Post #2555817

@LiseAndreasen@mastodon.world then there are some more digits which may also differ. But at each n+i, there are 4 possibilities (with equal probability): 0, 0; 0, 2; 2, 0; 2, 2. The identical pairs add nothing to the overall difference, and pair 0,2 adds 2/3^(n+i), whilst the pair 2,0 subtracts the same amount. Thus everything beyond n on average contributes 0 difference. So the probability is the sum of 1/[2^(n-1) * 3^n], which is a geometric series with limit 2/5 = 0.4 :)