Violent Resolution – Never Tell Me the Odds Part I

Tuesday , 14, April 2015 6 Comments

Roleplaying combat can be about telling stories through the medium of action and physicality. It can be a pure tactical exercise, driven by achieving the best outcome (say, “crushing your enemies, seeing them driven before you, and hearing the lamentations of their women”) at the least cost. It can also just be fun fantasy wish-fulfillment, where you get to act out the role of your favorite Chop Socky star seen through the lens of a paper avatar.

One thing that is important for all of those things is that both the player and the GM have a reasonable idea of how skillful their character actually is.

In short, and to invert the title of the post: you have to know the odds – even in a basically dramatic system.

Part I of this post will deal with three systems that use “roll vs. a fixed target,” and don’t encourage much active participation on the part of the defender. Part II will discuss the two remaining systems (of the five of which I’ve chosen to focus), which feature active defenses on the part of the target.

What Happened to “Never tell me the odds?”

Ultimately, when it comes time to exercise your right to fight, you need to know how good you are – or at least how good your character thinks he is. Your tactics, not to mention your confidence in the outcome (or in dramatic terms, the tension caused by an unknown result) will probably depend on what you can pull off.

This isn’t just about gaming, either. If you’ve been training in Tae Kwon Leap for twenty years, you’re going to know pretty much what you can do. Whether it’s a quick kick to the knee, a jab to the solar plexus, a (jumping!) boot to the head, or a complicated arm lock and throw, the serious practitioner of applied violence will know what she can and can’t do. If they’re really serious about it and have made an effort (or had effort thrust upon them) to obtain a degree from a branch of the school of hard knocks, they will probably have a fairly good idea of what works and what doesn’t, and what works particularly well for them, and what doesn’t.

But that visceral knowledge of skill isn’t necessarily present when what you have on your paper is Level 7 Thief (D&D), Judo-16 (GURPS), or perhaps Fighting d4 (Savage Worlds). That leaves you reliant on math and a feel for the resolution mechanics.

That’s not always easy.

Beat-Downs, Mechanics Style

How you approach a fight in an RPG depends on many things, but one of those things is a level of appreciation for how skilled you are at fighting relative to your foe. That appreciation will rest to some extent on an understanding of the basic mechanics – usually dice mechanics – in play. This post will look at the mechanics in my five example game systems.

Almost Certain to Succeed

More than once as we look at game mechanics, the concept of “almost certain to succeed” will appear. Somewhat arbitrarily, if a task has a 90% chance of success or better, the player will usually feel pretty confident in attempting the feat. As a result, the 90% break point, as well as the 50% probability point where you will succeed as often as you fail, will be used to look at the influence of mechanics on success.

D&D Fifth Edition

The basic mechanic for how you hit and hurt your foe in Dungeons and Dragons has remained more or less the same through all its editions: Roll a 20-sided die plus bonuses against a target number. If you meet or exceed that total, you hit, and roll some other dice for damage.

This mechanic is common for unarmed and armed melee combat, as well as ranged combat with muscle-powered ranged weapons. In the d20 Modern SRD, the basic concept is the same for shootin’ folks.

The basic die roll is

1d20 + B ≥ Armor Class (or Difficulty Class)

which can also be written as

1d20 ≥ Armor Class (or Difficulty Class) – B (and your Target Number is AC-B).

 Why the pedantic math? Just to emphasize briefly that the basic probability distribution is that of a 20-sided die roll, a uniform distribution where you have a pretty easy grasp of the odds of success. It’s a roll high system, so bigger is better, and your odds of success are 5% * (Target Number -1). So if you have a +5 bonus and your foe is sporting AC 16? Your target number is effectively 11, and you have a 50% chance of success. Easy to understand, with the straightforward linear probability curve shown below.


One of the neat new (to D&D at least, other games may have used it first) mechanics for D&D5 is the concept of the advantaged (or disadvantaged) roll. Basically, roll your die twice, and take the most favorable result if you’re advantaged, and the least favorable of the two if you’re disadvantaged.

DnD Probability

It saves a lot of time and mechanical effort to lump a whole lot of things that could be treated with flat bonuses into one category – advantaged – that basically skews the results to higher values. The amount of skew depends on your target number. With a flat roll, you are almost certain to succeed if your adjusted target number is 3 or lower (for example, 1d20+7 against AC 10). If you have advantage, your adjusted target number can be 7 or higher – someone with advantage with a to-hit roll of 1d20+7 (say a +3 proficiency bonus for level, and +4 from a relevant statistic like STR 18) can now hit AC 14 as frequently as he could normally target AC 10.

