Thread by @ammourazz

Math is scary, and often we stick to what we know because its easy, but the best games examine the mechanical choices they make, so I'm gonna demistify some shit about 2d6 math
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Alternate Title: PbtA designers, please stop using +/- x modifiers in your games.

Let's get into it.

To cover the basics, *most* PbtA uses 2d6 dice resolution, with a 6- being a miss or fail, a 7-9 being a partial success, and a 10+ being a full success (with any 7+ refered to as a hit).

Since 2d6 averages to a 7, you default to a slightly higher chance of a hit than a miss.

(Some PbtA use cards or no randomizer, but from here on out assume I refer specifically to the 2d6 subset)

The majority of PbtA then shifts that curve, often with stats that give you between -2/+3, or systems like answering questions to get +1 to a roll for every yes.

The advantage of that is it's really simple to math out, once you understand the curve, since +/- x just shifts the curve over by x. It also makes it easy for situational modifiers and temporary boosts to give you +/- 1 and is easy to add after a roll! That’s convenient!

The downside is while you can tell relatively what you're good and bad at, numbers don't *feel* like much as a player, especially small ones. They also bring a discussion of math into systems that try to put narrative first. But… you can get the same effects without them!

You can do this through a variety of systems that math out to the same but *feel* different. I'm going to go through a few I thought about now, the math behind them, and why you might use them to evoke different atmospheres at the table.

First up is a simple one many of you are familiar with from DnD: Advantage and Disadvantage. In this case, you'd roll 3d6 and take the highest or lowest. Mathematically, these average to +/- 1.46, means they work pretty well as an alternative for +/- 1 or 2!

The specifics of the curve are slightly different, since you still get the same range of numbers as +0, but we only care about bands, so that's ok! And as a player, it feels pretty meaningful to roll an extra die and see an extra number, not to mention the change in tactile feel!

Next one is a similar concept but with a different feel. Instead of rolling an extra die, what if you reroll the lowest or the highest? Well, mathematically, if you're always rerolling lowest that's on average a +1 (.97 technically), and a -1 on reroll highest.

And how does it feel? Well, if you're rerolling the highest die, you get the crushing feeling of seeing what could have been a 6 become a 1, or the victory as you roll another 6! And, even better, if you're always rerolling the highest, your double 1s could become a 7!

Now, the reverse is true for rerolling lowest if you get a natural 12, so you probably want to offload that choice into your players hand, which has the added bonus of giving them control of their fate.

(For the curious, rerolling only under 4 averages to + 1.35 to your roll).

What about something uniquely PbtA? What if instead of affecting the dice at all, you shift your success band up and down, so a miss becomes a partial and a partial becomes a full, or vice versa. This one is mathematically weird, but I'm gonna break it down.

First up, what you're doing here is shifting your probability bands, so if you're shifting up, your old chance to miss becomes your partial success chance, and your old chance to hit becomes your full success chance! That's all it is. Weirdly enough, this is approximately +/- 2.

The big difference is when rolling with a shifted success band, you completely eliminate a result category. I cannot stress enough how powerful this is. As a player, knowing you have that safety net and can't fail the roll makes you feel competent and that the narrative is yours.

On the flip side, knowing that you can't fully succeed, and that your chance of even a partial hit is incredibly slim, really amps up the tension. This should be using sparingly if at all, but in a horror game could work great for a climactic or deadly moment!

So now that you have these tools, why would you use them? Well, PbtA is meant to be about the narrative conversation, so shifting the roll bonus away from numbers to "does it make narrative sense for me to have advantage here" can help frame that focus mechanically.

Other modifiers like shifting bands can be used to make a situation feel assured or daunting. If there's no chance of failure in the narrative but perhaps of complication, then allow the player to roll and shift the success band to see what happens!

And these are just 3 methods I could think of! And I haven't even gotten into how you can interact them with other PbtA mechanics. (For example, using the roll +questions from earlier, 0 yeses could be disadvantage, 1 yes could be neutral, and 2 yeses could be advantage).

And chances are, y'all can think of more. So here's my offer: If you have a specific PbtA modifier you want to try out but are scared of the math, I will help, if you let me share it so that people can learn and be inspired by it (you could also pay me to do this if you’d like).

For those who want to see how I did my math, here’s the link to the excel sheet I used:


I'm also willing to answer questions about my math or how to approach it in this thread.

Go make good better games, and don't be scared of math! It won't bite...drive.google.com/open?id=1vNqbj…

Someone suggested using different die sizes, so I did some quick d8 math:

https://twitter.com/ammourazz/status/1161084769565888512?s=21

I'm gonna pull a @SimuLiu and @ some people whose design opinions I respect to see what y'all think about this (my brains scrambled so I may miss some):
@DungeonCommandr @_Mngwa_ @bleongambetta @LulaVampiro @trumonz @gshowitt