Warhammer 40K: Math Team

 

So back in the day, I wrote several series working on various parts of what is called Mathhammer where you look at the probabilities of events in table top games.  I had a series examining 3rd edition space hulk and then a series looking at vehicle damage for 5th edition 40K asking how many missiles to the center of a Razorback or what it takes to crack on Chimera.  

Now this is all in the way back machine but as probability problems they were interesting because unlike normal 40K attacking they were not linear problems.  A normal 40K attack has N dice but each die is treated seperately really.  Each die has a chance to hit, then a chance to wound, then forces a save attempt, then a feel no pain (or what ever now).  You can essentially calculate the chance for each step multiple them together to get the chance of something per attack.   Then if you are really just interested in the average number just multiple this chance for a single die by the total number of dice.  It is very straight forward and pretty easy to see how any change to any of the test will change the results.  

Current 40K has become slightly more complicated with like unblockable mortal wounds on 6's and such but these are usually secondary things that can be treated without much issue.  It makes this all not very interesting from this stand point.  Those series looked at event where how multiple dice interact like the dice pool combat in Space Hulk or dependent events where to kill the tank you might have two knock out 2 weapons first then immobilize it.  The pathways to the end are more complicated and the problems become more interesting.

The new kill team game is like this.  Since it uses dice pools for both the attacker and defenders with comparisons of results all to determine the outcome it cannot be broken down into little steps.  There are also lots of special rules which influence the test and it is not initial clear what is the best choice.  Is a Crit:P1 better than a Ceaseless all else being equal?  Is a 5th die more useful or more damage on the weapon.  

To take a look at this I built a software program to essentially roll the dice pools millions of times with a specific set of conditions and determine the outcome in terms of approximate probability of each damage result and then determine average damage or the chance of killing a model.  

For example a basic guardsman will do about 1.54 wounds to a tac marine on average and have a vanishingly small 0.04% chance of killing him with 1 shooting action.  While in return that tactical marine will average 5.66 wounds on the guardsman and kill him about 39% of the time in the single shoot action.  That guard better find some cover which drops the damage down to about 4.05 wounds and decreases the single attack death to 25.6% of the time.  Now one would normally expect the Auto defense of the cover to do more.  Should it not drop it by like a whole 3 points since that is what a retained hit does but you need to remember that 1/3 of the time that die would have been a success.  So that cuts the value.  Next sometimes the opponent has nothing to block with that success.  You either already got the successes to block all his damage or he only has criticals which it does not help with.

So As I go along I will be looking at some data cards and evaluating the weapons on them against some example targets to see how balanced they are.