If in ethereum network a miner has a device with 10 power(for example) and another one has a device with 5 power. Is person 1 get the mining reward for ever? Or is it possible to person 2 mine some blocks?


I'm assuming you're referring to the current Ethereum protocol, which uses proof of work to secure the network.

Statistically, the miner with 10 units of computation will mine 2/3 of the blocks on the network and the miner with 5 units of computation will get 1/3. I.e., a miner with x% of the computing power of the network will statistically mine x% of blocks.

"The most powerful device" != majority (e.g. eight users with one unit of computing power and one with two units -- the most powerful device is only 20% of the network). A miner with a majority (i.e., more than 50%) of computing power can do things like roll back transactions, however. Also, such a miner, if acting maliciously, can ignore the work being done by the minority miners and thus obtain 100% of the rewards.


in short:the mining(POW) is a probabilistic process so in your example the first has a probability of P=2/3 and the second has a p=1/3. in other term the second can get a reward but with a low probability.

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