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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?
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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.
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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.
No. Think about it this way. Lets say you control half of the network hashing power, so you are finding a block every 5 minutes on average. If you double your hashing power you will now find a block every 2.5 minutes. The rest of the network will find a block every 5 minutes on average, so the new average block time of the network will go down to 7.5 minutes. Thus, you double your odds. Once the difficulty adjusts you will be mining one every 3.33 minutes instead. Only then will you self-compete. – hedgedandlevered – 2014-04-19T14:40:49.857
@hedgedandlevered: It's true that if you double your hashing power, the rate at which you find blocks will double (for a given difficulty). However, the chance that you find the next block (compared to somebody else finding it first) increases as I have described. – Greg Hewgill – 2014-04-19T20:12:54.230
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I don't think anyone has directly addressed your question, and the answer is no, joining a mining pool will not increase the chance of you personally solving a block. The probability of you mining a block is the same whether you join a pool or mine solo.
The pool has a probability of mining a block that is approximately proportional to it's percentage of the network hashrate estimate.
This is only an approximation, appropriate for small mining efforts compared to the total network hashrate. – Greg Hewgill – 2014-02-10T19:30:25.480