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Ethereum: How is the probability of winning a block calculated from the difficulty?

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Understanding Block Winning Probability in Ethereum

The Ethereum network uses a proof-of-work (PoW) consensus algorithm, which requires miners to solve complex mathematical puzzles to validate transactions and create new blocks. The probability of winning a block is determined by the difficulty level of the puzzle.

In this article, we will explore how the probability of winning a block is calculated in Ethereum, specifically from the perspective of the Bitcoin wiki, which mentions it.

Weight Formula

The PoW weight formula is based on the hash rate of the network mining pool and the current time. The formula can be simplified as follows:

Difficulty = (hashrate * time) / 2^32

This formula takes into account the total number of hashes per second (hashrate), the current block number, and the desired difficulty level.

Relationship between difficulty and block reward

The Bitcoin wiki 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 block decrease. This relationship can be expressed mathematically:

P(win) = (1 / block_reward)

Calculating Probability

To calculate the probability of winning a block, we need to know the current block reward and the network difficulty level. The Bitcoin wiki 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 plug in the values ​​​to calculate the probability of winning a block.

block_reward = 10^18 * (1 / 4000000)

block_reward ≈ 2.5e-8

Difficulty = (hashrate * time) / 2^32

Sample calculation

Let’s say we know that the hash rate is approximately 100 TH/s and the current block number is n. We can use the above formulas to calculate the probability of winning a block:

block_reward = 10^18 * (1 / weight)

block_reward ≈ 2.5e-8


Assuming a block reward of 10^-9 satoshis per block

block_reward_per_block = 10^-9

Difficulty = (hashrate * time) / 2^32

weight ≈ 4000000

Probability_of_winning_block = block_reward_per_block / weight

probability_of_winning_block ≈ 1.25e-4

Conclusion

In conclusion, the probability of winning a block in Ethereum is calculated using the Bitcoin wiki page as follows:

  • The difficulty level affects the number of possible hashes required to solve the puzzle.
  • The inverse relationship between weight and block reward means that as the block reward increases, the chances of winning a block decrease.

By understanding this formula, we can gain insight into the underlying mechanics of PoW on Ethereum and make more informed decisions about our investments or participation in the network.

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