1

To my understanding, miners with small computational capacity are merged within a pool with the advantage to reduce the variance of rewards.

does this miner merge all the computational power so that Pow is calculated quickly??

But it is said that the even in the mining pool , there will be only one miner who will solve the puzzle and the reward is shared by the others miners in the pool depending upon the shares solved by them . The miner leader will identify the ones which are active in solving with providing the puzzle with lower difficulty and share the reward with them.

If there is only one miner finally which solves the problem. How is this miner helped by other miner for computation? if this one miner uses only its computation power then what is different in mining solely?

3

Mining is a game of luck, only one miner ends up mining a block but they all compete. Its like buying a lotto ticket. If one person buys a lotto ticket (i.e. mining by themselves), they will get to keep all the winnings to themselves if they win, but there chances are very slim at winning. On the other hand, if 20 people all buy lotto tickets together and agree to share the winnings between all 20 if any of the people wins, they have 20x higher chance of winning together, but get only a 20th of what they would have got if they were alone. That is what is meant by a more consistent income, you get a lot less per block but its more likely that you will at least get something, not nothing.

3

Whenever a miner makes an attempt to solve the mining puzzle, the probability that this particular attempt will be successful is independent of how many other people are trying and even independent of how many times that miner has tried before this attempt. So, they don't help each other at all in solving the puzzle.

All mining pools do is share the reward in proportion to the difficulty share you were able to compute. Think of it like a casino 777 machine, or lottery. If you win, you keep all the reward. But if you go with 100 friends and you decide to split the reward, you get more consistant income.

Your friends are not helping at all in winning the lottery, your chances of winning are still the same and expected reward is the same. Just that variance is reduced.

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