*(originally posted on MightyBell )*

This Google Doc details the breakdown of average rolls for each attribute and then for each increment of **Advantage** or **Disadvantage** for that attribute dice set.

*(originally posted on MightyBell )*

This Google Doc details the breakdown of average rolls for each attribute and then for each increment of **Advantage** or **Disadvantage** for that attribute dice set.

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*Grabs a pitchfork, looks at it, drops it for the electric razor instead.* Letās get him!

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Lol, my fault. I couldnāt tell who made it.

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For the code-minded among us, I made a quick exploratory script to chart out dice roll probabilities using the awesome Runkit:

https://runkit.com/briandonahue/openlegend-roll-analysis

With runkit, you can change the results view to a āchartā using the dropdown to get a better view of roll distribution.

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This is awesome, first off!

Second, this took me more than a minute to find, LOL! So FYI, hereās what to look for if youāre like me and canāt quite see how to do this. Firs, look for:

Click āProperties Viewerā

And youāll get a chart where you can select different chart types:

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Is this based on expected probabilities, or on experimental data?

I canāt speak to the methods of the two folks who posted their charts above, but they align with what I know to be true from the dice testing tool built a long time ago by one of my very early alpha playtesters. This is fun, you can crash your browser with this (maybe your computer too), but I put in **999,999** and it takes a few seconds. If you run this repeatedly, you find that itās sufficient to normalize the data within a few hundredths of a decimal place, which should be sufficient:

**EDIT**: read further down, this URL doesnāt generate accurate data

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Nice. Bookmarked that.

Iāve had some fun on anydice.com as well. It appears to calculate probability instead of simulating rolls, though on a large scale it shouldnāt matter. The main problem I find there is that it stops calculations if it requires more than a few seconds. For OL specifically, this could be a problem if you want to see probabilities for lots of explosions.

My spreadsheet was based off of 1,000,000 rolls of each combination of dice from http://spandox.com/rollopen.htm

Itās a great tool for dealing with exploding dice.

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Someone else used Anydice.com and posted on MightyBell, I donāt remember if the numbers were right or not

I am pretty sure anydice calculates probabilities instead of running simulations. I spent an evening trying to get the results in anydice to line up with the OP doc with no joy. I cannot discount the likelihood of a PEBKAC error additionally in the mix.

Although the **probabilities** should (and more or less do) line up with the experimental results from http://spandox.com/rollopen.htm1, I also notice that the **mean values** listed on anydice are lower than on the document. However, this actually makes sense, because anydice defaults to a maximum of 10 (I think) explosions, and it therefore has incomplete data with which to calculate mean.

Looking at these comparisons, however, I notice something interesting. The formula I used in anydice (output [explode 1d20] + [highest 2 of 4d[explode 1d6]] is for an attribute score of 5 with advantage 2) is representative of how explosions with advantage work in roll20. Roll all dice, explode results as needed, then remove the lowest n results.

This is NOT how the core rules say to do it. Take a look at the sidebar āEXAMPLE OF ADVANTAGE WITH EXPLODING DICE.ā

The process described in that sidebar will definitely result in a different probabilities than using the roll20 method, but my anydice results were consistent with the results from http://spandox.com/rollopen.htm. This suggests that the example and the tool are not using the same method.

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Thanks for this researched response! Iām actually working on building out the sheet linked in the main post with a second page of the results I get from AnyDice, and Iāve updated it to max out at 30 explosions, just to be safe .

Iāll keep you all posted.

Note: The formula you used was āoutput [explode 1d20] + [highest 2 of 4d[explode 1d6]]ā for Attribute 5, Adv. 2. As you mentioned, that explodes *before* removing the lowest dice (and, alternately for Disadvantage, before removing the highest), meaning you could get much higher averages, as you should only be rolling the 2 instead of rolling 3 or 4 which gives you more chances to explode again.

The formula I am using currently is āoutput [explode 1d20] + [explode [highest 2 of 4d6]] named āAdvantage 2āā. This should keep the highest 2 before exploding so that you only get to keep the results of those explosions as opposed to the explosions from several dice and keep the highest 2 of those.

Let me know if there is a way to improve the formula or if Iāve misunderstood/forgotten something!

EDIT: Ran into server timeout at 50 explosions, so I reduced it to 30. XD

EDIT2: It didnāt like 30 either for anything above Attribute 6, so now itās down to 20. <_<

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Yup, the exploding dice rolling mechanic is a known issue with Roll20 @Carl.

So, crazy news folks! For folks like @Hassurunous, @GartLarissa, @Daranar, youāll either find this hilarious or hate me

Iāve been too busy working on other things, my buddy who made http://spandox.com/rollopen.htm is a veteran computer programmer so I never bothered to check his work **UNTIL NOW**!

Iām laughing maniacally, knowing how itās not as big of a deal as people will think it is and also bracing myself for a storm of controversy.

Turns out, the the thing thatās wrong on Roll20 was also wrong on http://spandox.com/rollopen.htm this entire time

Iāve fixed the logic and forked a new (correct) version. The impact on the average (naturally) scales depending on how much advantage you have, and the miscalculation can be quite dramatic at high advantage totals.

Previously, getting a 70+ on that roll had a `4.06%`

chance

Turns out, itās actually `0.46%`

Without further adieu, you can check out the fixed stat generator (Iāll redo the user interface later when I have time) at:

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Well, guess Iāll redo the sheet this week. lol

@Hassurunous FWIW your final formula is exactly the same one I used. I feel a little less dense.

(Also FWIW my function also had the option to return the lower between the result and an arbitrary limit (usually 45), just so I could trim the long tail off the data and make it easier to compare stacked charts.)

@brianfeister HA! Now I feel even less dense. Also wryly resigned to the fact that I will not be able to resist the temptation to losing another night to number-bothering in the near future.

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@GartLarissa @Hassurunous @Carl, FYI you can see the source for this (most of it isnāt my code, so no poking fun, I just fixed the bug in how the calculations were run) on Github if you like:

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So, when I was messing with my own system before I came across Open Legend, I was mainly using d6 that exploded.

I actually did the mathematical permutation to figure out the average roll of a d6 (it was roughly 4.2, I had a more exact number, but Iād have to look it up now). This way I could figure out target numbers and the like.

You can actually figure out the mathematical average, b/c when it comes to averages, even though it can explode to infinity, based on the rarity, it stops affecting the total average after so many.

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The actual simple math forumla, to determine the average of an exploding dice, it increases over the expected dice by

N/(N-1) where N is the number of sides.

So a d6 average is 3.5

6/5 * 3.5 = 4.2

Of course, when it comes to having advantage, that can throw into a much more complex calculation. =P

Interestingly, I just found this article that explains it better than me:

now to figure out the math behind advantage.

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