This is my understanding of how it works. Fizzer or someone else will correct me if I'm wrong.

8 defenders, 70% kill rate: Expected kills would be 5.6, and would (straight) round to 6.

If you have 50% luck, and it rolled 7 kills (always an integer), do you get 5.6 * 50% + 7 * 50% = 2.8 + 3.5 = 6.3 which (straight) rounds to 6, or is it 6 * 50% + 7 * 50% = 3 + 3.5 = 6.5 which (straight) rounds to 7 which kills a commander...

If you have 50% luck and it rolled 7 kills, the number of armies killed is the weighted mean (50% of 5.6 + 50% of 7 = 2.8+3.5 = 6.3).

If it was 60% luck and it rolled 7 kills, the number of armies killed would be 40% of 5.6 + 60% of 7 = 2.24 + 4.2 = 6.44.

After it has determined how many armies should be killed, the rounding mode determines how a decimal is rounded. That is, SR would round 6.3(or 6.44) to 6.

WR would round 6.3 to 6(70% of the time) and round to 7 (30% of the time).

WR would round 6.44 to 6(56% of the time) and round to 7 (44% of the time).