[galvornman]

Greetings all,

After having my ass handed to me by Jexik on a few occasions, I asked myself - how many attacks would it take for a figure with M attack dice vs. a defender with N defense dice to inflict one wound, on the average?

Rather than deal with probability calculations - I ran simulations. I used R (code available to anyone who wants it), and each element in the table represents an average over 1000 simulated battles. Essentially the algorithm is the following:

Roll attack dice & count skulls.
Roll defense dice and count shields.
Is the number of skulls greater than the number of shields?
If it is, the number of attacks necessary to inflict one wound is 1, and we move on to the next simulation.
If it isn't, we try again, and keep counting the number of attacks until I get skulls greater than shields. This number will necessarily be something greater than 1, and I record it.

I do this process 1000 times, for every combination of attack and defense dice (up to 10 attack and 10 defense), then taking the average of all 1000 results.

Below I attach a table with my results. Note that these results have been rounded. Example interpretation: For an attacker with 3 dice (A3) against a defender with 3 defense dice (D3) I can expect to attack twice (2) in order to inflict one wound.

(apologies for the poor formatting!)


D1 D2 D3 D4 D5 D6 D7 D8 D9 D10
A1 3 5 7 10 15 23 33 51 81 116
A2 2 2 3 4 5 8 11 15 20 28
A3 1 2 2 3 3 4 5 7 9 12
A4 1 1 2 2 2 3 3 4 5 7
A5 1 1 1 1 2 2 2 3 3 4
A6 1 1 1 1 1 2 2 2 2 3
A7 1 1 1 1 1 1 2 2 2 2
A8 1 1 1 1 1 1 1 1 2 2
A9 1 1 1 1 1 1 1 1 1 2
A10 1 1 1 1 1 1 1 1 1 1

I was a bit surprised at first by the first row, specifically the A1 vs. D1. The average is, of course, not the whole story - simulations show that about 34% of the time one attack is enough to inflict one wound against a defender with 1 die (this is not surprising). In 22% of the simulations in this case it took 2 attacks, and in 13% of the simulations it took 3. The average, being sensitive to outliers, is pushed up by the presence of a few large cases - 12% of the observations were greater than 5 in this particular case.

For me, this table demonstrates what we've known all along - rolling a few attack dice many times trumps rolling a lot of dice only a few times.

Why is Q9 so good? He rolls a few dice many times, resulting in more net wounds.

Why are 4-man squads so dominant? If they have at least 3 attack dice and are ranged - again, lots of opportunities to roll dice and inflict wounds.

Why are rats good? If attacked by a 2-4 dice attacker, it takes an average of two attacks to take each one down - and in this time they get to move (assuming normal attacks) and cause trouble.

Why do the Deathwalkers die? Even 3 attack dice squads need only roll against DW9K an average of 9 times before he falls.

Nilfheim/Zelrig good? 3 attacks.

Why is bonding so awesome? More attacks.

Apologies if this work offers no new insight into this great game - it only confirms what we already know by experience. Excluding counter drafting and gimmicks (Thorian speed vs. normal ranged attacks), winning armies are those that allow you to roll a few dice as often as possible. Squadscape isn't going anywhere anytime soon.