This way is interesting, but in the end its up to weather theice go your way or not. So in saying that has anyone thought of just getting a full squad of banshees, scorpions and marines and just rolling some dice to see how they go, noting down the combat res over 4 rounds of combat and doing it for a couple of weeks at random times when your luck is better or worse, would make this test come out more real than a maths equasion on paper.

I need to correct the formula above (since I had time to think about it more carefully)

E= sum_{i=0}^{i=N} (1/6)^i * (5/6)^(N-i) *i *(n choose i).

If I have time I will try to do a deeper analysis of troops in the Warhammer universe. I just hope people use the models they like and not just the most efficient ones.

@ jack:

Wow nice. I didn’t even think about doing it this way. I just went “let’s do experiments and see what comes out”. Mathematical modeling of the problem is greatly appreciated.

First of all great experiment!
nice combination of simulation and hobby:)
If you don’t mind I share another idea which I think is nice to know when reading
the above (specially for those who don’t like to write computer simulations)..I actually do:)

An other idea is also (no guarantee that I didn’t make any mistakes):
You don’t need to simulate to investigate that problem, you can calculate this analytically.
This is surely correct, but my attempt to do so very quickly might not be.

The probability to kill a marine with one attack of a banshee is the product of the probabilities

probability to hit marine = 1/2 (4+ on a dice)
probability to inflict if hit = 1/3 (5+ on a dice)
probability to die if inflicted = 1 (no armour saves against energy weapon)

so the probability (product of the above) is
the probability to kill a marine with one attack from a banshee = 1/6

We can now wright down the analytic formula of: the expectation value E
of the number of killed marines “E” with “N” attacks from howling banshees, which is

E= sum_{i=0}^{i=N} (1/6)^i * (5/6)^(N-i) .

Programming this is trivial and it is nice to plot the expectation value of killed marines
against the number of Banshees. Getting the loss on the eldar side is now straight forward by calculating “E” as mentioned above and look how many marines survived and simply applying the same formula but for the Marine probability to kill a Banshee. Doing the same for the Scorpions will then give the results of your experiment (if simulated an infinite amount of times)

On the other hand it is now also easy to see how one can calculate not the expectation value but also other things like the probability of “n” marines getting killed by “x” banshees.

The same goes with all other experiments of that kind. It becomes interesting when looking at how much units cost and one can start adding weight factors. Like Expectation values of killed enemies per point..

Hope that was slightly interesting…

@ Iodine:

To be honest I have not played a real game of 40k in a few years now. I still like to keep up with the hobby from time to time though. I hit up /r/Warhammer and sometimes venture into various forums for rumors. :)

My experience against assault squads (which usually come with a pimped out Sargent) the aspect warriors usually don’t survive longer than a few turns, but it would be interesting to simulate it.

Heh. That was actually kind of interesting. Some time since I have played though (Marines – go figure), but it was fun. Also, I think perhaps you must be the person on the internet with the highest quantity of nerdy interests (This is meant as awe).

By the way I would like to see how those specialized melee eldars fared against specialized melee marines.