user8770: Just turned my attention to mining and the concepts are quite new to me. First of let me be clear: I realize that my hardware setup is far from ideal for mining. This is also the reason why I do not want to pool, I would simply provide a too small a share. I will be CPU mining at first, ASIC later on.
I would however like to test my luck. Mostly just for fun, I'm completely fine with the idea of never actually solving a block. I see it more as a lottery. I just want to confirm my idea so that I am not missing something: Do I have a chance of solving a block?
If a block is solved every 10 minutes, and the difficulty goes up continously. Do I even have the time to attempt a solution? I understand that the current work has to be abandoned when a block has been solved, rigth? Is there, for example, a lag here that yields my efforts useless? 
What are the odds? Are the actually the % of my speed vs the network's?

user909: It's better than being in the lottery!
The chance you actually find a block will sadly decrease over time (probably). Thing is, if you're lucky you win the lottery. And if you don't get lucky, you don't win and get nothing.
The advantage of being in a pool is that you play in more lotteries, so your luck averages out . If you get lucky 1% of the time and you try once, you probably won 0% of the time. If you try very often it will tend to balance around 1%.
So, all chance calculations aside, are you feeling lucky?
To answer your question more directly: the long block-intervals (10 minutes) are there to reduce network-lag's influence on people's ability to mine on the newest block. There's some influence, inevitably, but others endure it too. Pools can have a minor advantage if they're close together, but the miners connect through them instead of directly. I think there'd be no difference worth mentioning. Short: Yes, it is your % vs network %.
Small footnote should be made about selfish mining, if another pool is big enough they'll have a mining advantage. Smaller it'd be a disadvantage. It's not being done and I hope pools will stay spread thinly enough to make it ineffective. You can safely ignore this. It also doesn't likely matter when you're "lottery mining" (you're still betting just on your own luck!).
Note: you'll have more luck solo-mining LiteCoin or another GPU/CPU coin. Unless you own an ASIC, of course.

user3758: I'm solo mining AmericanCoin on a US$6/month VPS generating about 7 scrypt kilohashes per second, and just won block 55311 about an hour ago, after about 8 weeks of trying with the random-nonce scrypt-mining script linked to from my blog. so it can be done, if the difficulty is low enough. it might have worked just as well or better with the built-in linear-nonce mining code, but I figured using random numbers would give me an edge in the "luck" department.
here's the current difficulty. when I started it was about 1.9, then went up to about 4 before dropping back.
jcomeau@aspire:~$ americancoind getmininginfo
{
    "blocks" : 55328,
    "currentblocksize" : 0,
    "currentblocktx" : 0,
    "difficulty" : 3.51815597,
    "errors" : "",
    "generate" : false,
    "genproclimit" : -1,
    "hashespersec" : 0,
    "networkhashps" : 19038678,
    "pooledtx" : 0,
    "testnet" : false
}

so it's not nearly paying for itself, but as a proof-of-concept it was worthwhile to me, as well as being a cheap way of getting my gambling "fix".

user10664: I do not think the question was about the "how long" it would take in average, but what are the odds, which is something completely different from my point o view.
If I understand well the concept of solving blocks then there are always more people/groups/pools trying to solve one block.
If that's so then solving a block is always more about the luck than the brute force you have. Even if you have a 1GH rig, you can still find the solution quicker then 1PH pool.
Question is: what are the odds that it will happen?
I would expect a ration : to take place in the answer.
So if the current total H-power is about 7.6PH it means that with 1GH rig you have 1:7600000 probability to solve the block approx. every 8 minutes. Which is 1:116 per a year, if the total H-power does not change and it basically does not depend on the difficulty, as the difficulty is based on total H-power.

