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1. Do I have to run guiminer 24/7 to have more of a chance of solving a block or could I still solve a block if I run it for only 12 hours a day?
it's luck. it's statistics. you can solve a block CPU mining in ten minutes, or never solve one with 5 Gh/s. that said, the more consistently you mine the better your results.
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2. I'm a member of slush's pool. Does this mean I will never have the opportunity to solve a block and only get the fractional 0.10 btc every day?
you could be the miner who solves the block (i've solved a few), but it goes to the pool. that's what they call 'fair' - since we get paid for all the other miners who solve blocks on that (our) pool.
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3. Will I eventually solve a block or is it totally random, and therefore, may never solve a block? I have been mining for 3 weeks and have mined 2.2 btc.
keep at it and you probably will - but like i said, it goes to the pool.
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4. Does the number of shares have an affect on solving a block? At the moment guiminer shows I have accepted 16422 shares. What does this mean?
not sure - i use Diablo. but generally, the bigger your hashing numbers (whatever the nomenclature) the more you make. on slush's pool, the 'shares' on your account page are a reflection of your Mh/s.
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5. The bitcoin client only ever shows a maximum of 62 connections. I have forwarded the ports in my router. Is that normal? Does the number of connections have an affect on solving a block?
you don't need to run the client when you're mining in a pool. only when solo mining. and when solo-ing, no - there's no effect. it's all about the Mh/s.