Hello everybody,
I need help with a little math problem…
I tried to play low luck for the first time with my wife. First question arised was how to handle AAA guns…
We came up with two versions for the situation 1AAA & 3 airplanes:
1. roll one die on 3
2. roll three dice on 1
Question: Do you hit the same amount of airplanes with both versions? Is one better than the other?
My logic was:
in version 1, you have a fifty-fifty chance of hitting an airplane. So in 1000 fights, 500 airplanes will die.
in version 2, you also have a fifty-fifty chance of hitting an airplane. But in rare outcomes it is also possible to hit two or even three airplanes, which is not possible in version 1. Therefore version 2 kills more airplanes than version 1.
Then I wrote a small script that simulates 100000 combat rounds with 1aaa and 3 airplanes in both versions.
To my surprise, it seems that both versions result in exactly 50% dead airplanes.
Now my brain hurts and I don’t know where my error is. Can someone help me out and explain this to me?
Thanks a lot in advance :-D
Also: What do others use in low luck for AAA’s?
If playing a strictly low-luck game, you would roll 1 d6 at 3. Throwing 1 d6 at 3 give the same average results as throwing 3 d6 at 1 (on average, score 1 hit in every other toss of the dice).
Use of low luck rules trades the possibility of lucky dice rolls for the certainty of making hits if enough units are present in the combat.
So yes, you might shoot down three attackers with your AAA if you play by the base rules. But the most likely result is that you will shoot down 1 plane every other time - which is a result you would also get by tossing 1 d6 at 3.
So the answer you are likely looking for is:
If using AAA against three attacking planes, you toss 1d6 with a hit scored for ruling 3 or less.
-Midnight_Reaper