user12034: As long as you're in good communication with the network and have a hashrate measured in something better than minutes per hash, yes, you technically do have a chance of successfully mining a block, even if your hashrate is tiny compared to the whole network. Then the question is, what are your chances and should you do it? I think an analogy with a lottery is apt.
In one week, a lottery might cost you $2 (for one ticket) and give you a 1 in 175 million chance to win $100 million (ignoring smaller prizes, splitting prizes, etc.; complicates things too much). This gives it a return on investment (ROI) of about 29%, so we'll treat this as our baseline: if it's lower than this, it's worse than the lottery and you shouldn't "play".
If you buy a $34.52, 5 GH/s ASIC miner that uses 2.5W of power, you might spend about $0.06 in a week to have a 1 in 13,889 chance to win $11,349. Not counting the upfront investment, this is a 1,361% ROI, so it's worth it. If you factor in the cost of the device (split over a year) and a profitability decline (since the rest of the network will be speeding up), I think you're still looking at an ~80% ROI.
In one week of CPU mining (assuming 20 MH/s at 70 W), you might spend $1.75 in power to have a 1 in 3,472,222 chance to win $11,349. This is a 0.18% ROI, so CPU mining really makes no sense, even as a lottery (it'd be better to just buy a lottery ticket).
(my calculations are at http://pastebin.com/ERJHshFG)

user8717: Check this page: How soon might I expect to generate a block? 
So with the current difficulty  510,929,738, and a 1Ghash/s mining rig (faster than your CPU) you'd do this math:
510929738 * Math.pow(2,32) / Math.pow(10,9) / 60 / 60 / 24 / 365
So to find a block at this difficulty with a 1Ghash mining rig it would take you about 69 years on average.
Good Luck!
PS: Math.pow(2, 32) is simply the JavaScript version of 2^32

8770: <p>Just turned my attention to mining and the concepts are quite new to me. First of let me be clear: I realize that my hardware setup is far from ideal for mining. This is also the reason why I do not want to pool, I would simply provide a too small a share. I will be CPU mining at first, ASIC later on.</p>

<p>I would however like to test my luck. Mostly just for fun, I'm completely fine with the idea of never actually solving a block. I see it more as a lottery. I just want to confirm my idea so that I am not missing something: <em>Do I have a chance of solving a block?</em></p>

<p>If a block is solved every 10 minutes, and the difficulty goes up continously. Do I even have the time to attempt a solution? I understand that the current work has to be abandoned when a block has been solved, rigth? Is there, for example, a lag here that yields my efforts useless? </p>

<p>What are the odds? Are the actually the % of my speed vs the network's?</p>
 909: <p>It's better than being in the lottery!</p>

<p>The chance you actually find a block will sadly decrease over time (probably). Thing is, if you're lucky you win the lottery. And if you don't get lucky, you don't win and get nothing.</p>

<p>The advantage of being in a pool is that you play in more lotteries, so your luck averages out . If you get lucky 1% of the time and you try once, you probably won 0% of the time. If you try very often it will tend to balance around 1%.</p>

<p>So, all chance calculations aside, are you feeling lucky?</p>

<p>To answer your question more directly: the long block-intervals (10 minutes) are there to reduce network-lag's influence on people's ability to mine on the newest block. There's some influence, inevitably, but others endure it too. Pools can have a minor advantage if they're close together, but the miners connect through them instead of directly. I think there'd be no difference worth mentioning. Short: Yes, it is your % vs network %.</p>

<p>Small footnote should be made about selfish mining, if another pool is big enough they'll have a mining advantage. Smaller it'd be a disadvantage. It's not being done and I hope pools will stay spread thinly enough to make it ineffective. You can safely ignore this. It also doesn't likely matter when you're "lottery mining" (you're still betting just on your own luck!).</p>

<p>Note: you'll have more luck solo-mining LiteCoin or another GPU/CPU coin. Unless you own an ASIC, of course.</p>
 3758: <p>I'm solo mining AmericanCoin on a US$6/month VPS generating about 7 scrypt kilohashes per second, and just won <a href="http://jc.unternet.net/blog/?2013-12#T2013-12-26-0224Z" rel="nofollow" title="AMC block 55311">block 55311</a> about an hour ago, after about 8 weeks of trying with the random-nonce scrypt-mining script linked to from my blog. so it can be done, if the difficulty is low enough. it might have worked just as well or better with the built-in linear-nonce mining code, but I figured using random numbers would give me an edge in the "luck" department.</p>

