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Calculation of hashta based on arbitrary defined targets
As a passionate cryptocurrency and miner, he often asked me how to estimate the hashrat of a certain miner based only on their mining power and the difficulty of finding a block. In this article, we will explore the mathematics behind the calculation of Hashrat using an arbitrary target.
Mathematics:
Hashrate is the amount of calculation work needed to find a valid non -blockchain. It is measured in terms of “gas” units, which represent the number of instructions to be executed in the network to produce a block. The difficulty of finding a block is calculated by dividing the total number of gas units (ie the target) to the number of miners working together.
Suppose we want to calculate the hashrat using an arbitrary target, 100,000 gas units say. We can start by calculating the theoretical number of unique nonci that could be found in a given block:
hashrate = total_gas_units / (number_of_miners)
This is the maximum hashrat possible if all the miners worked together without obstacles or constraints.
Target:
Now, let’s define an arbitrarily defined target. For this example, we will choose 100,000 gas units as target. We can represent this in different forms such as:
- A single block with a fixed nonce (eg 1 million blocks)
- A large block of blocks with a number of nonc (eg 10^9 to 10^12 blocks)
Calculation of hashta
In order to calculate the hashrat based on an arbitrary target, we must consider the number of unique non -nons that could be found in that block or pool. We can do this by dividing the total number of gas units to the number of miners working together.
Here is a step by step calculation:
- Convert the target from gas units to blocks:
`Markdown
TARGET_BLOCKS = 100,000 / (number_of_miners)
- Calculate the maximum possible hashrat using the above formula:
Markdown
Hashrate = Target_Blocks / Number_of_Miners
Example:
Suppose we want to calculate the hashrat of a miner with an estimated mining power of 500 mh/s (millions of hash per second). We will assume that all miners work together without obstacles or constraints.
- Convert the target from gas units to blocks:
Markdown
TARGET_BLOCKS = 100,000 / 500
- Calculate the maximum possible hashrat using the above formula:
Markdown
Hashrate = Target_Blocks / Number_of_Miners
Calculation of probability
To calculate the likelihood that a block can be found in a given time (for example, one hour), we must consider the number of attempts needed to find a nonce. This can be estimated using the Poisson distribution, which shapes the number of events that take place in a fixed range.
Poisson distribution formula is:
P (n) = e^(-λ) \* (λ^n) / n!
where λ is the average rate of events and N is the number of attempts.
For our example, we will assume an arbitrarily defined target by 100,000 gas units. We can estimate the expected value of attempts using Poisson distribution:
Markdown
Lambda = Total_gas_units / number_of_miners
Now let's calculate the likelihood of finding a block in one hour (3600 seconds):
Markdown
Probability = e^(-lambda) \* (lambda^10) / 10!
`
Conclusion:
By understanding how to estimate the hashrat based on an arbitrarily defined target and calculating the appropriate probability using Poisson distribution, you can make the knowledge of your mining operation.