Now that we’re fully versed in the probabilities of the humble d6, let’s see what happens when we roll two of them together. Yes that’s right, we’re talking 2d6 baby, yeah!

…

Ok, like last time I’ll kick it off with a question, actually this time it’s a couple of questions:

A squad of

Chaos terminatorshas basic leadership 10. In an epic career of 1,000 unmodified leadership checks,how many would you expect to fail? Their Chaos marine brethren have leadership 9; if a squad ofChaos marinesalso had to take 1,000 unmodified leadership checks in their career how many would you expectthemto fail?

On 2d6 we can get results from 2 to 12, but unlike the d6 scenario the results are not all equally likely. The chart below follows the same format as this post so I won’t be as laborious in describing what each row means. (Note I’ve rounded to one decimal place to keep the chart smaller).

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |

= | 2.8% | 5.6% | 8.3% | 11.1% | 13.9% | 16.7% | 13.9% | 11.1% | 8.3% | 5.6% | 2.8% |

< | 0.0% | 2.8% | 8.3% | 16.7% | 27.8% | 41.7% | 58.3% | 72.2% | 83.3% | 91.7% | 97.2% |

> | 97.2% | 91.7% | 83.3% | 72.2% | 58.3% | 41.7% | 27.8% | 16.7% | 8.3% | 2.8% | 0.0% |

<= | 2.8% | 8.3% | 16.7% | 27.8% | 41.7% | 58.3% | 72.2% | 83.3% | 91.7% | 97.2% | 100% |

>= | 100% | 97.2% | 91.7% | 83.3% | 72.2% | 58.3% | 41.7% | 27.8% | 16.7% | 8.3% | 2.8% |

Ok, so the ‘equals’ row shows the odds of any particular result from 2 to 12, and as I noted above this is not the same for all results. In fact it’s quite different; as an extreme example you are 6 times more likely to get a 7 as a 2. 7 is the most likely result, and results get less likely the further you go above or below 7 (so 2 and 12 are the least likely results at 2.8% each). It’s worth noting that the odds of getting a 7 is 16.67%, which is the same odds as getting any particular result on a single d6 (i.e. the odds of getting 7 on 2d6 is one in six). This means that while 7 is the most likely single result, there’s only a one in six chance of getting a 7 (clear as mud eh?).

**What does this all mean in game terms?** The most common use of 2d6 is for leadership checks of various types (there’s also scatter dice but I’ll cover those in a separate post in the near future). Interestingly enough, while most of the time we hope for high rolls in 40k, for leadership we want to roll low. So the most useful row in the above chart is the ‘greater than’ row; it gives us the odds of failing a leadership check for a given Ld value.

The odds of failing a leadership check decrease fairly rapidly as Ld increases, but what’s most interesting is the step changes at the higher end of the leadership scale. In the long run, Ld9 fails twice as many leadership checks as Ld10; Ld 8 fails over three times as many times as Ld10, and **Ld 7 fails five times as many times as Ld10**.

Or to put it in absolute terms: **Ld 9 fails one in six times **(yes that includes you, Fateweaver), Ld 10 fails one in twelve times.

**This gets us the answer to our opening questions fairly quickly**. The Chaos terminators at Ld10 will expect to fail 83 of their 1000 leadership checks, whereas the Chaos marines at Ld9 will expect to fail 167! So in practical terms, for an unmodified roll, **Ld10 is twice as good as Ld9**. Adding an Ld10 aspiring champion to the Chaos marine squad means they would expect to fail half as many leadership checks.

That’s enough for now, any comments or questions welcome!

March 23rd, 2011 at 10:30 pm

You, sir, are a utter nerd and most vile numerologist. Although, I do like the leadership test section.

March 24th, 2011 at 10:02 am

Dear Douchebagsh,

I write to you regarding your recent comment Re: Fateweaver and would like to correct some of your “facts” regarding the isshue.

His name is Dr. Fateweaver, he didn’t spend 8 years at Chaos Doctor school to be called Mr. thank you very much.

January 8th, 2012 at 3:05 am

[…] you recall my article on 2d6 we saw a spike on the 7 result because the largest number of possible combinations added up to 7. […]

December 12th, 2012 at 10:56 am

[…] complicated as some units can get a reroll, and others can reroll specific dice (i.e. Fleet). As most of you know, 7 is the average result on 2d6, but this can lead to the unfortunate assumption that you should […]

January 2nd, 2013 at 6:00 pm

[…] The basics: 1d6 and 2d6 […]