Wednesday, November 18, 2009

Everyone Deserves a Second Chance - Calculating Re-rolls with Method 216

I don't get many things right the first time, in fact, I am told that a lot. - Ben Folds

So looks like I took another hiatus from 40K, luckily (a word I never use in conjunction with mathhammer) I'm back and brought an easy way to factor in re-rolls to Method 216.

Method 216 is a super easy and simple method for calculating expected kills in Warhammer 40K using some simple math in your head, on some paper, or even using the calculator on your cell phone.

If you don't know what Method 216 is, or just don't remember, then go learn all about it here Super Simple Method 216.

Now that you are a Method 216 expert, let's push it a step further and factor in the re-rolls.

Here's an example to start us off,
8 Guardian Jetbikes (with no Shuriken Cannon upgrades) are shooting at a Space Marine tactical squad.

The calculation for Method 216 would be,
(16 * 3 * 3 * 2) / 216 = 1.33~ Space Marines shot to pieces!

BUT WAIT A MINUTE, those Shuriken Cannons are twin linked, so how do I factor in the re-rolls?

For re-rolling failed hits and wounds all you have to do is add the Method 216 result from before times the re-roll multiplier in the chart below.

6+ 0.83
5+ 0.67
4+ 0.50
3+ 0.33
2+ 0.17

So since the Guardian Jetbikes needed a 4+ to hit before, you take the 1.33~ dead marines and add 1.33~ times 0.50.

1.33~ + (1.33 * 0.50) = 1.96~
An easier way to do with is simply 1.33~ * 1.50 = 1.96~ Dead Space Marines

If a Farseer had Doomed the Space Marine Tactical Squad, then the calculation would be,
1.33~ * 1.5 * 1.5 = 3~ Dead Space Marines

Now then for re-rolling saves you simply multiply the Method 216 result by the re-roll multiplier.

So if the 7 remaining marines were to rapid fire back (assuming they all just had boltguns) then you would have,
(14 * 4 * 3 * 2) / 216 = 1.56~ Eldar souls eaten by the warp

If the Farseer had cast Fortune on the Guardian Jetbikes then it would look like.
1.56~ * 0.33 = 0.51 Eldar souls eaten by the warp

Now go forth and mathhammer!!!


  1. Very good article and method. But think I have spotted a small error:

    > "Now then for re-rolling saves you simply multiply the Method 216 result by the re-roll multiplier."

    Surely this is not the case, as for hit and wound re-rolls, the reroll increases the chance of a kill, but rerolling saves decreases it. Hence you can not apply the same multipler for saving rerolls.

    The correct multiplier would be the "dice inverse" and a divider not a multiplier. In other words if the saving throw is a 5+, you need a 4- to kill which numerically is 3+. If you imagine that you are rolling the saving throw rather than your opponent, you need to roll "less than" rather than "more than" to affect a kill. Hence for a wound reroll you need to *divide* against the following table:

    6+ 0.17
    5+ 0.33
    4+ 0.50
    3+ 0.67
    2+ 0.83

  2. How would this work with preferred enemy?

  3. How about 2D6 armor penetration to a vehicle... like a melta... how would that work?