user133593: Several months ago I was doing research into calculating mining revenue for several crypto currencies. When trying to calculate BTC revenue I found this value 1/2^32 which was described somewhere along the lines of the probability of finding or solving a block. I found this on some website talking about the probability of finding a new block I think investopedia.
But how is this 2^32 found and how much does it change over time?

user208: In Bitcoin mining, there are a few related terms:

The "target" is for a given block candidate the maximum permitted hash value (i.e., if the hash of the block ends up being lower or equal to the target, the block is proof-of-work valid). At the time of writing (block 737759), the target is 862674725460762741916416231468109512880228678412271616 in decimal, or 0x901ba0000000000000000000000000000000000000000 in hex.
The "maximum target" is the maximum value the target can be. There are various rules that govern what the target is for various blocks. It is updated every 2016 blocks depending on the time it took those blocks to be mined. If that time is more than 2 weeks, the target goes up (making mining easier). If that time is less than 2 weeks, the target goes down (making mining harder). The target cannot change by more than a factor 4 up or down. Lastly, the target can never exceed (216-1)2208, which is 26959535291011309493156476344723991336010898738574164086137773096960 in decimal, or 0xffff0000000000000000000000000000000000000000000000000000 in hex. We don't know precisely how this value was chosen, but it is related to how the target is encoded in blocks. It is an absolute upper bound on the target; if the adjustment rule would take it higher, this value is used instead.
The "work" for a block is the ratio between 2256 and the target. It corresponds to the expected number of hash attempts a miner needs to make for a candidate block, and is the inverse of the probability that any hash attempt is valid. If the target has its maximum value, its work equals 2256 / ((216-1)2208) = 248 / (216 - 1) ≈ 232 + 216 + 1. When determining which chain to accept among multiple valid candidates, Bitcoin nodes pick the one with the highest accumulated work (sum of all the work values in all its blocks). The current work value (per block) is 134224506433140884946014.
The "difficulty" of a block is the ratio between the maximum target and its target. It is a value that's only used for human consumption, and doesn't exist at the protocol level. The difficulty is always at least 1, because of the way it is defined. The current difficulty is approximately 31251101365711.12.

Armed with all these definitions, it is easy to see that there is a fixed ratio between the work and the difficulty of a block. That ratio is exactly the work of the maximum target, or the work at difficulty 1: 248 / (216 - 1) ≈ 4295032833.000015, which is slightly more than 232 + 216 + 1. In other words, the probability that any hash attempt leads to a valid block is approximately 1 over 232 times the difficulty. Perhaps that is the number you're wondering about.
If so, the answer is simply that this number is a side effect of how the difficulty is defined, and never changes. It has no relation to how mining actually works, because difficulty is purely a human convenience; the actual protocol works with target values.
Other systems can define difficulty however they want, but that would be off topic here.

133593: <p>Several months ago I was doing research into calculating mining revenue for several crypto currencies. When trying to calculate BTC revenue I found this value 1/2^32 which was described somewhere along the lines of the probability of finding or solving a block. I found this on some website talking about the probability of finding a new block I think investopedia.</p>
<p>But how is this 2^32 found and how much does it change over time?</p>
 208: <p>In Bitcoin mining, there are a few related terms:</p>
<ul>
<li>The &quot;target&quot; is for a given block candidate the maximum permitted hash value (i.e., if the hash of the block ends up being lower or equal to the target, the block is proof-of-work valid). At the time of writing (block 737759), the target is <code>862674725460762741916416231468109512880228678412271616</code> in decimal, or <code>0x901ba0000000000000000000000000000000000000000</code> in hex.</li>
<li>The &quot;maximum target&quot; is the maximum value the target can be. There are various rules that govern what the target is for various blocks. It is updated every 2016 blocks depending on the time it took those blocks to be mined. If that time is more than 2 weeks, the target goes up (making mining easier). If that time is less than 2 weeks, the target goes down (making mining harder). The target cannot change by more than a factor 4 up or down. Lastly, the target can never exceed <em>(2<sup>16</sup>-1)2<sup>208</sup></em>, which is <code>26959535291011309493156476344723991336010898738574164086137773096960</code> in decimal, or <code>0xffff0000000000000000000000000000000000000000000000000000</code> in hex. We don't know precisely how this value was chosen, but it is related to how the target is encoded in blocks. It is an absolute upper bound on the target; if the adjustment rule would take it higher, this value is used instead.</li>
<li>The &quot;work&quot; for a block is the ratio between <em>2<sup>256</sup></em> and the target. It corresponds to the expected number of hash attempts a miner needs to make for a candidate block, and is the inverse of the probability that any hash attempt is valid. If the target has its maximum value, its work equals <em>2<sup>256</sup> / ((2<sup>16</sup>-1)2<sup>208</sup>) = 2<sup>48</sup> / (2<sup>16</sup> - 1) ≈ 2<sup>32</sup> + 2<sup>16</sup> + 1</em>. When determining which chain to accept among multiple valid candidates, Bitcoin nodes pick the one with the highest accumulated work (sum of all the work values in all its blocks). The current work value (per block) is <code>134224506433140884946014</code>.</li>
<li>The &quot;difficulty&quot; of a block is the ratio between the maximum target and its target. It is a value that's only used for human consumption, and doesn't exist at the protocol level. The difficulty is always at least 1, because of the way it is defined. The current difficulty is approximately <code>31251101365711.12</code>.</li>
</ul>
<p>Armed with all these definitions, it is easy to see that there is a fixed ratio between the work and the difficulty of a block. That ratio is exactly the work of the maximum target, or the work at difficulty 1: <em>2<sup>48</sup> / (2<sup>16</sup> - 1)</em> ≈ <code>4295032833.000015</code>, which is slightly more than <em>2<sup>32</sup> + 2<sup>16</sup> + 1</em>. In other words, the probability that any hash attempt leads to a valid block is approximately 1 over <em>2<sup>32</sup></em> times the difficulty. Perhaps that is the number you're wondering about.</p>
<p>If so, the answer is simply that this number is a side effect of how the difficulty is defined, and never changes. It has no relation to how mining actually works, because difficulty is purely a human convenience; the actual protocol works with target values.</p>
<p>Other systems can define difficulty however they want, but that would be off topic here.</p>
