Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Monday, February 22, 2016

D&D 5e: Planning for Out of the Abyss

While the group I DM for is still working its way through Tyranny of Dragons, I've had my eye on Out of the Abyss since it was released, and received my own copy at Christmas. I've started reading through it, thinking about how to prepare it for play, and thought I'd share some of my thoughts on modifications and adjustments (as well as simple execution tips).


***SPOILERS DEFINITELY AHEAD***

You really don't want to read any further if you're going to be playing in an Out of the Abyss campaign.

Even when other bloggers and commentators had begun to discuss it, I knew Out of the Abyss would be handled a bit differently--that even more than Tyranny, it would be testing (at least my!) DM skills. This was only confirmed further when I read Power Score's review/read-through of the adventure path. I highly recommend reading Power Score's read-through on this. It might take a while, but it's worth it. At least read through the first few chapters. (Don't worry, I'll wait.)

All set? Okay.

Power Score's read-through brought a few things to my attention that I saw more clearly in my own read-through:
  1. The adventure relies on a lot of traveling. How that traveling is handled will determine a great deal of the success of the adventure as a gaming experience.
  2. The layout of the book is not linear. How a DM navigates the book and what is or is not at his/her finger tips at any given time will dictate how cleanly a DM can cleave to the "as written" adventure.
  3. The ability to prep random encounters or travel encounters ahead of time is not clear. The sandbox nature of the adventure, along with the sliders of travel speed, party size, party composition, and "getting lost," all factor into how a potential path comes together. To put it in traditional terms, this adventure has a ton of moving parts.
Traditionally, a set of random encounters can be readily generated ahead of time by simply plotting out the PCs' course and rolling out where the encounters will be along the route. My gut instinct was to do this, and it looked something like this:

Day 1: Travel: No encounter
Day 1: End-of-Day Camp: No encounter
Day 2: Travel: Terrain encounter
Day 2: End-of-Day Camp: No encounter
Day 3: Travel: Terrain and Creature encounter
Day 3: End-of-Day Camp: No encounter

...and so on and so forth.

Unfortunately, this kind of prep work doesn't take into account what happens if the party gets lost, and doesn't take into account different pacing.

At least with regard to the travel in Chapter 2, I chose to combine the "Summarizing Travel" rules and the traditional ahead-of-time-prep.

The key is to stop looking at travel as a function of "days" and to start looking at it as a function of miles. By looking at travel in terms of distance instead of in terms of days, it allows for the party to change speed at will, and still to account for encounters at an appropriate pace.

To the left is what one of those travel maps would look like, represented as a single arcing line of squares.

The two shaded squares represent the starting (upper left) and ending (middle right) points.

As is listed on the sketch, each square represents two miles of travel. (The scale is because the travel speeds are all listed in even numbers.)

"-C-" indicates an encounter that happens when the PCs camp after passing the indicated point. A "-T-" indicates an encounter that happens as the PCs pass the indicated point. I determined these somewhat at random, occasionally even allowing a camp encounter to be a terrain one (having the PCs reach a cool terrain feature at the end of their "day" of travel).

A single page (like this) can sketch out the encounters the PCs would encounter across hundreds of miles in a compact, easy to generate way. I think this particular page took less than 15 minutes to generate, and would probably take my players at least one full session to get through. I made a second page like it to track the number of hours the PCs may spend while lost, and the additional encounters they might run into while not making progress toward their destination.

One other change I made is in the frequency of encounters. Chapter 2's summarizing rules ask for 1d6+1 days between encounters. Since these encounters don't always involve more than a short narration and many don't involve a real challenge--let alone combat--I thought this seemed a bit sparse. My first rolls indicated a journey of a hundred miles with only three encounters and no combat encounters. (For those of you following along at home, the trip from Velkynvelve to Sloopbludop only had a single non-combat, non-challenge encounter.)

To remedy this and up the danger level (something my players felt was lacking in my running of the Tyranny of Dragons arc), I decided to alter the frequency rolls. First, I had to convert "1d6+1" days into miles. My conversion is this: 1 day = 6 miles. Second, I lost the "+1", making an encounter each 1d6 (x6) miles. If the encounter I rolled was not a challenge for the players (for example, a non-combat encounter that didn't increase the drow pursuit), then the next time I rolled, it would be 1d6-1. If I got another non-challenge encounter, it would become 1d6-2 in the next case. When I rolled a zero or a negative number, I employed an absolute floor of 4 miles between encounters.

