I used to mine and the most important formula for me in determining whether I could be profitable or not was:

 [2¹⁶-1]/[2⁴⁸D] which (since we're working with such large numbers) you can boil down to

 1/2³²D

where D is the current difficulty 24371874614345 (you can find it here: https://chainquery.com/bitcoin-cli/getdifficulty).

 That formula gives you the probability of any computed hash leading to a valid block.

 1/104,676,404,410,824,387,461,120

 So for a single 110TH miner the probabilty of a block in one second is

 1/951,603,676

  Solo pools don't share the reward among all the miners but they still pool their resources to work on the same block.  In this case, only the miner who finds it gets the reward but the combined hashrate of all participants would be used.

 CK solo pool (https://solo.ckpool.org/pool/) has about 2000 users with about 13,000 devices and shows a hashrate of 37.6 PH/s so the probability of a valid block in one second is

 1/2,783,947

 which indicates they should solve about one block every month.

 Of course, the hashrate fluctuates as users come and go and difficulty changes ~every 2 weeks but finding 2 blocks in a month with their current hashrate is pretty lucky.  However, if you look back at their previous history, they have been rather unlucky; finding only 4 blocks in all of 2020 and only 2 in 2019.  You can't cheat at hashing bitcoin - it all comes out in the wash.  It's normal distribution but very exciting for CK I'm sure.