Sunday, November 20, 2011

How Many Tesla Carbine Shots Are Required to kill Plague Marines?

Nurgle's plague marines are tough; no doubt about it.  But how worried are plague marines when taking incoming fire from Tesla Carbines (as used by Necron Immortals)?  Let's look at some statistics.

An immortal will hit a plague marine on a 3+ (probability = 0.67).  
The tesla carbine will wound on a 4+ (new combined probability = 0.33).
The plague marine saves the wound on a 3+, followed by a feel no pain roll of 4+ if required.  Hence the probability of the wound being saved is 2+.  Therefore an unsaved wound has a probability of 0.056.

But the Tesla special rule will activate on a hit roll of 6.
So we'll modify the above calculation to count for only a roll to hit of 3, 4, or 5.  That yields a probability of an unsaved wound of 0.042.  
Now let's add in the roll to hit of 6 (probability of 1/6 = 0.167).  This causes an automatic 2 extra hits.
So we're taking 3 hits with a wound caused on 4+.  That's 1.5 wounds * 0.167 = 0.25 wounds.
Each wound is saved (as above) on 2+.  This gets reduced to 0.042 unsaved wounds if the necron rolls a 6.

Combining the two results (0.042 unsaved wounds on a hit roll of 3,4,5 with 0.042 unsaved wounds on a hit roll of a 6) yields 0.083 unsaved wounds per incoming tesla carbine shot.  That means 12 tesla carbine shots are required to down a plague marine, on average.  That compares to 27 bolter shots (or indeed, gauss flayer shots) to down a plague marine.  So an immortal armed with a tesla carbine is more than twice as deadly as a regular necron or space marine to my plague marines.

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