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IMO, the concept that's at the core at almost any mechanics or dice math conversation in one of swinginess. Even when it's not the topic being directly discussed, it informs our opinions and discussions.
So I wanna break down the concept of swinginess.
#TableTopChopShop
So I wanna break down the concept of swinginess.
#TableTopChopShop
Here's a quick roadmap for the thread:
Part 1: What is swinginess
Part 2: Basic probabilities of standard die models
Part 3: Complex tools and tricks
Part 4: Getting creative with 'em
In each part I'll break down the math basics, as well as the feel the swinginess brings.
Part 1: What is swinginess
Part 2: Basic probabilities of standard die models
Part 3: Complex tools and tricks
Part 4: Getting creative with 'em
In each part I'll break down the math basics, as well as the feel the swinginess brings.
Now, there's actually a part 5 to this thread:
How does swinginess affect your narrative on the thematic level. I will not be covering that here, but instead laying the groundwork to understand that discussion.
Luckily, I'm not alone writing this thread, for you see...
How does swinginess affect your narrative on the thematic level. I will not be covering that here, but instead laying the groundwork to understand that discussion.
Luckily, I'm not alone writing this thread, for you see...
This thread is a collaboration! A duet proposed by the phenomenal @DichotomusPrime who approached me with the idea and will be taking over to walk you through his segment after you're done here. That's fucking rad and his words are well worth reading.
Alright, Let's get into it.
Alright, Let's get into it.
Part1:
So what actually *is* swinginess. Based on the red lines grammarly keeps giving me it's not a standardly defined term.
So for the purposes of this thread, here's the meaning I'll use:
Swinginess is a measure of how much swing a mechanic introduces to the game.
So what actually *is* swinginess. Based on the red lines grammarly keeps giving me it's not a standardly defined term.
So for the purposes of this thread, here's the meaning I'll use:
Swinginess is a measure of how much swing a mechanic introduces to the game.
Now ok, I cheated a little because swing isn't fully defined in this context either, but swing essentially is a measure of consistency vs chance.
Something important to note about this definition is that it's entirely neutral; it places no inherent value on swing.
Something important to note about this definition is that it's entirely neutral; it places no inherent value on swing.
And that's a really important framework to this discussion. I'm not here to make a value judgement about swing, rather discuss how different mechanics facilitate or hamper different experiences of swinginess.
Making an abstract value judgement about it is actually impossible imo
Making an abstract value judgement about it is actually impossible imo
especially in a void. Talking about how different feels and experiences of swinginess supplement your game or narrative, however, is an entirely different and totally worthwhile discussion.
Which is why Vince is leading you through that portion right after!
Which is why Vince is leading you through that portion right after!
Part2:
Alright so let's go through the standard polyhedrals we all know and love. That's the scale of dice that goes as follows:
d4, d6, d8, d10, d12, d20, d100 (or d%)
This standard set of dice is used by a lot of games. The other most common randomizer is a deck of cards.
Alright so let's go through the standard polyhedrals we all know and love. That's the scale of dice that goes as follows:
d4, d6, d8, d10, d12, d20, d100 (or d%)
This standard set of dice is used by a lot of games. The other most common randomizer is a deck of cards.
A randomizer, of course, being the thing that introduces chance to your game, and thus a degree of swinginess. Now, I've talked before about the d20 and d100, notable for their swingy feel. I'm gonna restate basics, but you can find that deep dive here: https://twitter.com/ammourazz/status/1188164194631409664?s=20
Going through that standard list, here is the chance of getting a specific number on any of those dice:
A d4: 25%
A d6: 16.66%
A d10: 10%
A d12: 8.333%
A d20: 5%
A d100: 1% (Hence the name d%)
Looking at that, we can notice that some of these are a lot prettier than others
A d4: 25%
A d6: 16.66%
A d10: 10%
A d12: 8.333%
A d20: 5%
A d100: 1% (Hence the name d%)
Looking at that, we can notice that some of these are a lot prettier than others
D6's, despite being super common, are really annoying to do math with, cause no-one wants to keep adding 16.66%.
Luckily, we have an intuitive feel for the d6 because of its cultural prevelance. Meanwhile, a d12 doesn't share that level of benefit, and can be even more obscure.
Luckily, we have an intuitive feel for the d6 because of its cultural prevelance. Meanwhile, a d12 doesn't share that level of benefit, and can be even more obscure.
The reason I mention that is because understanding the math affects how we feel about the swinginess imo. It gives us a level of control when we make decisions whether to roll the die, because we can prepare for the result, while also amplifying our understanding of its swing.
And how much we know about the swing in question affects how we feel about it. The more cognisant or in control we feel affects how we receive it in different ways. Each person and each game can play with that feeling, but knowledge affects how we process it.
Now, there's a couple things to note here:
First, the bigger the die the bigger the range. The fact that you can roll either a 1 or a 20 on a d20 means the range of results you can receive varies so widely it's almost impossible to be consistent. For example, if you have a +10..
