Friday, March 27, 2015

Math By Request: Bloodthirster Vs Imperial Knight

One of the regular readers, Mundo, made a request for some calculations related to the new bloodthirster of insensate rage fighting an Imperial Knight.  When I took this on I thought, "Oh this is going to be easy."  After a few hours days all I can say is that destroyer weapons are painful for more than just their target.

**Update: The math in this article has been redone to include the chances of killing/destroying with wound/hull-point removal.  Go here for more accurate numbers.**

This is a tough fight for the bloodthirster.  Any roll of 6 on the destroyer table will end your day right there.  The main source of protection for the bloodthirster is it's weaponskill 10, so a knight is going to need a 5+ to hit.  The invulnerable save can help negate some of the lesser hits, but the biggest danger comes from losing the bloodthirster instantly.

Since the initial three attacks, assuming that the knight did not charge, go before the bloodthirster then there is a possibility that the bloodthirster won't get to attack back at all.  After some tedious calculations I found that a knight has a 16.25% chance of killing a bloodthirster with it's initial three attacks.  To put this in perspective a 1/6 chance is 16.67%.

If the bloodthirster does get killed there is a 94.37% chance it was from a 6 on the destroyer table.  Chances are a knight is not going to be doing many regular wounds to your bloodthirster.  This means that daemonic gifts or psychic powers that would normally increase your survivability aren't going to be much help here.  If your target is a knight then run your bloodthirster naked.

So, our bloodthrister gets an 83.31% chance of swinging back, and when he does it is going to hurt.  Once again any roll of 6 on the destroyer table will end the knight instantly.  The bloodthirster also has 8 attacks on the charge.  To be honest I am not going to calculate the chances of a bloodthirster hulling out the knight, because I would be here until next week.  On the charge a bloodthirster has a 61.03% chance of instantly blowing up the knight with the destroyer table.  It also has a 5.63% chance of causing six or more D3 hull points.  These two possibilities alone give the bloodthirster a 66.66% chance of destroying the knight.  This does not include the possibility of 2-5 hits destroying the knight (That would take way too long.  I want to read the new codex this afternoon).

The knight isn't done attacking yet, because it still has the stomp attack. I'm not worried about anything other than the instantly destroyed option.  So there is another 1/6 chance of being destroyed.

If the knight is destroyed there is another destroyer hit on the bloodthirster.  Once again there is an additional chance to be instantly destroyed.

Putting this all together:

Chances of the bloodthirster killing the Knight: 55.53%
Chances of the knight killing the bloodthirster: 38.29%

Chances of the bloodthrister killing the knight AND surviving: 34.27%
Chances of the knight killing the bloodthirster AND surviving: 21.81%
Chances of both of them killing each other: 16.97%

If I wanted to hunt an imperial knight I would bring along a maulerfiend with lasher tendrils.  The tendrils will drop the knight down to one attack, dramatically limiting its damage potential.  If it attacks the bloodthirster it now only has a 5.56% chance of killing the bloodthirster before the bloodthirster gets to strike.  Adding the maulerfiend dramatically increases the chances that the bloodthirster is going to get to swing.

So with this in mind here are the new chances (ignoring any attacks from the maulerfiend).

Chances of the bloodthirster killing the Knight: 62.95%
Chances of the knight killing the bloodthirster: 33.34%

Chances of the bloodthrister killing the knight AND surviving: 43.72%
Chances of the knight killing the bloodthirster AND surviving: 11.73%
Chances of both of them killing each other: 19.23%

I made a LOT of assumptions and simplifications with my calculations.  Destroyer weapons are fairly complicated from a mathematical perspective.  I did give the knight the option to do enough wounds to try an kill the bloodthirster with its initial attacks, but every other calculation is based off of an instead kill.  Accounting for these assumptions would increase the chances of the bloodthirster killing the knight, but by how much I cannot be certain.  What I do know is that I wouldn't send any monstrous creature to kill a fully functioning knight by itself.


  1. Great data andrew! Thanks for taking the time to calculate this all out!

    1. I'm just happy that I have readers who are interested in following my long rants on probability.

    2. I always find it really interesting, because when things happen in games, you like to have the #'s behind it.

      Like for example, I had a scarab swarm assault my stompa and blow it up (it had 6 hp remaining). I was flabbergasted. Knowing that it was a pretty unlikely chance made me feel better :).

  2. Nice work as always man. It's actually better than I expected, though not great...

    I'd be very interested in the maths for Screamers/Be'lakor vs a knight, as those are the only tools I have right now!

    1. A while back I did the stats on screamers vs a landraider with and without prescience. It isn't exactly what you are looking for, but it is the closest thing I have for the moment.

      Knights are tough for CSM and daemons to deal with, so I am always looking for new ways to destroy them.

  3. Thanks Andrew, really interesting - and I appreciate getting an answer despite it being pretty painful to get there!

    The odds aren't great for the Bloodthirster to survive, and effectively you are trading your points spent on him for those on the knight (~70pt margin?) Plus there is a fair risk the Bloodthirster will die before even swinging. Invisibility would help you here, but that is another 350pt investment in Be'lakor to get it for sure.

    On these odds, I don't think the Bloodthirster will be a good investment to deal with an Adamantine Lance army. Still, it is a pretty badass model. :)

  4. Hi Andrew!

    I just wanted to take the time to say your work here (as in the blog in general) is amazing, this kind of hard data is priceless!

    Keep the excellent work, and thank you!

  5. This comment has been removed by the author.