The break-even target numbers for a regular roll and an advantaged roll are 11 and 15, respectively . . . but don’t think that it’s always a +4. It’s not. As your target number goes up, the advantaged roll is always better, but gets much closer to the unmodified probability.

How Awesome am I?

This depends mostly on your level, which sets your proficiency bonus (which ranges from +2 at Level 1 to +6 at Level 20), and your attributes, which can contribute a bonus of up to +5 for an attribute (usually STR or DEX) of 20. There are some powers that allow extra bonuses, like a Paladin’s ability to boost hit rolls for a minute using Sacred Weapon by his CHA bonus. That means you will be looking at bonuses from about +2 on the (very) low end, to as high as about +15 – perhaps more with magical items and other boosts. Still, with AC in the 20-22 range still being fairly high-end, you will rarely be almost certain to succeed vs a reasonable opponent (say, medium armor and a DEX bonus for AC 16) unless your target number is 3, which means a huge +13 bonus. That’s a 17th level character with maxed-out stats and a +2 weapon!

That doesn’t much matter, though. D&D combat features wars of attrition in many respects, as the combatants’ ablate each others hit points until they exhaust them, which brings the fighters from “fully functional” to “incapacitated” with a jolt and audible squelch. The key here is “hit more, do more damage, more frequently,” and that’s aided by high level fighter types getting as many as four or five attacks, depending on your level and how you’re armed.

Critical Thinking

Finally, D&D allows for “critical hits,” which double the value of the dice rolled for damage – this includes spells, melee, sneak attacks, whatever. Most people score a critical if they roll a natural 20 on the die roll, but some classes get Feats that allow a critical on 19-20 or even 18-20. So the basic chance for an unusual event is 5% (almost 10% with advantage!), but it can grow to 1 in 10 or even 1 time in 6, which makes a critical unusually usual.

Parry! Dodge! Duck!

In D&D, there’s really no such thing as a defense roll – the best you get is a Saving Throw, and that’s usually against attacks that don’t roll themselves: “The Magic User casts his spell. Save and take half damage, or fail and take full damage,” or the ever popular “Save or Die!”

But in hand-to-hand combat, all defensive actions are subsumed into a combination of Armor Class (“the blow thrown was good enough to be effective and reduce hit points”) or Hit Points – which can represent exhaustion, shock, and defenses as much as bleeding, bruising, and evisceration.

The two options that are present are a defensive dueling feat, which increases your AC (raises your foe’s Target Number), or Dodge, which gives your foes Disadvantage when attacking you.

Savage Worlds

This system also embraces the concept of rolling polyhedral dice, and in this case, it’s taken to a bit of an extreme. Your stats and skills are rated by die size – having a d6 is considered average, d4 is poor, and the highest die type in the Deluxe game is a d12. So an amazingly strong, agile, and skilled fighter might roll Fighting d12 to hit, while an untrained, unskilled NPC might only roll the lowest d4 with an additional -2 for being untrained. The basic target number to hit is the foe’s Parry score (2+half your Fighting die, so a number from 2 to 8) for melee, and 4 for ranged combat – longer ranges subtract from your roll, rather than increasing the target number. If you exceed your target number by 4, it’s called a Raise, and nice things happen. Note this means if you’re striking untrained (d4-2), you’re effectively rolling 1d4 against a target that will range from 4 to 10 depending on your foe.

SW Basic Prob Plot

Two things are key about success rolls in Savage worlds. One is that maximum rolls on dice “explode,” referred to as an Ace in the game, which means you get to roll them again and add the result. So even a 1d4 roll can (in theory) roll a 20, or even 200, though the probability of that event will be exceedingly low. The other piece is that the probability of success is different for each unique combination of dice. Dealing with d4 through d12, adding from nothing to another d12, results in 20 unique probability curves.

That being said, the basic die types show strong differentiation in probability for that first success level of a 4+. A d4 will only succeed 25% of the time, while the d12 is 75%. Going from d4 to d6 is a big deal.

However, and somewhat surprisingly, perhaps, is that it can be better for basic successes to roll two small dice than it is to roll one large die. The d4+d4 is better than even a d12 until you hit a target number of 5. To get your first Shooting Raise at 8, d4+d4 is basically as good as d10. It also does funny things to the probability curve to roll two exploding dice, as the d4+d4 line on the plot shows.

If one were to make a full plot of all possible probability curves for one or two dice, it shows that – at least to me – it’s doubtful whether anyone could ever know exactly what the probabilities of success might be. The best you can really do is get a feel, generally, that the higher the sum of the maximum die face types, generally the better, though there can be some odd behavior for any given target. Since most targets seem to be low, basic success and even a Raise or two seems likely. Basic success is often 2-6; does one really ever need a success and six Raises? Maybe, maybe.