First, the bigger the die the bigger the range. The fact that you can roll either a 1 or a 20 on a d20 means the range of results you can receive varies so widely it's almost impossible to be consistent. For example, if you have a +10..
You can still go as low as an 11 on your roll, whereas someone with even a -5 could roll better than you.
This is not a bad thing, per se, but it's a really specific thing. It creates a feel where sometimes what you're good at just does not matter, and luck takes over instead.
This is not a bad thing, per se, but it's a really specific thing. It creates a feel where sometimes what you're good at just does not matter, and luck takes over instead.
That can be frustrating if you're that person with the +10, or super exhilarating if you're the person with the -5 who pulls something off against all odds.
There's another thing to note here: the bigger the die, the less the modifier affects the results and swinginess.
There's another thing to note here: the bigger the die, the less the modifier affects the results and swinginess.
You notice here that a +10 and a -5 can still technically be competitive with the right rolls, whereas with a d12 and lower, that would be entirely out of the question. The smaller range band on the die makes the results tighter together, and means the modifiers matter more.
That's the other major factor that affects feel. Having your modifier have a higher or lesser impact changes how you feel about the roll. Lower swing and higher modifiers gives you a competent feel, whereas higher swing means every roll is a gamble, for better or for worse.
The other common randomizer is cards, which have a little funkier math because of there being a set number in the deck. But if you shuffle after you draw, a deck of cards essentially has 13 different outcomes, replicated across 4 suits. In that sense, you *can*...
use it as a d13, but doing unique things with the suits and ability to say cards are used is part of what creates a unique feel to decks. It creates a dynamic experience of swinginess, where at the start anything can happen, but at a certain point, you can guess what's likely!
And those are kind of the basics of swinginess. A lot of folks who have played games have an intuitive understanding of the concept but it's worth explicitly highlighting before I move into the more nuanced discussion. If you're still uncertain, grab a d6 and a d20 and keep...
rolling them a bunch of times. If you don't have or can't utilize physical dice, find an online software that's accessible to you, like discord bots or roller websites. A quick search reveals this one is recommended by folks for accessibility purposes! https://dicelog.com/dice
As you roll the dice and exam the results, watch the range of the rolls, and notice how your d6 will hit the same results quite often, whereas you could roll a d20 over 50 times and never see one of the faces with pretty decent probability.
That's swinginess 101!
That's swinginess 101!
Part 3:
So now that we've seen the groundwork, let's talk about some of the more common complex tricks that the most common systems use to get around swinginess.
The first is adding multiple dice, and introducing everyone's favourite bell curve. PbtA's 2d6 model is one example!
So now that we've seen the groundwork, let's talk about some of the more common complex tricks that the most common systems use to get around swinginess.
The first is adding multiple dice, and introducing everyone's favourite bell curve. PbtA's 2d6 model is one example!
Powered by the Apocalypse, started by Meguey and Vincent Baker's Apocalypse World, makes you roll 2d6 for a check, and divides your results into bands 6-, 7-9, 10+.
This tackles swinginess on a few levels.
First, the bell curve. When you roll multiple dice, your probabilities..
This tackles swinginess on a few levels.
First, the bell curve. When you roll multiple dice, your probabilities..
Are no longer equal for each number. Instead, they lie on a curve that peaks in the middle and thins quickly on the edges. In the case of 2d6, you're just as likely to get a 7 then you are to get either a 12, 11, 3, or 2, combined!
That means your rolls are way more consistent!
That means your rolls are way more consistent!
PbtA also works with swinginess on a second level that I've yet to talk about: The way you interpret results.
PbtA does this in two ways. First, it bands the results into groups, which further affects the probabilities by saying we don't care about specific results. Instead...
PbtA does this in two ways. First, it bands the results into groups, which further affects the probabilities by saying we don't care about specific results. Instead...
It focuses on your chance to get a specific group.
Second, PbtA specifically designs its groups around the bell curve, making the most likely category the 7-9 or mixed success area, showing you are most consistently going to get that. For more on that: https://axostories.com/en/2019/09/28/how-math-can-support-fiction-in-pbta-design/
Second, PbtA specifically designs its groups around the bell curve, making the most likely category the 7-9 or mixed success area, showing you are most consistently going to get that. For more on that: https://axostories.com/en/2019/09/28/how-math-can-support-fiction-in-pbta-design/
So let's go through some of the other systems. In the article I linked above I mention advantage, wherein you roll two dice and pick the highest one.
Forged In The Dark uses a d6 pool system where you choose the highest result of your roll that is then interpreted in bands!
Forged In The Dark uses a d6 pool system where you choose the highest result of your roll that is then interpreted in bands!
We see once more the level of controlling swing on an interpretation level, this time saying that 3 or lower is failing, but how does rolling multiple dice affect the math?
It actually creates a sloped graph, where the more dice you add the more likely you can get a high number!
It actually creates a sloped graph, where the more dice you add the more likely you can get a high number!
But its not a straight increase. Going from one to two dice effectively doubles your chances of getting a 6, but going up to 4 dices only triples it from one die, rather than quadruples it.
