Quote from: citb0in on January 28, 2023, 08:43:15 PM

the correct answer in my opinion is

1- [chance with 50 PH/s for 3h] = [chance with 25 PH/s for 6h] = [chance with 5 PH/s for 30h]

because it takes into account the shares submitted.

The problem can be generalized to :

is [x draws in n attempts] = or > [x/y draws in y*n attempts] ?

My answer is based on these extreme case examples :

1) Alice gambles on the 6 numbers of the dice and rolls it 1 time --> Alice is 100% sure of hitting a number

2) Bod gambles on 1 number of the dice but rolls it 6 times --> Bob may not hit a number (even if he gambles on the same number). But he is "expected" to hit a number if he increases the number of his attempts.

For me this is why strictly speaking [x draws in n attempts] > [x/y draws in y*n attempts].

3) Let's assume that Bob gambles always on the same number --> The probability of hitting this number at least one = 66.5% in 6 rolls or = 98.7% in 24 rolls (1-(5/6)^n for the formula).

In the case of bitcoin mining, the winning number is new every 10 min. Then what matters is the available hash rate during these 10 min.

The discussion is interesting, I'll be glad of hearing clarifications from experts.