This may be of interest to PBTA design folks and enthusiastic players alike.

This may be of interest to PBTA design folks and enthusiastic players alike.

This may be of interest to PBTA design folks and enthusiastic players alike. When I was wrapping my head around the math in 2d6+Stat, and looking at what happens when you use Advantage and Disadvantage, I used anydice to make myself this reference chart.

Two things I took away from the chart is that keeping your modifier in the 3 to + 3 range will always make 6 and 10+ possible, if very unlikely at the extreme edges of the probability curve. Advantage keeps this math unbroken, while making a big enough difference to the roll to matter. Also seeing the triumphant 6 or heartbreaking 1 on that third dice is a visceral sensation for players.

The other thing worth noting is that + 1 is the median point for probability. On a + 1, misses and full hits are equally likely. Systems that use 2 and -3 as modifiers are actually going to have a greater focus on the 6 result, which I find very interesting.

I also included 7+ as a result, since that result often gives the player at least some of what they want.

Disclaimer: I’m a probability and math dummy, so take all of this with a grain of salt, and trust someone with better math skills than myself on the numbers.

18 thoughts on “This may be of interest to PBTA design folks and enthusiastic players alike.”

  3. Cool. I have recently done a similar analysis in Excel with some charts. You can find it here: drive.google.com – PbtA Analysis Rolling with Extra.xlsx – Google Drive

    My analysis calls it “with extra” since I was playing Spirit of 77.

    The binomial distribution of 3d6 is much smoother than 2d6 as you can see. We are getting even closer to the 4 Fate dice distribution with advantage / disadvantage 😉

    EDIT: you need to download the file and open it in Excel to see the charts.

  4. Cool. I have recently done a similar analysis in Excel with some charts. You can find it here: drive.google.com – PbtA Analysis Rolling with Extra.xlsx – Google Drive

    My analysis calls it “with extra” since I was playing Spirit of 77.

    The binomial distribution of 3d6 is much smoother than 2d6 as you can see. We are getting even closer to the 4 Fate dice distribution with advantage / disadvantage 😉

    EDIT: you need to download the file and open it in Excel to see the charts.

  5. Btw, I’m a mathematician and my analysis is not based on random numbers but I went through all combinatorials. They are not so many. But your result looks totally plausible, Adrian Thoen. Thanks for sharing!

  6. Btw, I’m a mathematician and my analysis is not based on random numbers but I went through all combinatorials. They are not so many. But your result looks totally plausible, Adrian Thoen. Thanks for sharing!

  7. This is really interesting stuff. Assigning Ad/Disad in D&D5 is kind of arbitrary, and it seems like Advantage doubles your chances of getting a 10+ and halves your chances of getting a 6-. In what kinds of situations do you see the characters getting Advantage (or Disad, for that matter)? The same kinds of stuff from 5th Ed, where they set themselves up for success, or something situational significantly benefits them?

  8. This is really interesting stuff. Assigning Ad/Disad in D&D5 is kind of arbitrary, and it seems like Advantage doubles your chances of getting a 10+ and halves your chances of getting a 6-. In what kinds of situations do you see the characters getting Advantage (or Disad, for that matter)? The same kinds of stuff from 5th Ed, where they set themselves up for success, or something situational significantly benefits them?

  17. jim miller I’ve done extensive playtesting on my own game using this mechanic. I fell that just like than +1 forward, the triggers for Adv/Dis really matter to make it meaningful. Generally, having the trigger and use be immediate makes sure the players don’t forget about it.

    In a game where you get XP on a miss, Disadvantage can be something the players will hunt just as much as the Advantage – so long as you still make those misses as engaging and interesting as any other result.

    Physically, Adv/Dis taps right into the gambling part of our brain, since it lets you see what might have been. Taking away that 6 that would have made a failure a success on Disadvantage makes the 1 you keep extra painful, and throwing away that one to hold aloft the 6 your replace it with on Advantage triumphantly is a tactile reinforcement.

    There’s also a smug satisfaction when you don’t even need the replacement die because all your rolls are high.

    I know there are other games that use A/D, but the two I can think of off the top of my head are Spirit of ’77 and Fellowship.

  18. jim miller I’ve done extensive playtesting on my own game using this mechanic. I fell that just like than +1 forward, the triggers for Adv/Dis really matter to make it meaningful. Generally, having the trigger and use be immediate makes sure the players don’t forget about it.

    In a game where you get XP on a miss, Disadvantage can be something the players will hunt just as much as the Advantage – so long as you still make those misses as engaging and interesting as any other result.

    Physically, Adv/Dis taps right into the gambling part of our brain, since it lets you see what might have been. Taking away that 6 that would have made a failure a success on Disadvantage makes the 1 you keep extra painful, and throwing away that one to hold aloft the 6 your replace it with on Advantage triumphantly is a tactile reinforcement.

    There’s also a smug satisfaction when you don’t even need the replacement die because all your rolls are high.

    I know there are other games that use A/D, but the two I can think of off the top of my head are Spirit of ’77 and Fellowship.

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