This is because when adding more dice we have to account for overlap in rolls.
This is because when adding more dice we have to account for overlap in rolls.
What do I mean by that? Well, if you roll 2d6, intuition says that since we have a 1/6 or 16.6% chance on either, we'd get a 2/6 or 33% chance for both.
However, the case where you roll both as 6's is an overlap in the probability, meaning we need to subtract 1/36 from above.
However, the case where you roll both as 6's is an overlap in the probability, meaning we need to subtract 1/36 from above.
This gets us a total of 11/36. Now, another way to look at this is to count all the possibilities where you roll a 6. There are 5 cases where I roll a 6 on either die but not a 6 on the other die. This happens for each die, so overall, 10 outcomes involve only 1 die having a 6.
Additionally, there is one outcome where both dice have a 6 on them, meaning 11 outcomes where we have at least one 6. With two dice, you get the total number of outcomes by multiplying 6 by 6, or 36.
Hence, 11 out of 36 outcomes give us at least one 6.
Hence, 11 out of 36 outcomes give us at least one 6.
As you add more dice, there's obviously more rolls that could have overlaps that we need to subtract and account for. Hence, we get closer to having a 100% chance of rolling at least one 6, but there's always a hypothetical chance, even if I roll 1000d6, of rolling no 6's.
And, to it's credit, FitD explicitly addresses the overlap. If you roll multiple 6's you get an exceptionally great result. That's pretty neat. If you wanna check it out in action, I'll always plug Mutants in the Night by @DungeonCommandr at every chance: https://dungeoncommandr.itch.io/mutants-in-the-night
Alright, final model for today: let's talk about dice pools. Dice pools are fascinating to me and breaking down the specific math of them may be a task for another time, but what I'm talking about are systems that take the idea of rolling more dice and make each one matter.
Some systems have you count how many successes you get against a target number. Some systems have you combine dice in unique ways (kinda like Yahtzee) in order to get unique results. The math might seem complex but its usually just a combination of the concepts I discussed above!
However, dice pools introduce two aspects to the feel:
The first is quantity. The frustration you might feel from rolling 1 die and have it go poorly can be mitigated if you're rolling a bunch at once, cause you'll usually get the bad with the good (unless you're real unlucky).
The first is quantity. The frustration you might feel from rolling 1 die and have it go poorly can be mitigated if you're rolling a bunch at once, cause you'll usually get the bad with the good (unless you're real unlucky).
The second is control. If you're deciding how to use the dice in your pool, you have a bit more power over the results of your swinginess that makes things a little bit more satisfying.
This can be similar to the consistency feel of a bell curve in some cases!
This can be similar to the consistency feel of a bell curve in some cases!
Part 4:
So, now you've got all these tools, here's a secret: You don't have to use them in isolation. You can combine different tools that give the experience and feel of swinginess you want at the table. You could totally do a d20 dice pool system for a high swing system...
So, now you've got all these tools, here's a secret: You don't have to use them in isolation. You can combine different tools that give the experience and feel of swinginess you want at the table. You could totally do a d20 dice pool system for a high swing system...
that gives you a ton of results and thus mitigates some of the uncertainty of the d20, since you no longer are evaluating it in the context of an individual roll.
You can also look at some of the concepts discussed from PbtA and FitD on designing your system to account for swing
You can also look at some of the concepts discussed from PbtA and FitD on designing your system to account for swing
Here's a weird example:
For the Queen by Alex Roberts is a game where you draw a prompt card each round to tell a story. Because of the randomness of drawing from a deck of cards, you can hypothetically have two games with entirely different prompts.
Guess what? That's swing!
For the Queen by Alex Roberts is a game where you draw a prompt card each round to tell a story. Because of the randomness of drawing from a deck of cards, you can hypothetically have two games with entirely different prompts.
Guess what? That's swing!
But I don't think anyone sitting down to play FtQ has ever gone "Wow such a swingy game." And that's because of the feel of the swing. All the results of the prompts are centered and focused around a cohesive feel of play, and even if they're different, they're united.
So on that bombshell, where do you go from here? Well, like I mentioned earlier, the answer is to @DichotomusPrime, who is gonna expand on that last idea on how the different feels of swinginess can support different narratives. I'll link the thread here once its started!
As for me, I hope you got a better understanding of some of the math and models behind different systems of swinginess. It's a conversation worth keeping in mind as you choose the mechanics for your games!
Some additional notes as they occur to me:
There are some other tricks to mess with the swinginess. With dice you can do evens and odds for always a 50/50 shot. With cards you can divide into numbers and faces. You don’t have to use your tools in the straightforward way
There are some other tricks to mess with the swinginess. With dice you can do evens and odds for always a 50/50 shot. With cards you can divide into numbers and faces. You don’t have to use your tools in the straightforward way
Also I should clarify explicitly as was mentioned in this side convo: mathematically, a dice pool of 10 dice and rolling the same die over 10 tries are functionally the same, but the time factor creates different feels to how we perceive the swing! https://twitter.com/jacobskellogg/status/1290781988811669505?s=21
