The search for nonces changes every 10 minutes. An address with a lot of coin might be in cold storage and you might be able to search for months uninterrupted and your reward might be very high.
It's about 3,513,612,269,993,879,528,303,320,959,297,632,275,254,396,583,673,016,120,886,766 times harder to crack an address than to find a nonce that mines a block. Given that mining a block yields 25 bitcoins and cracking an address yields at most 21,000,000 that means that even if you crack the address that holds every single bitcoin that will ever exist, it's still 4,182,871,749,992,713,724,170,620,189,640,038,422,921,900,694,848,828,715 times worse than finding a nonce.
Joelkatz, thank you very much for exactly th answer I was looking for. I am not into stealing but I am into understanding why this will entire bitsphere will work.
Apparently i still don't understand mining. Isn't mining finding the nonce for the next block and that nonce is dependent on the previous block? So as soon as there is a new block, nonce searching has to start all over?