user13312: I heard somewhere that joining a mining pool logarithmically increases your odds of mining a block.. is that for some reason true?  Or was it someone who didn't know what they were talking about and it would be be a linear increase in the likely hood of mining a block? 

user11253: The chances of finding a block relate to the proportion of total mining power that you contribute, compared to the network as a whole. For example, suppose you are mining with 1 GH/s and the rest of the network is 99 GH/s. Your chance of finding a block is:
1 / (1 + 99) = 0.01 = 1%

If you double your hashing power, then you have 2 and the rest of the network still has 99.
2 / (2 + 99) = 0.0198 = 1.98%

The reason it's not exactly 2% is the total network is now 101 GH/s, not 100.
If you control 40% of the network hashing power, things get a bit different:
40 / (40 + 60) = 0.40 = 40%

After doubling your hashing power:
80 / (80 + 60) = 0.5714 = 57.14%

As you can see, if you have a significant amount of hashing power then doubling your effort doesn't double your chances of finding a block. However, for small mining efforts the relationship is very close to linear.

user85: Each hash you do has a certain chance to successfully mine a block. Do twice as many hashes, and you have twice as many chances to mine a block.

13312: <p>I heard somewhere that joining a mining pool logarithmically increases your odds of mining a block.. is that for some reason true?  Or was it someone who didn't know what they were talking about and it would be be a linear increase in the likely hood of mining a block? </p>
 11253: <p>The chances of finding a block relate to the proportion of total mining power that you contribute, compared to the network as a whole. For example, suppose you are mining with 1 GH/s and the rest of the network is 99 GH/s. Your chance of finding a block is:</p>

<pre><code>1 / (1 + 99) = 0.01 = 1%
</code></pre>

<p>If you double your hashing power, then you have 2 and the rest of the network still has 99.</p>

<pre><code>2 / (2 + 99) = 0.0198 = 1.98%
</code></pre>

<p>The reason it's not exactly 2% is the total network is now 101 GH/s, not 100.</p>

<p>If you control 40% of the network hashing power, things get a bit different:</p>

<pre><code>40 / (40 + 60) = 0.40 = 40%
</code></pre>

<p>After doubling your hashing power:</p>

<pre><code>80 / (80 + 60) = 0.5714 = 57.14%
</code></pre>

<p>As you can see, if you have a significant amount of hashing power then doubling your effort doesn't double your chances of finding a block. However, for small mining efforts the relationship is very close to linear.</p>
 85: <p>Each hash you do has a certain chance to successfully mine a block. Do twice as many hashes, and you have twice as many chances to mine a block.</p>