<p>here's the current difficulty. when I started it was about 1.9, then went up to about 4 before dropping back.</p>

<pre><code>jcomeau@aspire:~$ americancoind getmininginfo
{
    "blocks" : 55328,
    "currentblocksize" : 0,
    "currentblocktx" : 0,
    "difficulty" : 3.51815597,
    "errors" : "",
    "generate" : false,
    "genproclimit" : -1,
    "hashespersec" : 0,
    "networkhashps" : 19038678,
    "pooledtx" : 0,
    "testnet" : false
}
</code></pre>

<p>so it's not nearly paying for itself, but as a proof-of-concept it was worthwhile to me, as well as being a cheap way of getting my gambling "fix".</p>
 10664: <p>I do not think the question was about the "how long" it would take in average, but what are the odds, which is something completely different from my point o view.
If I understand well the concept of solving blocks then there are always more people/groups/pools trying to solve one block.
If that's so then solving a block is always more about the luck than the brute force you have. Even if you have a 1GH rig, you can still find the solution quicker then 1PH pool.
Question is: what are the odds that it will happen?
I would expect a ration : to take place in the answer.
So if the current total H-power is about 7.6PH it means that with 1GH rig you have 1:7600000 probability to solve the block approx. every 8 minutes. Which is 1:116 per a year, if the total H-power does not change and it basically does not depend on the difficulty, as the difficulty is based on total H-power.</p>
 12034: <p>As long as you're in good communication with the network and have a hashrate measured in something better than minutes per hash, yes, you technically do have a chance of successfully mining a block, even if your hashrate is tiny compared to the whole network. Then the question is, what are your chances and should you do it? I think an analogy with a lottery is apt.</p>

<p>In one week, <a href="http://www.powerball.com/powerball/pb_prizes.asp">a lottery</a> might cost you $2 (for one ticket) and give you a 1 in 175 million chance to win $100 million (ignoring smaller prizes, splitting prizes, etc.; complicates things too much). This gives it a return on investment (ROI) of about <strong>29%</strong>, so we'll treat this as our baseline: if it's lower than this, it's worse than the lottery and you shouldn't "play".</p>

<p>If you buy a $34.52, 5 GH/s <a href="http://rads.stackoverflow.com/amzn/click/B00JCABMSI">ASIC miner</a> that uses 2.5W of power, you <a href="http://www.bitcoinx.com/profit/">might spend about</a> $0.06 in a week to have a 1 in 13,889 chance to win $11,349. Not counting the upfront investment, this is a 1,361% ROI, so it's worth it. If you factor in the cost of the device (split over a year) and a profitability decline (since the rest of the network will be speeding up), I think you're still looking at an <strong>~80%</strong> ROI.</p>

<p>In one week of CPU mining (assuming <a href="https://en.bitcoin.it/wiki/Mining_hardware_comparison">20 MH/s</a> at 70 W), you might spend $1.75 in power to have a 1 in 3,472,222 chance to win $11,349. This is a <strong>0.18%</strong> ROI, so CPU mining really makes no sense, even as a lottery (it'd be better to just buy a lottery ticket).</p>

<p>(my calculations are at <a href="http://pastebin.com/ERJHshFG">http://pastebin.com/ERJHshFG</a>)</p>
 8717: <p>Check this page: <a href="https://en.bitcoin.it/wiki/Difficulty#How_soon_might_I_expect_to_generate_a_block.3F">How soon might I expect to generate a block?</a> </p>

<p>So with the current difficulty  <code>510,929,738</code>, and a 1Ghash/s mining rig (faster than your CPU) you'd do this math:</p>

<p><code>510929738 * Math.pow(2,32) / Math.pow(10,9) / 60 / 60 / 24 / 365</code></p>

<p>So to find a block at this difficulty with a 1Ghash mining rig it would take you about <strong>69 years</strong> on average.
Good Luck!</p>

<p>PS: <code>Math.pow(2, 32)</code> is simply the JavaScript version of <code>2^32</code></p>