In fact, if we look at it just that way, looking at the chance of getting a 4, 8, or 12 – a success vs a 4, plus 1 or 2 Raises, you can see that it’s just good to roll two dice. Once you’re fishing for a Raise, the odds of getting one go up about 5% for each +1 to the maximum total. So going from d8 to d8+d4 should increase the chance of you getting that Raise by 20% (exact value is closer to 30%). Two Raises is pretty improbable until you’re rolling a pair of d8s or so.

Complicating this for player characters and important NPCs – Wild Cards in Savage Worlds’ lexicon – is the Wild Die. Wild Cards roll an extra d6 – the Wild Die – and take the better of that die and the die you usually roll on any Trait test (a roll against an attribute or skill). That does odd things to the probability chart in some places.

How Awesome am I?

Include Wild Die Effects

Generally, then, bigger is better. The target numbers for at least basic success are low enough that, including the effects of the Wild Die, even if you’re rolling a d4 you’ll still succeed about 60% of the time. Even with a d12, though, you’re not quite hitting 90%.

That being said, with a d12 (which is really the max of d12 and d6), you’ll get a Raise 50% of the time. A quirk of how the dice explode makes a d6 and d8 (plus Wild Die) equivalent for getting the first raise, so having a d10 in a Trait is probably the entry level for being awesome here.

So only if you’re rolling a d12 plus a Wild Die are you almost certain to succeed. If you ever get the chance to roll more than one die and add them together (like damage rolls), your ability to get multiple Raises goes way up. That’s a strong post-success incentive.

Critical Thinking

One very interesting thing about the exploding dice is that they can be (not should be, can be!) used to simulate events of vanishingly small probability. As an easy example, you can actually stat out a “one in a million” event by setting a target number of 54 on d4, or 80 on d10. Why you would do this, I cannot say, but if you’re rolling d10 to see if a one in a million event occurs, it will if you get a success and 19 Raises.

Savage Worlds is – by self-declaration – a “roll and shout” system, designed for fast and loose play. It has, however, the finest resolution of any of the systems examined here.

You can critically fail, though – if you roll a 1 on both the main die and your Wild Die, the GM gets to do something evil to you. There’s no unique “critical success,” since multiple levels of Raises take care of extraordinary outcomes on the positive side.

Parry! Dodge! Duck!

As with D&D, Savage Worlds represents defenses with an increase in target number. There is Defend, which raises your target number by 2, and Full Defense, which actually allows you to substitute a Fighting roll at +2 for your normal 2+half of Fighting as a target number. So if you have a d8 (normal Parry 6), you roll d8+2. On the average, you’ll increase your defense by 1/2, but with the exploding dice, defenses can get very high.

Night’s Black Agents

D&D and Savage Worlds both have something in common: rolling polyhedral dice against a target number. D&D uses the d20 for hit resolution, while Savage Worlds uses exploding d4 through d12. Night’s Black Agents, a genre-specific treatment of the GUMSHOE engine, also rolls vs. a fixed target number – but the only die you roll is a single d6, and the target number is either 2 or 3 (for mooks), or 3 or 4 (with Athletics at 8 or higher) for major humans. Target numbers for nasty critters can be arbitrarily high.

The way combat works in NBA is really one of dramatic emphasis. It’s a skill test – roll 1d6 and if you want, you can spend from your pool of Hand-to-Hand, Weapons, or Shooting. Pool spends take some mental adjustment. A high pool (a level of 8 or higher) is typical for the better abilities for a character in NBA, whose premise is “Jason Bourne fighting vampires and their minions.” But even though the odds of hitting a mook with a TN of 3 are 66%, that’s not necessarily very Black Ops, since you can do that with or without training. But you can spend your points and get success – even guaranteed success.

But you can run out pretty fast. At a two-point spend for an automatic success, you’ll exhaust your pool in four blows, and have to refresh somehow. After that, you’re no better than an untrained person when it comes to exchanging blows. Sort of.

Player-Facing Combat

One of the key bits of the rules that also speaks to “I’m awesome” is that against certain kinds of opponents – namely the faceless  mooks and guards that, by definition your Bourne-esque character is mind-bogglingly better than – the combat resolution system changes. Explained in a box on p. 64 of the Night’s Black Agents hardback, the resolution mechanism is simple. Make an appropriate “I’m sneakier than a black bat on a dark knight” skill, but if you fail, you can spend some of your “I’m awesome” general point budget to succeed anyway. Then make a single attack against your foe’s usual target threshold. Thus far, that’t not really that different from the regular mechanics. The difference is that the “effect roll” is more or less bypassed; the mook goes down in as dramatic (or dramatically quiet) way as the player wishes them to. A silenced sniper shot, the knife-thrust to the neck or heart that manages to instantly drop and incapacitate a foe, the single arrow shot that manages to do the same thing. Basically, the staple of every commando movie ever, given mechanical weight. This is, quite explicitly, to keep the drama high and not let a die roll ruin a perfectly good plan.

