I think you're right about how the probabilities are applied, and I think that's the source of your confusion. You'd be right that A * B * C is how to get to the probability of a container being empty, but once you have that, the number of trials required to infer a bug in the system should be pretty low.
With due respect, I'm pretty sure your math is wrong too, or at least not as helpful as you might have thought.
First, I think you're treating
open containers (with 0% chance of loot) the same as
closed but lootless containers. Both are treated as "empty," even though they are very different from the player's perspective.
To see how this affects things, let's go with your numbers, as I understand them:
A = "Normal" odds of container
being closed = 50% (0.5)
B = Loot Abundance modifier = 50% (0.5)
C = Odds of a non-zero # of items in a
closed container = 91% (0.91)
Now, I believe what Gnomaana said is true, and the loot abundance modifier affects the percent chance of items spawning
within closed containers. But I could easily be wrong so we'll try it either way.
If I'm right: for any run of 200 containers, statistically 100 of them (50%) will be open. The chance that any of the remaining 100 will have loot is B * C = 0.5 * 0.91 = 0.455 (or 45.5%).
So as a statistical average, the number of containers that will have loot is 100 * 0.455 = 46 containers (rounding up). 100 of them will be visually empty so you know you don't have to search them. So
of the closed containers, 54 will be empty - more than half.
Now, let's say I'm wrong and the loot abundance modifier is for the
number of closed containers. So the chance of a container being closed is A * B = 0.25 (or 25%). But the chance of each closed container having loot is still 0.91 (91%).
Out of 200 containers, the statistically average number of closed containers is 200 * 0.25 = 50 containers. Of those containers, 50 * 0.91 = 46 (rounding up) will have loot in them, the same as before. But 150 of those containers will be visually empty so you know you don't have to search them. So
of the closed containers, only 4 will be empty.
Either way, that leaves 154 containers that will be "empty"
even if loot generation is working precisely as it should. Sure, the chances that all 200 being empty is vanishingly small, but is the difference between 154 and 200 empty containers so big that players would notice?
But second, even this does not tell the whole picture. It's not as simple as A, B, or C. If I understand the XML files correctly:
* The same POI might have a chance of spawning different containers in the same location.
* Containers have different sets of loot, and each loot type has a different spawn count, and different percent chances of spawning.
* For most containers, there is some percent chance that
additional higher-level loot will spawn, but not additional lower-level items, and the percent increases with game stage.
And all that only affects closed containers. I still don't know for sure what the loot abundance affects, or how the chance of a container being closed is calculated.
So the chances of accurately calculating the odds of 200 containers in a row being empty is far more complicated than anything we can do on these forums.