Help me calculate this average please !

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**godardc**

Hi guys,
I don't really know how to calculate this average and I haven't found anything able to do it on the internet.
So, how would you calculate several d3 with rerolls ?
Like, rerolling if it's a 1 but not a 2 or 3 ?
I would like to calculate how many wounds would 8 wounds by grav guns against a crawler inflict to the crawler (but if I use D2 as an average and say 16*0,66 = 10,56 it's not taking the reroll into account).
Thanks !

**flandarz**

You just add the percent chance that the reroll number will come up to the average number without it.

For example 1D3, reroll 1s: chance you'll roll a 1= 33%. Average value on the dice is 2. So the average, plus reroll, is 2.33.

**Daedalus81**

Here's a rudimentary way of thinking about it.

You roll:

1 - going to reroll this - chance of 1, 2, or 3 (average 2)
2 - keep
3 - keep

So your results are :

2
2
3

And the average of those is 2.33

**Catulle**

All the re roll does is pull it up slightly from (towards) a median 2, as Daedalus says - what you care about is the variance introduced by that reroll coming up 1-3rd of the time.

(The mean of a d3-only-reroll-ones strategy is 2.2, but that's misleading as to the expected outcomes in small sample pools)

**Inquisitor Lord Katherine**

As a side note, assuming the re-roll is baked in and you're not paying CP for it or something, you should re-roll on a 1 or a 2, not just a 1.

Assuming the re-roll is free, it's only a bad thing if it gets worse, which it only has a 33% chance of doing. You have a 67% chance of doing as good or better by taking the re-roll.

**Catulle**

Inquisitor Lord Katherine wrote:
As a side note, assuming the re-roll is baked in and you're not paying CP for it or something, you should re-roll on a 1 or a 2, not just a 1.

Assuming the re-roll is frefe, it's only a bad thing if it gets worse, which it only has a 33% chance of doing. You have a 67% chance of doing as good or better by taking the re-roll.

This is bad maths if you're looking for broad trends as 11/5 is better than 15/7 in re means.

If you're chasing 2s, then an 80% also beats out a 71.4%

If you're looking for 3s, then yeah, 40% is worse than the 42.8% chance generated by the "reroll not-3s" strategy.

As in all things, make the right chonce for the job at hand.

**Insularum**

Spoiler:

Rerolling 1's only and rerolling 1's and 2's on a D3 will yield the same average of 2.33, but with greater variance. There are plenty of times where rerolling everything is absolutely the superior strategy, for example when you have zero chance of killing a unit, but chasing 3's can make the difference between taking it down a damage chart bracket or not; or when shooting at 3 wound models.

**Dysartes**

Per d3, where only a 1 is re-rolled...

Odds of a 1:
1/3 * 1/3 = 1/9

Odds of a 2 or 3:
1/3 + (1/3 * 1/3) = 1/3 + 1/9 = 4/9

If we assume 8 off these rolls, I'd say 1 result of a 1, 3 each of 2 and 3, and 1 at 2.5, for a rough total of 18.5 wounds. Not sure, off-hand, why the initial example is then reducing this by 1/3 ( a 5+ FNP, at a guess?), but that'd drop the total to 12 and a bit.

**godardc**

Yes I was trying to calculate against a plague crawler and it's fnp5+, to see if it was worth shooting at it with the stratagem. 12 wounds is enough to destroy one, so I may try it at least I know I should be able to destroy it statically.
Thanks a lot guys !