Cairn-ish Content: Odd Math, Part 4

Well, I've had the data ready and just needed to whip up the blog post... last week? I don't know. Time flies. But then my favorite board game publisher dropped a playtest kit for an expansion to one of my favorite games. I've been... uh... distracted. (If you like board games and you like flavorful fantasy role playing games, you might just like Oath, too!) And then I realized I wanted more data than I had gathered, so I had to refactor and rerun my simulations! And then I realized I had a critical bug in my refactored code, so I had to fix that and rerun my simulations again. Slow and steady, friends.

Today is all about Ganging Up. 

After some script tweaks, I can now simulate an arbitrary number of player characters vs. an arbitrary stat block. (If you want to play with that, check out the code here.)

NOTE: I'm not going to code up anything for multiple v. multiple opponents, and here's why: A multiple vs. multiple scenario quickly devolves into a series of 1v1s with maybe a 1v2 in there, or a few. If the enemies outnumber you, all I can tell you is I hope you've got a bomb or something, because you should just not do that otherwise. Get of there, you're not going to win.

Ganging Up

In games like Cairn, multiple attackers each roll their attack die, and the largest result is kept. I could rave about why I think this is good design, but we're here to talk about the math. Long story short, if you can gang up, it's a big deal!

Remember, here's our stack up for 1v1:

Ok, so let's line up what happens when we add more players. For simplicity, we'll start with just 2 players:

Let's start with that left table:

• In an even matchup, a 2v1 becomes a near certain victory. This makes sense.
• 2v1 lets you comfortably punch up one tier.
• Armor continues to be a major factor. Full armor, we've noted, is like bumping up a tier, and 2v1 appears more or less additive in that regard: now you can punch up 2 tiers.
• The stronger you and your teammate are, the more you gain from ganging up! Very intuitive; you can each soak a lot more damage. Our Sturdy attackers can punch about 2 tiers up by working together. The Average guys can do it too with just one point of Armor.

Ok, but what's the second table? Well, this is the average number of deaths (like... dead dead. 0 STR dead) that your win will cost you. It's not terribly interesting yet, because for the most part it matches pretty well with the table on the left; if your odds of winning are especially high, the average number of deaths to "buy" that win are pretty low. Usually. The next table is more interesting.

One more note on this before we move on: this table also tells you how good dual-wielding is, since the rules are the same. So enjoy that!

Let's look at 3 players:

Three attackers is of course, even better. The bump isn't as good as you got from going to two attackers, but it's still nothing to sneeze at. The weak attackers can now punch up two tiers!... but you'll lose a member of your party. Like, reliably. Even when your team is armored up a bit, one of you is going down.

So, why the diminishing return? Remember, my first post where I talked about those heuristics? The average-rounds-to-STR-damage and the minimum-rounds-to-STR-damage? Well, all ganging up does is push the average closer and closer to the minimum; if you and your allies are poorly equipped there's only so much you can do with a guaranteed 4 damage against someone who's average is 4.5. This is why we see the weakest attackers continuing to fail to overcome the strongest attackers, even with numbers.

Let's look at four and five players (and we'll regroup after that to draw final conclusions):

More players continue to increase your odds, of course. The most interesting thing I can say about it is that the Average tier can become wildly effective by ganging up; yet the Weak tier can only gain so much. Higher "level" opponents with armor are just kind of insurmountable. And that makes sense of course, because d4's suck against armor. So: if your group has a bit of armor and non-trivial weapons, you can probably get quite a bit out of ganging up. (Remember, we established in a prior post that armor and weapons are the greatest contributors to success, so when we see that the Average tier sans armor is a lot more effective than the Weak tier, we can first and foremost attribute that to the increased weapon, then the extra HP, and trailing weakly behind is the extra STR.)

However. 

Once again, it's useful to recognize what your "wins" cost you in these matchups. Those Weak players may be able to punch way above their weight class, but it comes with a high likelihood of casualties. And there's an interesting detail I don't want you to miss: a lot of the values on the right hand tables go up with more players. I think the reason for this is simple: you have more bodies to lose. More players are just more meat shields. So, while the increase is small, just recognize that ganging up still comes with a risk; a "smart" enemy isn't going to spread their hits around if they don't have to, and that means the one they're focusing their punishment on is almost as bad off as the one on one matchup.

Detachments

Since ganging up is so impactful, I wanted to make sure and check how it pans out against a Detachment.

Remember that this is how a single player fares against a Detachment with varying stats:

It's very very bad for the player.

To keep this shorter, I'm just going to show you how a party of three or five does by comparison:

The gains here are not trivial! ...They're just not terribly substantial, either. 

Ok, so maybe I'm being too harsh. This is almost beginning to look like the even matchup chart from way back. With some obvious gaps: very armed Detachments are downright scary. So it's true that if the Detachment is unarmored, it's possible to eventually gain some traction by ganging up.

The moral of the story--with some finality I hope--is that the Detachment tag does what it's meant to do. It takes a stat block and elevates it substantially, and considering that most "official" Detachments in the Bestiary have pretty decent stats, they remain serious threats that are probably better avoided.

But! Even if they're not, even if you get creative forming "detachments" from weaker beings, they can still become quite threatening.

Outro

Well, this was fun! Once more, you can find my code here, and the data I gathered (in various stages of order and disarray) here. It should be up to date. Unless someone finds a serious mistake in there somewhere, I think it's time I got back to focusing on dungeon rooms! (I've been sitting on a bunch of draft rooms and bonus ideas and I just need to do the inking and layout!)