Will more hashes per second increase bitcoins per hash per second? I read this article:


  We have paid 0.034 BTC for the 10 GH/s ... Yesterday we have received our first daily payout and it was exactly 0.00041279 BTC ...   Doing a quick calculation has shown that if the Bitcoin network difficulty remains the same and the daily payout is also the same as the one we got the first day we are going to need a little over 82 days to get back what we have spent for the mining contract. 


In this case BTC per GH/s is 0.00041279/10 BTC/(GH/s). All of this is in one day, but for simplicity I removed day from the units.

Will buying more GH/s increase BTC per GH/s (in one day)? Since there is more power solving the problem, and there would be more probability to solve the problems?

How could I calculate decrease of BTC/day vs time with a fixed hashing speed?
The short answer is: No. The average number of bitcoins per hash is fixed, and is roughly equal to B / (2^32 * D), where B is the bitcoins per block and D is the difficulty. Every calculated hash is either a block or not; if it's not, it doesn't bring you any closer to finding a block.

However, for completeness it should be noted that there are several sophisticated attacks that allow superlinear gains on hashrate, such as lie-in-wait and hashrate amplification (also known as selfish mining). Superlinearity can also be a side effect of a short block interval. All of these require huge hashrate to be effective, on the order of a quarter of the network hashrate - not something which should be of concern to the average miner.