I was fooling around with dice and math recently, comparing Blades in the Dark to the standard PbtA 2d6 roll, and I found a really neat spot where they line up.
If you use something like Blades in the Dark dice pools with ten-sided dice, you get very similar probabilities to 2d6+adds rolls, but with more room for differentiation in the “sweet spot” of +1 to +3 stats.
This seems like a natural fit for PbtA design: you get slightly less granularity in the “low end” of the scale, but a bit more in the “sweet spot”, where most PCs live.
Of course, you need to have d10s on hand, which may limit its utility for some - certainly, they are not as easy to find as 2d6.
*** The Proposed Mechanic ***
Roll a pool of d10’s. Look at your highest result.
On a 7 or lower, it’s a failure.
On an 8 or 9, it’s a partial success.
On a 10, it’s a full success.
(Optionally, additional 10’s are some kind of critical result - they will be rare!)
To match PbtA odds, we’re rolling from 1d to 7d, for seven discrete steps, in the usual scale of the game. However, since additional dice give diminishing returns, we can continue to 8d or more, as desired, without ever leaving the desired range. It scales nicely up to about 10d, which happens to match a +4 almost perfectly.
This means that PbtA’s -2 to +4 range (seven discrete steps) converts to a 1d to 10d range (ten discrete steps), but with all the granularity at the “top end”, where “character competence” lives.
If you’re designing a PbtA game where you want incremental character improvement (granted, it’s not the most interesting or fulfilling part of most PbtA games, but there may be a place for more small-steps character development in a particular design), you now have - for example - the equivalent of three separate steps between +3 and +4.
Let’s look in more detail:
*** Comparing Odds ***
The odds are very similar at a few places.
For example, 1d is quite similar to rolling a -2 stat, but with improved odds of a 10+.
(I’m rounding off the odds here.)
2d6 - 2
miss - 72%
7-9 - 25%
10+ - 3%
miss - 70%
8-9 - 20%
10 - 10%
I’d argue that this is a more “interesting” distribution, as well, with its increased odds of a 10+/full success.
Now, we have reduced definition through what would be the -1 to +1 zone: there are only two steps here, 2d and 3d (instead of PbtA’s three steps: -1, 0, and +1).
Rolling 2d is pretty similar to rolling a straight 2d6, no adds (like a +0 stat), but with slightly more misses and full successes and fewer partial successes (~10% fewer). (Personally, I like the volatility here: almost 50% chance of a miss is worse than 2d6+0, but not as punishing as 2d6-1, but our odds of a 10+ are 19%, more than either. It’s very similar to rolling a single die in Blades in the Dark - tense, and the odds are against you, but there are lots of opportunity for success, as well.)
Rolling three dice turns out to be quite similar to rolling at +1:
2d6 + 1
miss - 28%
7-9 - 44%
10+ - 28%
miss - 34%
8-9 - 39%
10 - 27%
This is a really good “baseline” for PbtA rolls; if you’re using this mechanic, I’d advise 3d as the baseline or default roll - just a little worse than a +1 is perfect for most PbtA designs, or a for an average starting stat.
4d is similar, but just as 3d is like a +1 but very slightly worse, 4d is like a +1 but very slightly better. We effectively have two different “+1”-like rolls available to us, at 3d and 4d. (4d’s distribution is almost the same as 3d’s, but reverse the odds of a miss and a full success.)
From here, things get interesting, though, as in the 4d to 8d range, our partial successes always stay in the 40%-ish range (from 38% to 42%). This tends to be ideal for PbtA, and the range where we tend to play (for most characters and abilities).
While with 2d6, our next step up - (2d6 + 2) - would be just one step forward, with d10s we get a match two steps further, at 5d, and here the match is within 1%!
2d6 + 2
miss - 17%
7-9 - 42%
10+ - 42%
miss - 17%
8-9 - 42%
10 - 41%
Then, in PbtA, one more point of improvement would take us to +3. Here, however, with d10s we have room for two more steps - 6d and 7d.
7d turns out to be almost identical to rolling 2d6+3 (with, arguably, a slightly more interesting distribution).
2d6 + 3
miss - 8%
7-9 - 33%
10+ - 58%
miss - 8%
8-9 - 40%
10 - 52%
At this point is where PbtA tends to top out, although some games like to give the opportunity for occasional +4 stats. +4 is so unlikely to miss, however, that it’s a rare game where it’s desirable to ever roll at +4.
With d10 pools, though, we now have three more steps available to us before we hit that point.
Rolling at +4 in PbtA is almost exactly like rolling 10d with this method (with, arguably, a slightly more interesting distribution, again):
2d6 + 4
miss - 3%
7-9 - 25%
10+ - 72%
miss - 3%
8-9 - 32%
10 - 65%
Having three extra “steps” as you move from the equivalent of a +3 (where characters should probably top out) to the equivalent of a +4 (for occasional rolls where you’ve really milked all available advantages) could be good for games where slight, incremental improvement is desirable (you want players to keep chasing those XPs), or you want to be able to pile up bonuses (since each additional die offers diminishing returns), so I think it offers some interesting possibilities for designers.
I’ll leave this here, in case it inspires anyone with something useful.
The universal appeal of 2d6 is hard to beat, but this requires no math (quicker read of the roll) and could be useful for designs where playing with bonuses, skills, or advantages in the +1 to +4 range is a focus of the game. Instead having only three steps in that range, you now have six or seven, and you can design mechanics which add together dice pools with less fear of “bottoming out”.