Understanding the probability of winning a block in Ethereum
The Ethereum network uses a Proof of Work (POW) consent algorithm, which requires miners to resolve complex mathematical enigmas to validate transactions and create new blocks. The probability of winning a block is determined by the level of difficulty of the puzzle.
In this article, we will deepen the way in which the probability of winning a block is calculated in Ethereum, in particular from the point of view of the Wiki Bitcoin page that mentions it.
The difficulty of difficulty
The formula of difficulty in POW is based on the rate of hash of the network extraction pool and current time. The formula can be simplified as follows:
`Python
Difficulty = (hashrate * time) / 2^32
`
This formula takes into account the total number of hash per second (hashrate), the current block number and the desired level of difficulty.
The relationship between difficulty and reward of the block
The Wiki Bitcoin page mentions that the probability of winning a block is inversely proportional to the block reward. In other words, as the block reward increases, the chances of winning a decrease in the block. This relationship can be expressed mathematically:
Python
P (win) = (1 / block_reward)
`
Probability calculation
To calculate the probability of winning a block, we must know the current block reward and the level of difficulty of the net. The Wiki Bitcoin page on Ethereum provides the following formula for calculating the Block reward in Ethereum:
block_reward = 10^18 * (1 / difficulty)
Using this formula, we can connect the values to calculate the probability of winning a block.
Python
Block_reward = 10^18 * (1/4000000)
Block_reward ≈ 2.5E-8
Difficulty = (hashrate * time) / 2^32
`
Example calculation
Let's say we know that the hash rate is about 100 TH/if the current block number isn '. We can use the formulas above to calculate the probability of winning a block:
Python
Block_reward = 10^18 * (1 / difficulty)
Block_reward ≈ 2.5E-8
Assuming a block reward of 10^-9 -9 Satoshis for block
Block_reward_per_block = 10^-9
Difficulty = (hashrate * time) / 2^32
Difficulty ≈ 4000000
Probability_of_winning_block = Block_reward_per_block / Difficulty
probability_of_winning_block ≈ 1.25E-4
``
Conclusion
In conclusion, the probability of winning a block in Ethereum is calculated using the Wiki Bitcoin page as follows:
- The level of difficulty affects the number of possible hash required to resolve the puzzle.
- The reverse relationship between difficulty and reward of the block means that as the block reward increases, the chances of winning a decrease in the block.
By understanding this formula, we can obtain information on the mechanics below Pow on Ethereum and make more informed decisions on our investments or participation in the network.