When D&D4 came out, that made a lot of people very mad. Which got us some interesting games on the way. A major grievance was the “gami-ness” of combat.

It got us the distinction of

1. Combat As Sport
2. Combat As War

Just to recap the common wisdom and update it. If someone has the original source, please tell. I wasn’t able to find it.

Anyway, D&D4 indeed had a distinct focus compared to 3.x which much less clear in its intended playstyle. This mode got more refined in more recent games like Lancer and further games it inspired like Beacon. In a state of the art Combat as Sport game, combat definitely is the main attraction. When combat starts, we can be real clever with tactics and character abilities and party synergy.

Combat as Sport games like clear and public information. A map of the arena is par for the course. Informational actions might be used to learn the stat values and abilities monsters. The GM typically has an encounter budget to buy the monsters with. There might be different combat scenarios. In our last Beacon game, the PCs fought a Holdout action. Meaning that they had 6 round and in round 6 at most #number_of_PCs enemies were allowed in the designated area. And by the rules the monsters just keep coming.

These encounter specifications are to be communicated at encounter setup. Players have to know them to strategize accordingly. It’s great fun. Why, during such a Holdout, our Chronomancer drew his once-per-mission ability and shuffeled everyone’s initiative in the last round. So the monsters didn’t get to act in time and our heroes just barely won.

While this particular ability is specific to Beacon, character abilities that mess with the action economy – a term invented for this playstyle – are quite common. Leaders might hand attack actions to their allies or allow free movement. Likewise Defenders will have defined abilities to attract enemy fire.

Non-combat parts are much more freeform. Sure we can engage in character play and make a skill check here and there. But these are filler in the best of ways. Free play provides context on why we want to fight those fights.

Now, Combat as War is a different beast. Here combat is rather lethal and best avoided. This – importantly – is often possible. Monsters might be circumvented. Some might be reasoned with. You might flood the dungeon or manufacture other hazards. The fictional terrain is therefore important. The PCs will typically enter an adventure area and have to learn about it. Without knowing features of the place you cannot manufacture hazards. Without knowing other factions in the area you cannot negotiate.

That is great fun too. I fondly remember a group of PCs convincing the magic tree that they were the good guys and the tree needs to defend itself from those other people. Or another group kiting a security golem and finally sicking it on some demons. In this mode the fun is seeing what players can come up with based on established fictions and their own interpolation. My personal favorite here is Brighter Worlds.

Of course, when there’s two options, there is probably more. That is important to remember. Often observations of the type “There are two ways to play” turn into “There are only two ways to play”. That is not a good approach things. Thankfully, I’m late to party, Bankuei made notes about a third approach in 2012.

Combat as Theater. In Combat as Theater, challenge is irrelevant to showboating and drama. This might be a game where there’s really little or not tactical consideration to have, and stacked with no heavy consequences to losing.

I would add that for theater, we might be more interested in emotional outcomes than physical trauma. Possibly there aren’t conventional hit points or wound tracks, as Bankuei notes. We might see declarations of vengeance or love. The villain might try to tempt a hero to the dark side. This mode is thus a contiunation of character play by other means. It’s best when the villains have some kind of personal relation to at least some of the PCs.

Fictional place therewhile is largley perfunctory for this mode. Yes, the show necessarily happens somewhere, but that’s background. The place is not operationalized as a CaS arena or CaW dungeon.

But when there are three, there might be another. And it is quite common. And sadly it’s predictable, boring and best not done. I’m talking about Investigate – Investigate – Showdown. It’s when our heroes stumble upon some strange happenings, they look for clues, they find a trail, and they come about the random warlock in the middle of the ritual. And then everyone rolls initative.

That is not Theater. It’s a just a random warlock, not your nemesis. They might not even monologue properly. It’s definitely not War. We will reach this showdown and we will play it. No circumventing about it. It might be Sport, but often the fighting isn’t that mechanically interesting. And if we were really here for the Sport, we wouldn’t need that extended investgation phase beforehand. Just some frame and motivation and maybe a bit of coloring for the characters and then we could just proceed to clobbering time.

So, what does Daggerheart do?

In Daggerheart, with most any roll, the PCs can either add to their Hope or give the GM a Fear. Those tokens can be saved up. In fact the GM will likely have a sizeable pool at… showdown. So while we investigate that warlock, if we roll good, we get much Hope and the GM gets little Fear.

This feeds into the game’s rather unique initiative system. To recap, the PCs can act in any order they like and continue to do so, until they fail a roll, produce Fear or the GM spends Fear to take a single monster turn instead. After that the GM can spend more fear to use more monsters. So those Fear tokens that have been accumulated over the adventure are monsters’ action budget during showdown.

Daggerheart does like using special environmental features in fights. They aren’t very sportive though. The GM might put a counter visibly on the table. But that doesn’t automatically say what the counter is for. And there isn’t a defined mechanic to get this information. We might negotiate something at the table, but there is no established Search action that will provide those info. It’s primarily a mechanism for suspense.

Character abilities in Daggerheart are colorful, but not so varied on a strategic level. The general strategy is to just burn your resources at showdown. Distance and position do matter for many abilties, but except for pure Theater that might be generally so everywhere: Consider War stories about fireballs in corridors.

So it seems to me, while Daggerheart has some elements of contemporary Sports games, it might rather be the first game that really tries to make Combat as Showdown worthwile.

