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For both scenarios that I will describe below, assume the 2 things.

  • that network propagation for blocks always 6 seconds.

  • that we start looking at my analysis from time = t0 and at that t0, every node has the same exact chain.

Scenario 1: block time = 10 min

If block time is 10 min and minerA solves blockD at time t0 + T, and shares it immediatelly, during the time t0+T and t0+T+6, others miners might solve their own block that they were working on. Let’s call the variable how many miners solve it during this time to be “X”

Scenario 2: block time = 4 min

If block time is 4 min and minerA solves blockD at time t0 + T, and shares it immediatelly, during the time t0+T and t0+T+4, others miners might solve their own block that they were working on. Let’s call the variable how many miners solve it during this time to be “Y”

As it turns out, Y > X.

Question 1: Am I right that Y would be greater than X ? ofc, not in 100% cases, but in terms of probability.

Question 2: How do I make myself sure that it’s mathematically true that Y > X ? I know it must be about how difficulties and target are set. It seems like the less difficulty, The higher the chance to solve a block during ANY 6 second period. (NOTE the word: “ANY”). This is important because we don’t know exactly when minerA solves the block, but as I’ve read, probability that Y > X is true for ANY 6 second period, and this 6 second period doesn’t have to be closer to 4 minutes or 10 minutes or whatever it is. What would be a mathematical approach to this so I believe in this ?

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