Sunday, March 1, 2009

What Difference Does Twin-Linked Make?

This posting is inspired by Ron, who asked me the other day: will twin-linked weapons matter?, in relation to my exploration of the central limit theorem posting.

What I'm going to do is to compute the likelihood of hitting with a given ballistic skill (BS), and compare it with the likelihood of hitting if the shooter has a twin-linked weapons. One of the most common examples (especially for myself as a chaos marine player) is that of a marine (BS=4) shooting a bolter, versus a terminator (also BS=4) shooting a twin-linked bolter.

Without Twin-Linked.
This is straight-forward to work out. For BS=4, the marine is hitting on 3+ with a d6. This means that two-thirds of the time a hit is scored (or 66.7% probability).

With Twin-Linked.
Twin-linked weapons allow the re-rolling of the die to hit, if a miss is scored. Hence, the probability of hitting on the second time around is also 66.7%.

So what is the combined probability to hit with BS=4 and a twin-linked weapon? The answer is 66.7%, plus 66.7% of 33.3%. (The 33.3% is the probability that you missed on the first d6 roll). Two-thirds (66.7%) of one third (33.3%) equals 22.2%. Therefore the combined probability is 88.8%. That's almost 9 times out of 10 that a BS=4 marine will hit with a twin-linked bolter. Pretty good.

Below, I've tabulated the twin-linked probabilities for other BS's:

NOT Twin- Twin-
BS Linked Linked
1 16.7% 30.6%
2 33.3% 55.6%
3 50.0% 75.0%
4 66.7% 88.8%
5 83.3% 97.2%
6 86.1% 97.2%
7 88.9% 97.2%
8 91.7% 97.2%
9 94.4% 97.2%
10 97.2% 97.2%

Note that on page 18 of the rulebook, the twin-linked rule gets preference over the chart for BS=6 or greater (dice can only ever be re-rolled once!). This explains why all probabilities to hit with a twin-linked weapon at above BS=4 are all exactly the same. Therefore, if the shooter has BS=10, then they don't exactly need a twin-linked weapon.

Finally, I should also add that twin-linked flamers (and the like) don't roll to hit anyway. If twin-linked, they re-roll to wound (rather than to hit) and can re-roll armour penetration against vehicles. Twin-linked blasts are a different story (re-rolling the scatter die), and that's a story for another day.


Adam Hunter said...

I'm going to talk about twin linked weapons indepth and what makes them worth taking in next weeks 'How to in at Warhammer 40K' post.

jabberjabber said...

Looking forward to reading about it already mate!

I've long been a fan of havoc launchers myself - they're remarkably good mounted on cheap rhinos.

Andy said...

Thanks for that, this shows that for BS4 marines it is well worth having the twin linked option when possible.

Mike Howell said...

Thanks for the % breakdown. I love math-hammer. :-)

Twin linked template weapons can reroll to wound or reroll armor penetration rolls.

jabberjabber said...

Hi Mike -- excellent point! Cheers!

Template weapons that are twin-linked indeed re-roll to wound / or armour penetration. I'll re-word the article to reflect this.

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