The analogy with throwing dice is for illustrative purposes only.
This is the problem. 100K account
does have advantage over 100x 1K accounts. But this advantage is small. In ur example it's noticeable coz u use conventional dice. If u used dice with 2^64 faces u would get other results.
Um, okay. Let's look at it with continuous probabilities on the range 0..1 then.
Wallet A has a 100K account and wallet B has a 50K account. Wallet A throws am infinite-sided die mapped to 0..1 and gets N1, wallet B throws the same infinite-sided die and gets N2.
Wallet A then takes a default generation time of (say) 10M seconds and divides by 100K x N1, while Wallet B takes the same default generation time and divides by 50K x N2.
If B gets the shorter/first time, B forges the new block while if A gets the shorter/first time, A forges the new block.
So, for A: 10M seconds(100K x N1) = 100 seconds N1
while, for B: 10M seconds/(50K x N2) = 200 seconds N2
And that means that if N1 < N2 (ie half the time) A always forges the block.
Otherwise, if N1 < N2/2, (ie, half the remaining time) A always forges the block.
Otherwise, N1 > N2/2, and B forges the block.
I ignore the case where N1 == N2/2; we were throwing infnite-sided dice so the probability is infinitesimal.