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As I understand, when multiple persons mine blocks, only the first one who solves block is the winner and gets rewarded.

Basically the winner is the one (solo miner or group in pool) who has the most computing power.
That said, when the next block is being mined, again the same person will win because of his computing power.

My question is, how the other mines with less power get chance to win i.e to find the hash of the block before the most powerful miner (regardless if that is person or group) ?

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That said, when the next block is being mined, again the same person will win because of his computing power.

No. Higher mining power means just higher chances to mine a block.

If there are 3 miners:

  • Miner A with 4 Gigahashes per second
  • Miner B with 6 Gigahashes per second
  • Miner C with 1 Gigahash per second

Together, they can hash 11.000.000.000 times per second (4+6+1 gigahashes). The probability for the first miner to win is 4/11 = 36%, the probability for the second miner to win is 6/11 = 55%, the probability for the third miner to win is 1/11 = 9%.

If miner B hashes the block, the next block can of course also be hashed by miner A, B or C.

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    In order to mine block the miner needs to find the appropriate nonce. Let's say the needed nonce is the number 5423. Each miner starts from 0 and increments it by 1 until 5423 is reached. How miner with less power would get to that number before someone with more power ? – nozo Jan 20 '18 at 14:23
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    (1) There is not only the nonce. Look at coin.dance/blocks#blockDetails In the column coinbase text, you can see strings there. If miner A has a different string than miner B (default case), then they can both hash with the same nonce (even with the same transactions) and there are different results. – Alpha Jan 20 '18 at 14:44
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    (2) You don't even need to start at 0. You could pick random nonces each time. You could pick 1.111.321, then 912.110, then 889.099, then 1.555.555... – Alpha Jan 20 '18 at 14:45
  • @nozo, in practice, it's more like a lottery. There is no ideal way to find the nonce, but by trying more attempts in the same time period you increase your odds. This is the same as buying more lottery tickets. – Jestin Jan 20 '18 at 22:02
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If you buy 10 lottery tickets, then you have a smaller chance of winning than someone with 1000 lottery tickets. But you can still win.

It sounds like you are assuming that the person with the most lottery tickets will always win the lottery. That's not how lotteries (or randomness) works.

And yes, mining is a lottery. Each hash is a lottery ticket.

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