Damage dice re-rolls. When should you?

[chapter master 454]

So as of late, there is one thing I have been running through my head while I drive buses (can't have music so musing on 40k based things has to do!) and one of the key things I have currently got hung up on is in relation to the fact grav-cannons can get re-roll damage dice. Not exactly a common re-roll type to get en mass, normally its a "re-roll 1" or "roll 2d6, take highest" sort of thing but this is kind of weird because now we have a question (well I do but I wonder how you guys see it).

 

What numbers do you re-roll on the dice?

 

So in terms of the grav example, when it gets to roll D3 damage vs. a 3+ save unit we have 3 results. 1, 2 and 3.

We will ALWAYS re-roll 1 and never re-roll 3.

The objective is to achieve maximum damage, not any break points. For all purposes of this question, the target will not be bracketed, killed/destroyed, stopped or hindered by the rolls no matter their number however you are simply seeking to do as much damage as possible within rolling your set of D3s, allowing for 1 re-roll per die (so no re-rolling a re-rolled die as per usual).

 

I am personally coming to the conclusion is that you should re-roll 2s. After all, if we are playing odds then odds should favour you re-rolling 2s since 2 outcomes don't hurt you out of 3 (and 1 even benefits you). However when running some really quick maths in my head (remember...driving buses, not sitting in an office!) it however would appear that re-rolling 2s would however only end up just being the same overall.

 

I did run this idea against D6s but I quickly considered that question far less interesting as the % stay the same really as I concluded it is best to re-roll 3s and less.

 

So I put it you my fellow fraters, whats your conclusions?

[Medicinal Carrots]

The average damage is identical whether you're rerolling only 1s or rerolling 1s and 2s. Rerolling 1s gives a more consistent 2+ chance, while rerolling 1s and 2s spreads a bit higher and lower.

Rerolling 1s gives a 4/9 chance to roll a 3, 4/9 for a 2, and 1/9 for a 1

3x4/9 + 2x4/9 + 1/9 = 7/9, or 2.333 avg damage

 

Rerolling 1s and 2s gives 5/9 to roll a 3, 2/9 for a 2, and 2/9 for a 1

3x5/9 + 2x2/9 + 2/9 = 7/9, or 2.333 avg damage

 

If you need to roll 2+ for 2 wound models, reroll 1s. If you need to roll 3+ for 3 wound models, reroll 1s and 2s. Otherwise you could try to work out on the fly whether you need more 2+ or 3s based on what you rolled vs wounds left on the target. Or just stick to rerolling 1s since it's faster.