I haven't had a chance to run this yet, so it's possible that this will be too deadly, but I think this is an appropriate modification.

Happy prepping!

Thursday, August 13, 2015

D&D 5e: Skill Checks, Success, and Statistics


As someone who has run D&D games (of the latest three editions) on and off for the last fifteen years or so, I have gotten into a pretty standard rhythm and take a lot for granted. As I discussed elsewhere, I have finally gotten the chance to play a character in a "normal" campaign (not a one-off, not a total homebrew) and I am very grateful to my new DM for letting me sit on "the other side of the table."

As a result of my new perspective, I've realized that one thing I always took for granted is skill check timing. The pace of a game's skill checks is critical to how certain skills, abilities, and even role-playing strategies are understood, utilized, and effected.

For example, consider how often you (as a DM) or your DM asks for:
  • Stealth checks
  • Perception checks
  • Persuasion checks
  • Deception checks
 Let's take Stealth as our exemplar.
  • If the check is asked for once per "stealth session," a good roll allows a skilled Rogue to go through an entire castle worth of bad guys undetected.
  • If the check is asked for a few times per "stealth session," a good roll allows a skilled Rogue to get in the door--but doesn't quite guarantee success. [As I'll discuss below, theoretically, a bad roll could be mitigated by a second or third check, given the right circumstance.]
  • If the check is asked for multiple times per round, a good roll means little--the chance of failure goes up as the number of rolls increases.
This model, I feel, bears out in all of the above skills.
  • The key is,  the more rolls a PC has to make in a (certain kind of) skill, the greater the chance for failure in the endeavor.  
  • Similarly, and just as important, if only one opportunity for success is offered, the chance for failure feels greater.  
  • And lastly, a limited/low number of rolls where a failure can be mitigated by a few successes provides (statistically and, I hope, satisfyingly) the greatest chance of success for PCs. 
My point is, I believe there's a sweet spot between a single skill check and an ever-increasing number of skill checks that ultimately provides the greatest chance at general skill success. (Note: that doesn't mean the DM should always be searching for that sweet spot; it is possible that the chance for success should only be offered in a single check, or that multiple checks should be required. It depends upon the situation.)

For the skeptics, let's try some math to back up my assertions. Using our above example, assume a low-level Rogue has a +4 in Stealth and a +2 proficiency bonus for a total of +6. She wants to sneak into a fort, at night, past two guards who are reasonably alert. There are plenty of places for cover, but it's a fifty-foot trip past the guards and through the doorway at a distance behind them. Seventy-five feet if you want to really take a wide arc.

The DM calls for one stealth check to go the whole way, though it will take about three rounds for the Rogue to traverse the distance (depending on how speedy she is and how slowly she's going). The guards roll (or the DC is) a 15. With a +6, she needs a 9 or better, meaning a 55% success chance. Not great, but not terrible either considering how low a level she is and the difficulty of the DC.

Now, what if the DM calls for a check twice a round for all three rounds? That's a total of six checks, and any one failure among them alerts the guards. The probability of making the check successfully all six times drops to 2.7%! That's unreal. Even if the DM only calls for three checks, assuming one failure fails the batch, the chance for success falls to 30%.

But, what if we add in a safety net?

What if we make it so that a failure can be mitigated by other successes, but keep the three checks? In this case, the math is easier if we look at the odds of two failures happening over three checks and then reverse it. In fact, we can look at our old 30% from our last experiment; it's the same as the failure rate in this one. That means we increase the odds of success from 30% (when you must succeed at all three) to 70% (when you must succeed at only 2 of the 3).

Such a simple change, but it makes a huge difference.

 In other words, a DM can actually increase the success rate of a player's skill checks by adding additional checks provided those additions are offset by a simple one-failure-is-mitigated safety net.

I had stumbled onto this idea intuitively, but only when I saw how another DM was pacing his checks did I realize that I could math my way to a better understanding. Again, I don't endorse using this mechanic all of the time, but the DMs out there can use this information to be mindful of the effects of asking for multiple skill checks. The DCs/opposing-checks are designed (in most cases) to be one-offs, and the more checks you throw the worse the odds are for the PCs. On the other hand, building in the possibility of an "acceptable failure" is a way to increase the odds.

In either case, the key to successfully using this methodology is to generally not let the PCs know what the DC is (when possible) so that you can decide in media res if this particular skill check sequence should have a fail-safe.

Hope this idea is somewhat enlightening! Happy gaming.