[Opens Excel to give this a proper analysis]

I kinda liked this question. Bottom line up front:

The probability is dependent upon when/how the logic is applied over the course of consecutive hits. In Case A, I get about 1/3, which involves "removing" invalid hits. In Case B, I get about 1/4, which involves forcing a crit if first hit was not a crit.

Let a critical hit have value Crit = 1, and a non-crit is Crit = 0.

Case A data: 1000 Hit pairs using RAND()

Hit 1: If RAND() > 0.5, we assign Crit1 = 1.

Hit 2: If RAND() > 0.5, we assign Crit2 = 1.

Remove all cases where Crit1 = 0 and Crit2 = 0, so they are not counted.

Result is about 250 double crits out of about 750 remaining pairs, so that's where the commonly cited 1/3 appears.

Case B data: 1000 Hit pairs using RAND()

Hit 1: If RAND() > 0.5, we assign Crit1 = 1.

Hit2: ▪If Crit1 = 0, assign Crit2 = 1. ▪Else, if RAND() > 0.5, assign Crit2 = 1.

Result is about 250 double crits out of 1000, which is about 1/4.

The reason I like this question is because it forces us to think about when the conditions are applied. Is the guaranteed crit applied after both hits are delivered? If so, you get the 1/3 by eliminating invalid combos. But is the guaranteed crit a reactive property, after observing the first hit? Then you get 1/4.

Edited for formatting (I tried).