PbtA Mechanics with d10s - improved "ladder"

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.

I’ll explain:

*** 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%

1d10
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%

3d10
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%

5d10
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%

7d10
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%

10d10
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”.

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(On the other hand, if you’re visiting your grandmother and she has no dice handy, taking a deck of playing cards and removing all the face cards would work very well for a PbtA game using this method!)

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Flying Circus does this, though they use 10-, 11-15, and 16+ as their ranges.

That sounds different - 2d10 + adds, right?

That will give you more levels to play with, but more numbers to add, and none of the fun bell curve effects this version enables.

Hm. I could’ve sworn you mentioned something like that, but rereading I can’t find it. My brain is not doing its best work today. =/

As a simple example of the difference, a +2 on a 2d10 scale operates (pretty much) exactly like a +1 does in a 2d6-based PbtA game. That can be useful, but stack them and you risk getting into undesirable places on the bell curve pretty quickly.

Under this version, you can make a version where gaining a +1d or +2d is a fairly achievable thing, and it will make a very dramatic difference for the unskilled/incapable (e.g. reducing your odds of failure by a factor of 2, if you start with 1d), but won’t take your capable characters out of a workable range (the way a +2 would in a 2d6-based PbtA). (For example, even a bonus of +3d only reduces a 7d character’s chances of failure by about 5%.)

It works in reverse for penalties, if your system needs or wants them: competent characters can suck them up, but unskilled characters will really suffer.

These properties allow us to do something different things in design.

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I like this a lot. Two thoughts:

  1. For me, adding dice to a roll–rather than using modifiers–is always more engaging. Not the most critical part of the game, admittedly.

  2. I don’t have a bunch of d10s. However, drawing a bunch of playing cards could be fun. I like that idea.

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You should totally check The Resistance toolbox, which is an open version (and PWYW) of the system behind games like Spire and Heart. Its core is essentially what you’re proposing, but with smaller dice pools.

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I wouldn’t be too surprised if I wasn’t the first person to stumble on this kind of technique (I was really just looking to see where Blades in the Dark and PbtA odds “lined up”).

What is the core mechanism in the games you’re referring to here?

The standard roll is 1d10, +1d10 if you have an appropriate Skill, +1d10 if you have an appropriate Domain (like Themes), +1d10 if you have Mastery of an appropriate Skill, Domain or the situation. So, dice pools will always range between 1-4d10, because traits don’t get ranks, you either have them or not. I like how important each extra D10 is.

Their result chart is also a bit different: 1 is a critical failure (take double stress), 2-5 is failure (take stress), 6-7 is success are a cost (take stress), 8-9 is success (take no stress), and 10 is critical success (inflict +1 stress for each 10).

Sounds like they’re basically building on Blades in the Dark in terms of their resolution, but with far fewer complications. It seems like a wasted opportunity to reduce the odds of the “yes, but” outcome!

I think it might have to do with the other elements in those games. The focus on the Resistances is a big one, which makes the stress dynamics way more impactful here than in many PbtA I’m familiar with.

I’d like to say, though, that your insights are really helpful. I was oversimplifying things by looking at each +1d in Spire as a close match to a +1 in PbtA games. Thanks!

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Indeed - one can’t simply consider a dice mechanic outside of the context of the larger system; there can be reasons to make the odds move in one direction or another. (For example, getting that 4th die requires using a very rare resource, so you really want it to count, far more than each of the previous steps.)

But I do find it curious. For instance, that 4d10 roll, in their system, produces roughly a 75% of a full success. Similar to a +4 in PbtA; that’s quite a dramatic “peak”, with very little variance (rolling at +4 in PbtA isn’t terribly interesting!).

In comparison, Blades in Dark 4d6 roll has odds similar to 2d6+3 in PbtA (but with slightly fewer full successes, around 51%, and slightly fewer misses).

The two methods, of course, have the same chance of a miss, however.

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And if your grandmother is Italian, Italian cards already have 10 cards per suit :slight_smile:

Now, onto a Scopa-based resolution system.

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Thank you ! I have always thought that la scopa was spanish.

This is especially cool, since it’s the “face cards” that correspond to successes! Very quick to see.

I guess you could do this in a regular deck of Poker cards, too:

  • Remove all the 9s, 10s, and Jacks.

Draw a hand of one card per “die”. Play your best card!

  • The Ace is a full success.
  • The Queen and King are both mixed successes.
  • Anything else (non-face cards) is a failure.

(I removed the Jacks and used the Aces so we don’t have to worry about whether male or female face cards are “better”. But you could also make your game treat the Queen and King differently, which could be fun - two different “types” of 7-9 results.)

I’m going through similar considerations for my fantasy PBTA at the moment.

I started off using 2D10, and settled on ranges of 11-15 for a partial hit and 16+ for a strong hit. This very closely matches the usual 2D6 PBTA odds but provides more headroom for modifiers. In practice I’ve found this is not useful, it just leads to modifier inflation. It gives too much headroom.

I’ve re-worked my play materials to use Blades dice instead. Stats range from 0d to 3d for starting characters and a weak hit is a best result of 4-5 while a strong hit is a best result of 6. We’ll be play testing it tonight.

My motivation is because with higher stats and a few modifiers the conventional PBTA dice lead to heavy weighting towards strong hits and crits even at +3. I’m looking for a little bit more headroom on modifiers before the odds tip over too much and it looks like Blades dice do that for me.

Using a pool of D10s is interesting in terms of odds, but I’m not too worried about matching the PBTA 2D6 odds exactly. Pools of D10s worked ok for World of Darkness, but D6s are much more common and should work fine. I’ve run Blades and I like the mechanic so I’ll see how it works out for me.

Nice. That’s basically what I’ve been arguing for here, as well - just increasing the scale doesn’t help change the basic dynamics here.

The Blades system (I’m also fond of d6s!) works nicely, except that the range is really narrow and each die halves (!) your odds of failure. Otherwise, it has all the benefits of the system described here, just with far fewer “steps”.

4d6 in Blades is very similar to 7d10 or 2d6+3. (With slightly lower odds of failure.)

5d6 in Blades is very similar to 10d10 in the system described here.

That’s quite a handful of dice (or maybe I just don’t play a lot of dice pools) but the math is very compelling

Yeah, it can be! Depending on how strong the characters are (most PbtA games I play are perfectly happy with stats up to +2, which is 5d10).

I do only own 6d10 myself, though, so that’s a real concern.

Of course, you can use dice beyond your limit as rerolls, instead - e.g. treat 7d10 as 5d10, but you’re allowed to reroll two of your dice. That’s probably what I would do!

That doesn’t change the math, since only the best result matters (just don’t reroll you best die).

Of course, the card deck is also an option… but these days I feel like most gaming is online, anyway, so you can just use a dice roller.