Or is FTD for Funky Dice Tricks? Or Fancy Dice Tricks? Who knows. I’m talking about when you do not just roll and read teh dice, but mangle the results somehow to get different probabilities and ranges.

RPGS have found a lot of these over the years. I assume you know how to get probabilities for a single fair die.

Of course, this does not make a dice mechanic. For a dice mechanic, like for any other mechanic we need to know when to use it, what parameters we require and what happens after. They can change the feel of mechanic though, so much so, that they are the first thing players might recognize.

Brutal

Named after a weapon property in D&D4. On a certain results, you get a reroll. Repeat until the result is not in the critical numbers anymore. This means that you basically use a non-standard die. The critical values are effectively excised. You can never get it. So if you have a d6/brutal(1), you effectively have a d5+1.

Luck

Similar to Brutal, but you get only one reroll. Halflings do this in D&D, they have d20/luck(1). What does that do to probability? To get a final result of 1, you have to roll 1 twice in a row. So P(1) = 1/20² = 1/400. For any other result, you can either it directly (1/20 = 20/20²) or first roll a 1 and then that result (1/20²). We can add together for 21/400.

For a general formula: The lucky numbers for your dx have 1/x², the normal ones (x+1)/x².

Advantage

Advantage is like having a reroll, but always taking the better result, so you just roll two dice and take the highest. Let’s do this for d6. Our result space is pair of number between 1 and 6. That is 36 (6²) possibilities total. We just have to write down all the possible pairs and divide by 36.

#	Pairs	Formula
1	(1,1)	1/36
2	(1,2), (2,2), (2,1)	3/36
3	(1/3), (2,3), (3,3), (3,2), (3,1)	5/36
4	(1/4), (2,4), (3,4), (4,4), (4,3), (4,2), (4,1)	7/36
5	(1/5), (2,5), (3,5), (4,5), (5,5), (5,4), (5,3), (5,2), (5,1)	9/36
6	(1/6), (2,6), (3,6), (4,6), (5,6), (6,6), (6,5), (6,4), (6,3), (6,2), (6,1)	11/36

As you can see, with 2 dice it goes up by two options every time.

Explosion

A rather common mechanism. It makes a die “bigger” by allowing a reroll on the maximum number and adding the new result to the old. Sometimes the two heighest numbers etc. are used. Let’s look at d6/explode(6). The number 1..5 have P=1/6 as usual. The 6 can never appear. We roll again. Next, P(7)=1/6 * 1/6. We roll a 6 and then a 1. Same for 8..11. The 12, again, cannot happen. We roll again. For P(13) we get 1/6 * 1/6 * 1/6.

Digitifying

This is what we typically do with a d100. We digitify(d10, d10). Games like In Nomine digitify other dice. Thankfully probabilities are simple. Each particular resulting number has a probability 1/(n1 * n2 * … * nx) for a combination of dice with sizes n1 to nx.

Flip-flopping

From Unknown Armies. UA uses a d100, but under certain conditions, you may reorder the digits for a result you like better. So it’s like digitifying but combinations are the same under reorder. Let’s look at that d100. This actually seems to be the place where the term fancy/funky dice tricks originated from.

There are ten combinations, that only appear once. 11, 22, 33, … 99, 00. So P=1/100 for those. Every other combination exists twice, 2/200 = 1/50.

So for (dn,dn), you have n repdigits with P=n². And every other value has P=2/n².

Success counting

Until now we kinda kept to the original dice somehow. With success counting you turn dice into a resulting number by counting which are higher or lower than some difficulty. So if you roll xdy, you transform your expectation from 1..y to 0..x. You can roll anything between no and x successes.

Thankfully, this problem is so common, that Mr. Bernoulli (one of them) has made a nice formula for that. The parameters are

• p: the the probability to get your success on a single die. Say, 1/3 to roll a 5+ on a d6.
• n: The number of dice you roll.
• k: the number of successes you want.

And then you plug it into that formula

That exclamation mark is Factorial.

Sets

This method is used in One Roll Engine games. It is similar to success counting. We want a set of particular width (a pair, a tripple) with a certain height (the number shown by the dice). You can use the Bernoulli formula here as well, possibly doing it several times. Say, we roll nd10. We want a set with width 3 and a height from 8..10. We would use B(1/10, n, 3). This gives us the result for one particular height. Then multiply by 3 for 8,9,10.

Unlike with the success counting, we cannot mix the heights here. So (9,9,9) and (8,8,8) is good, while (8,9,10) is not.

Adding

The most common strategy. We take several dice and add their numbers. Mathematically that is surprisingly complicated, so much in fact that the mathematical word is convolution. So it’s easier to do it by hand. Write down all the combinations that add to a certain number, count the combinations and divide by x² for dx.

The number of combinations will rise until the middle of your result space. So on 2d6 the 2 has one combination (1,1). Likewise the 12 is only (6,6), while there are six combination that add to 7.

Combinations

Of course, many games actually combine these strategies for more complex ones.

• 7th Sea has you roll nd10, keep the highest k and add their result.
• Shadowrun 3- uses success counting on nd6 and each die may explode to hit a difficulty beyond 6.
• Exalted/Scion uses success counting on d10, but 10s count as too successes. (In classic WoD a 1 instead substracts one success. Don’t do that.)
• Legends of the Wulin digitifies the width and height of sets in a roll with d10s.
• The Silhouette System of Tribe 8 uses yet another thing. Roll nd6. Return the highest number. If you roll more than one 6s, for every 6 after the first you get +1. So if you have two 6es in your roll, the result is 7.