Anydice.com question

[Genth]

Hi guys, wondering if you can help me to pose a few questions to Anydice.com.

I want to include the 'Righteous fury' dice from W40k, where if on a 1d10 you roll a 10, you can roll another 1d10 and add that to the total. How would I show that for anydice?

I want, essentially, to compare damage output of normal vs tearing damage (where tearing rolls 2d10, and takes the best one) I can do this easily without the righteous fury rules, but I want to see how much more of a difference it makes

[meschlum]

Hi guys, wondering if you can help me to pose a few questions to Anydice.com.

I want to include the 'Righteous fury' dice from W40k, where if on a 1d10 you roll a 10, you can roll another 1d10 and add that to the total. How would I show that for anydice?

I want, essentially, to compare damage output of normal vs tearing damage (where tearing rolls 2d10, and takes the best one) I can do this easily without the righteous fury rules, but I want to see how much more of a difference it makes

Easy!

81% of the time, no 10s are rolled, and you get the maximum between the two. That can be broken down as follows:

(1, 1): 1% of the time, 1 damage
(2, x): 3% of the time, 2 damage (x is 2 or less)
(3, x): 5% of the time, 3 damage (x is 3 or less)
...
(9, x): 17% of the time, 9 damage (x is 9 or less)

For a total of 5.25 damage (average with one die ranging from 1 to 9 is 4.5)

18% of the time, one 10 is rolled, and explodes. An exploding die gives you 10 plus another die that might explode too - so if has an average of X, you get X = 4.5 (average from 1 to 9) + (10 + X) / 10 (10% chance to get a 10 and add an exploding die to the mix), so 0.9 X = 5.5, meaning the average of an exploding die is 6.111.

So you get 16.1111 damage on average 18% of the time, for a total of 2.9 extra damage.

So unless you roll wo 10s, your average damage is 8.15

1% of the time, you roll two 10s, so you get a base damage of 10 and roll again. Per the reasoning on exploding dice, we get Y = 8.15 + (10 + Y) / 100, so 0.99 Y = 8.25.

That gives an average damage of 8.333.

The improvement over a single exploding die is therefore 2.2222, which isn't bad!

If the dice were non-exploding, two dice give an average of 7.15, versus 5 with a single die - so the overall impact of the exploding die is to add a bit more than 1 damage on averge.

[Illogictree]

Hi guys, wondering if you can help me to pose a few questions to Anydice.com.

I want to include the 'Righteous fury' dice from W40k, where if on a 1d10 you roll a 10, you can roll another 1d10 and add that to the total. How would I show that for anydice?

I want, essentially, to compare damage output of normal vs tearing damage (where tearing rolls 2d10, and takes the best one) I can do this easily without the righteous fury rules, but I want to see how much more of a difference it makes

For "righteous fury" you'd use the explode function.

output [explode 1d10]

For tearing, you'd use the following:

output [highest 1 of 2d10]

More information is under the Function Library tab.

[Genth]

I was looking for distribution, but thanks!

ah, this seems to work;
output [explode [highest 1 of 2d10]]

Wow. Actually, wow, with the tearing rules, I have a 6.84% chance of getting 19 or higher!