Quote from: pontiacg5 on October 01, 2013, 03:43:50 AM

I found a block when it should have taken me over 300 days,

So your chances of finding a block were about 1 in 43,200

Quote from: pontiacg5 on October 01, 2013, 03:43:50 AM

was at it for around a month. When I found the block

So you had about 4,464 trials at a chance of 1 in 43,200 for each trial
In other words the chance was about 1 in 10.186

Quote from: odolvlobo on October 01, 2013, 06:40:30 AM

The fact is that if you mine 0.00000123 BTC in a day, then the chance of finding a block each day is 0.00000123/25, or about 1 in 20 million.

The OP's chances of solving any particular block are 1 in 20 million.

Quote from: pontiacg5 on October 01, 2013, 03:43:50 AM

so it is possible.

Sure, but there is a big difference between 1 in 43,000 and 1 in 20,000,000. And that's if the OP had only been running for 1 day to get the 0.00000123 BTC. If it took them several days, then their chances are even worse.

Quote from: odolvlobo on October 01, 2013, 06:40:30 AM

Anyway, the amount you earn from mining in a pool is expected to be about the same amount that you will earn mining solo. It is a mistake to believe that if you earn 0.00000123 mining in a pool, that you can earn more mining solo.

I haven't tried the math, but intuitively I'm not sure this is true. Pool mining pays out based on the current block reward. So you get a small percentage of at least 25 BTC for every block you participate in during the next three years. Meanwhile, if your odds of finding a block while solo mining are really bad, then there is a decent chance that you won't find a block until after the reward as dropped a few times. Therefore, for the next 3 yeaars, you'd be expending electricity at a level that is supported by a reward of at least 25 BTC for a solved block, but the actual reward you receive when you finally solve a block a few years from now may only be 12.5 BTC.