Propability formular for scrypt blocks

Question

I am currently reseaching and looking for a formular to calculate propability for solving blocks in scrypt. Just something like https://www.litecoinpool.org/calc where one enters hash rates/second and sees their propability of solving blocks.

Please note, I know that solomining is not profitable and I know that there are pools that I could simply use for a miner. But this is not a question about mining in general but the backgrounds of crack propability calculating. It is meant just for research purposes how to calculate propabilities in block finding not to discuss crypto currency mining.

TIA

Answer 1

Difficulty * 2^48 / (2^16 - 1) / Your_Hashes/s = Expected_time_to_solve_a_block_in_seconds

simplified version (not loosing much accuracy) is simpler: Difficulty * 2^32 / Your_Hashes/s = Expected_time_to_solve_a_block_in_seconds

for example:

current diff = 3815, you manage 123 MH/s rigs, then:

Expected_time_to_solve_a_block_in_seconds = 3815 * 2^32 / 123000000 = 133214s = 1.54 days

of course, if you'd manage 123 MH/s rigs you'd probably already know that :)