com/posts/bitcoin_relays_part_1/

Alas, this link misses the main issue that Matt shut down the public relay and there are no available replacements for the general public that use the FIBRE code that is much faster than any other public relay.

idk but my plan was to build a USB mining rig with a couple of super old bitcoin block erupters (for luck/look, not performance lmfao) and a handful of OC'd newpacs and point em to ckpool as a "lotto miner" / art piece. no idea how to set that up, i never really was a lotto player but idk i feel like this would be fun just to tinker around. and it does help decentralize the network lol

What does block-relay mean in this context?

How many transactions/blocks you have relayed to or have been relayed by other clients.