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Does any one know how to do this calculation?

What would do more wounds from a flamer. Being able to reroll the number of shots or being able to reroll failed wound rolls?

This case in question is to shoot an alaitoc crimson hunter, using 10 - 15 flamers to bring it down. You'd be wounding t6 on 5s.

Scions can use orders to reroll wounds against vehicles while catachan can reroll the number of shots from flamers, trying to work out what would be more effective

Depending on what you're shooting at. But generally flamers aren't worth it.

You could go to www.dice-hammer.com and click the reroll hits and wounds checkboxes for your unit of choice and see the results

ravenerioli wrote:
Does any one know how to do this calculation?

What would do more wounds from a flamer. Being able to reroll the number of shots or being able to reroll failed wound rolls?

This case in question is to shoot an alaitoc crimson hunter, using 10 - 15 flamers to bring it down. You'd be wounding t6 on 5s.

Scions can use orders to reroll wounds against vehicles while catachan can reroll the number of shots from flamers, trying to work out what would be more effective

Great question. The average number of shots on a D6 is 3.5. What's the average if you can reroll ones twos and threes? I think it's the average of all weighted possible outcomes: (4+5+6+3.5+3.5+3.5) / 6 = 4.25. that's a 21% improvement.

The value of rerolling failed rolls actually increases when the difficulty increases. Rerolls to a 6+ are more valuable than rerolls to a 2+. Here's the math for wounding on 5+:

To keep the numbers round, let's roll 36 hits (six squared). An average roll will yeild 12 successful wounds and 24 failures. Rerolling those failures adds another 8 successes for a total of 20 wounds. That's a big 66% improvement!

What's the break even point? Rerolls on a 2+ is only a 16% improvement, while even rerolling a 3+ yeilds 33% more wounds.

In conclusion, we can say this:
Rerolling wound rolls of 3, 4, 5, or 6+ is more valuable than rerolling number of shots.
Rerolling number of shots is more valuable than rerolling wound rolls of 2+.

I'm sure there is an easier way to calculate it but.

To figure out how much better rerolling how many shots you'd first need to find what is the best expected value for rerolling your flamer number of shots. Rerolling failed to hit or to wound rolls is always a positive, but rerolling flamer shots is not always positive.

So to do it we have to take the average of rerolling each result and replace it with the one reroll.

For instance if we were only rerolling 1's we'd replace 1 in the average die roll with a 3.5 as thats the average expected value for the one.

So our possible values goes from 1, 2, ,3,4,5, & 6, to 3.5, 2,3,4,5, & 6. (average result now being 3.91) As you can see that's a large jump in expected average results. At this point we can do a quick sanity check to save us some time. We know that if the average value of a reroll is 3.5 or likely better than 3 we can replace the values 1, 2, & 3 with 3.5. Which gives us an average expect number of shots to be 4.25.


Now that we've figure that we can do the rest.

For our none rerolling number of shots flamer against a crimson hunter we have:

3.5 shots (expected average of a d6 roll) * 2/6 (chance of successful wounding)* 10/6 (1+ number of average rerolls) * 2/6 (3+ armor save for a crimson hunter)=.65 average damage

vs

4.25 shots (expected average of a d6 rerolling 3 or less)* 2/6 (chance of wounding)* 2/6 (3+ save)=.47 average damage.

Doing a sanity check here, we know that rerolling the to wound modifier is pretty great because it's basicly like having 3/6 more attacks. Where as rerolling the number of shots only boost your damage potential by about 21% which is less than the 50% boost in damage from the reroll to wounds.

Thanks guys had no idea you substitute the average into the equation like that. So scions are better flamers against monsters and vehicles than catachans are but catachans get to use their flamer order against all unit types.