Wednesday, 23 September 2009

Re-rolls and probability

I noticed this interesting post over at The D6 Generation yesterday. It's from a listener who writes about the probability of scoring a certain number on a D6 with and without a re-roll, so for example when firing a twin linked weapon. You can read the way the binominal probability works in the post, but I just wanted to share the most important part, the probability table:

2++ = 97%
3++ = 89%
2+ = 83%
4++ = 75%
3+ = 67%
5++ = 56%
4+ = 50%
5+ = 34%
6++ = 31%
6+ = 17%

+ = w/o a reroll
++ = with a reroll

Let's take an example. Say a Chaos Terminator with a twin linked bolter (rapid fire, twin linked) and a Space Marine Terminator with a storm bolter (Assault 2) are both firing at a target 10" away. Both are BS4, and both weapons are the same strength and AP.

Each shot from the Chaos Terminator has a 89% percent chance of hitting, and so has a 79% chance of hitting with both shots (0.89 x 0.89).

Each shot from the Loyalist Termaintor has a 67% chance of hitting, and so has a 44% chance of hitting with both shots.

So on pure stats, the twin linked bolter is better at this short range. Of course, at more than 12" the storm bolter would get an extra shot perhaps giving it the edge there. Being in terminator armour, the unit can still charge after firing it's bolters.


jabberjabber said...

This was one of the reasons to convince me that Chaos terminators were actually rather cool compared to their imperial cousins. I used to be a bit on the fence about chaos terminators, but have now been in favour of them and their weapon options for a long time.

Sholto said...

I have been telling people for some time that Gun Drones are better shots that Fire Warriors, but everyone looks at BS2 and waves their hands in horror.

Interesting data points:-

The jump for BS2 and 4 if you twin-link is a 22% increase in accuracy.

The jump for BS3 if you twin-link is a 25% increase in accuracy.

Twin-linking BS1 and 5 is hardly worth the effort.


Hudson said...

To build on what Sholto said, look at Orks (Deffcoptas, Dreads, etc) with twin-linked rokkits -- slightly better odds than a guardsman (55% vs 50%) As I discovered painfully this past weekend.