2D3 vs D6 is there a difference?

[Inquisitor_Lensoven]

Noticed the icarus rocket pod on the thunderstrike is 2D3 shots, why not just D6 shots? Just to guarantee the minimum of 2 shots while giving the same possible max shots (or damage, or whatever)

[Brother Tyler]

Where a D6 gives you an equal chance of getting any result 1-6, the 2D3 gives you 2-6 shots, but also has the highest likelihood of getting a 4, a median likelihood of getting 3 or 5, and the least likelihood of getting 2 or 6. The 2D3 creates a bell curve.

[Brother Tyler]

Here's a graphic depicting the comparative distributions...

[Lord_Ikka]

The bell curve, as Brother Tyler showed, means that while 2d3 has a lower likelihood of getting a 6, it has a much higher average damage than just a d6 due to the variance of the d6 roll. Basically, 2d3 will show a better average damage in the long term than just a d6. 

[Inquisitor_Lensoven]

Interesting thanks for the chart!

[Valkyrion]

I weirdly love stuff like this....is there a similar chart for the pros and cons of D12 rather than 2D6?

With no research whatsoever, I'm guessing D12 is worse when trying for high numbers (e.g, damage) but better for lower numbers (e.g passing a leadership test).

[Marshal Reinhard]

d12 is the same as the d6 in that each number is exactly as likely an outcomes as any other, ie 1/12 or about 8.33%. There's no bias towards low or high numbers

 

with 2d6, you again get a bell curve with the ends (2 and 12) being the least likely (1/36 or about 2.77%) because they have the fewest possible combinations, while 7 being the center has the most and thus is the most likely at (6/36 or 16.66%)

 

Here's some graphic i yoinked off the internet:

 

 

The two take aways for any of these situations is: the 2 dice has a slightly higher average than the single variant (4 vs 3.5 in the case of 2d3 vs 1d6, 7 vs 6.5  in the case of 2d6 vs 1d12). This is due to the fact that the distribution does not include the result for 1.

 

The 2 dice distribution is a bell curve vs a flat distribution for the single dice, this means the 2 dice have a higher chance to get the middle result vs the single dice where every result is as likely as any other.

 

On a whole in the game it's prefferable to have 2d3 to 1d6 (or 2d6 vs 1d12) if you want to roll consistently higher results. You're rolling higher on average, and you're guarded against ever getting the lowest result. If you want the very top result as frequently as possible though, 1d6 (1d12) may be prefferable.

Edited August 1, 2021 by Reinhard

[Rik Lightstar]

As everyone else has mentioned the 2 dice option will give you more results in the midlle of the range giving you far more reliability and consistency. The main downside being the reduced chance of the highest outcome.

 

The other downside however is that it becomes less manageable for making multiple rolls, getting two hits each doing 2d3 damage is fine, but if it gets into double figures it's just time consuming (same issue with 2 dice and take the highest). That's the main reason Terminators lost their 3+ on 2D6 Save from waaaaay back in Second Edition.

 

Rik