Understand the probability of winning the block

The Ethereum network uses the work (POW) test consensus algorithm, which requires mining workers to determine complex mathematical puzzles to validate events and create new blocks. The probability of winning the block is determined by the difficulty level of the puzzle.

In this article, we deepen how the probability of overcome the block in Ethereum is calculated, especially from the perspective of the Bitcoin Wiki page that mentions it.

Difficulty

The SOW difficulty formula is based on the Hash speed of the network quarry group and at the current time. The formula can be simplified as follows:

`Python

Difficulty = (Hashrate * time) / 2^32

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

The relationship between difficulties and reward

The Bitcoin Wiki page mentions that the likelihood of winning the block is inversely proportional to the block fee. In other words, as the block fee increases, the chances of a block reduction to win. This relationship can be expressed mathematically:

Python

P (WIN) = (1 / BLOCK_REWARD)

Calculation of probability

In order to calculate the likelihood of winning the block, we need to know the reward of the current block and the difficulty of the network. Ethereum's Bitcoin Wiki page offers the next formula for calculating the block prize in Ethereum:

Block_reward = 10^18 * (1 / difficulty)

By using this formula we can combine values ​​to calculate the likelihood of winning a block.

`Python

Block_Reward = 10^18 * (1/4000000)

Block_Reward ≈ 2.5e-8

Difficulty = (Hashrate * time) / 2^32

Example calculation

Suppose we know that the hash speed is about 100 th/s current in then. We can use previous formulas to calculate the probability of winning a block:

Python

Block_Reward = 10^18 * (1 / Difficulty)

Block_Reward ≈ 2.5e-8

Assuming that the block fee is 10^-9 Satoshis per 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 summary, the probability of winning the Ethereum block is calculated using the Bitcoin Wiki page:

• The difficulty level affects the number of potential hashs needed to solve the puzzle.

• A reverse relationship between the difficulties of the block and the prize means that as the block reward increases, the chances of reducing the block.

By understanding this formula, we can obtain information about the underlying mechanics of POW in Ethereum and make more conscious decisions about our investments or network participation.