You might say I’m a bit of a TTRPG fan.

For those of you who don’t know what  that is: TableTop Role-Playing Game. You might have even watched  me play them on the internet, like TitansGrave or Mentopolis.

And maybe that helped inspire you to get a group of friends together and  dive into your own adventure. I mean, it’s okay if your inspiration  was Stranger Things or Baldur’s Gate 3. I’m not disappointed.

That’s fine! Whether you’re playing Dungeons  and Dragons or one of the other gajillion games out there, there’s a good  chance your campaign failed miserably. And no, you didn’t mess up by having a party made entirely of chaotic neutral rogues.

You messed up by having too  many people in that party, because all those people can’t find  a time when everyone can gather. It’s the same problem you may have had  when trying to schedule a work meeting with a bunch of people or picking a  restaurant that appeals to everyone. Once your group gets to a certain size, good luck.

But that’s not just life experience talking here. Scientists have done the math. And they have identified the exact  number of people that will probably sink your DnD campaign and also  everything else you’re trying to plan. [♪ INTRO] So this whole thing actually got started  when a trio of physicists got fed up with all the scheduling polls they were  filling out, and they decided to calculate how likely it was  that those polls would fail, and there’d be no time that everyone could meet.

Scheduling a meeting is perfectly  suited to a branch of mathematics called combinatorics, which deals with counting. And your odds of getting that  meeting scheduled successfully depend on three things: the  number of people in your group, the number of time slots they  have available to choose from, and the number of those available  time slots that each person rejects. To make the calculations easier,  this research team assumed that each person rejects the same number of time slots, and all time slots are  equally likely to be rejected.

No wiffle-waffling, either. You have to give  either a “yes” or a “no” to each option. And here is the equation they  derived, which calculates the probability that none of the times will  work for literally everyone in the group.

But you don’t need to call up  the nearest knowledge cleric, or beseech the god Oghma to explain it to you. I have got an example ready to go. Let’s plan a hypothetical  Dungeons and Dragons campaign.

We will be meeting once a week, for a few hours. And no, I will not be DM-ing. That’s too much responsibility  and it’s Brennan’s job.

This is my hypothetical so  he’s onboard for this, too. The official Dungeon Master’s Guide  recommends that in addition to the DM, you have a party of three to five adventurers. So let’s recruit three more of my friends, and we’ll plug in a “5” wherever  this equation has the letter “m”.

Now, let’s pick a number to  use for that cursive “l” there: the total blocks of time we have to choose from. Now let’s pretend we’re not  just playing in a fantasy world, but living in one, because none  of us work over the weekend. So Saturdays and Sundays each have three possible blocks: morning,  afternoon, and evening.

And then there are weekdays. Since this campaign is just going to be  for fun, we can’t meet during the work day. Let’s also say that all of  us work standard 9-to-5 jobs and none of us take work home with us.

Again, a fantasy world. And it’s a truth universally acknowledged that no one wants to go anywhere on a Monday evening. That gives us four more blocks, and ten total.

So the cursive “l” in our  fancy equation becomes a “10”. That just leaves “r”: the number of  potential meeting times each person rejects. Now, depending on what “r”  is, we might be guaranteed to find a time that works for everyone.

That will happen when the size of the group,  multiplied by the number of rejections, is less than the total number of  time slots under consideration. So in my hypothetical, if each  person only rejects one time slot, there will be a time that works for everyone. But as soon as each person rejects two time slots, it becomes possible that our DnD  campaign will fail before it even starts.

And by possible, I mean that  we’d have a 0.061% chance of not finding a time that everyone can agree on. But obviously, that rejection  rate is a tad optimistic. We have families and stuff.

So what happens if each of  us is already booked for half of the 10 possible meeting times? If you do the math…we have a  whopping 71% chance of failure! And that chance of failure  changes a lot with each person you add or remove from the group.

For example, if we only have  four people to deal with, we’d have just better than a 50-50 chance  of finding a time everyone can attend. But if we have the maximum recommended  party size, that percent drops to 15. Meanwhile, if those six people  are just a bit pickier…rejecting just one more time slot…then we  only have a 4% chance of succeeding.

And that’s just for scheduling  one session and it’s not even considering the fact that I  want my campaign to be weekly! So really, it’s no wonder so  many TTRPG adventures fall apart, even with so few people involved. But fortunately for anyone who  organizes even larger groups, the numbers do change a lot based on the total number of possible time  slots and how picky people are.

Like, maybe you’ve set aside your  dream of a years-long DnD campaign with your friends, and just need  to schedule a 1-hour work meeting sometime between 9 and 5 o’clock. If everyone is already booked for  half of those 40 hour-long slots, your odds are pretty good of getting five  people in a room, while six is a coin flip. But If your coworkers only have prior  commitments for just 10 hours per week, then you can probably swing a 14-person  meeting without pulling your hair out.

Of course, you can also increase your  odds of success by redefining success. Like, maybe it’s okay if one person can’t meet at the only time that everyone else can meet. If you’re trying to schedule  a weekly DnD get-together, and only one person can’t do, say,  Wednesday evenings because every three weeks they’ve got a writers  group…maybe you could just… not have them there?

And you can just go and create  like an in-universe explanation for why their adventurer  disappears every once in a while. Or maybe instead of diving right into a  campaign that’ll take you years to complete, you test the waters with different adventures that can each be completed in a single session! Or maybe you and your friends can really  live the dream and figure out a way to turn playing TTRPGs into a job.

Don’t ask me to join, though. I’m too busy. [♪ OUTRO]