How Awesome am I?

The real key is not thinking of point spends as ability level – what they represent is screen time. In an action-adventure movie, when you’re spending points, you’re basically swinging the camera your way. You can do that a few times per scene, and if you reach a Haven, you can fully refresh three general abilities. So you can shine more often than others in any given scene, and do that repeatedly during an adventure.

But that’s really it. The mechanics aren’t truly success-based, in the way that the other games are – though of course you are, in fact, rolling for and buying success. They’re drama-based, focused on how often you’re doing something great on camera. Thus the player-facing combat option, which keeps the spotlight squarely on the PCs doing awesome things with little resistance from foes that are merely scenery. Maintaining that perspective, in combination with a firm grasp of the narrative role of your character, is where it’s at for Night’s Black Agents.

Critical Thinking

You can roll a critical in NBA. A natural 6 on 1d6, plus exceeding the target number by 5, gets you double damage. For a target of 3, the only way to secure that is a 2-point spend, so you roll 8 total with a 6 on 1d6.

Parry! Dodge! Duck! Weave!

The game provides several defensive options, all of which boost your hit number. Since the die roll is always 1d6, even a 1-point boost is a significant change in the odds, but if you’re fighting someone with a high point pool, you’re going to run out first.

Finish Him!

All of the games presented here take a fairly straightforward approach to the basic theme of beating the snot out of someone. On your turn, roll against a target number, and if you succeed, you inflict damage. Any skill or ability to fend off blows tends to be wrapped up into an adjusted target number. D&D is explicitly this way, with extra-thick plate armor giving a higher Armor Class. Night’s Black Agents and Savage worlds have variable target numbers based on fighting skill to some extent, but within that range, your target is what it is, subject to player choices to exercise certain defensive options.

Once you get used to this – and if you started in D&D, anything else often feels more than a little odd – the potential lack of agency in having to be a PC-shaped training pell or reactive target fades into the knowledge that your foe just gets to sit there and take it on his turn as well.

Reactive Target

Who’s Ready for Round 2?

Next week, this post will continue, looking at Fate and GURPS. These are a narrative, or fiction-forward system in Fate, and a second-by-second tactics-focused engine in GURPS. Both provide at least the illusion of enhanced player agency in the form of defense rolls.

Or do they?

  • Daniel says:

    I should let you get to GURPS, but I always thought that the “latent” defensive measures of Armor Class seems more natural and reactive to me.

    How many times does the GM simply say “Miss?” Instead, in my games at least, it is always, “Incredible, despite having his back turned, Deathen hears an arrow fly – it whistles past his ear, and he instinctively turns to face his would be assassin.” All an outgrowth of AC – built in.

    Whereas the mechanics of games where every action has an opportunity for counteraction gets bogged down. It has been a long time (and we didn’t do it that much because they were not fun), but I seem to recall that wizard duels in Rolemaster (I think) were extremely boggy precisely because there was too much reaction.

    In a real fight, the offensive strikes tend to involve about .1 second of thinking. The defensive maneuvers are automatic. Now, once you become elite, both offense and defense just sort of flow. I think diceless attempts to hit that. Doesn’t always work, however.

    • Douglas says:

      Daniel: I think this will depend greatly on what the players want. There’s a separate post coming on game mechanics and player agency, and the speed -vs- choices thing features importantly.

      Also, my point in writing this one isn’t ever going to be “and this is why GURPS is awesome.” I’m very familiar with it, it’s a great example of a system that is quite high resolution, point buy, and a few other things that other games don’t do, and has been around for nearly 30 years in various editions. So it’s a good foil for D&D and in some respects hits the other extreme from both that game and some of the more recent narratively focused games.

      In short, I hope to not proselytize, but I won’t hide the fact that it’s my go-to system for many games.

      Except Star Wars. That will always be WEG d6 to me.

  • Dustin says:

    Excellent. I have played dnd as the go to for its simplicity. its good to see some of the new d5 changes in statistical form. I just discovered GURPS this last year. GURPS is really a fantastically different game system in comparison. Fate as well
    they each have a very distinct feel. The others I have no real experience with. I am glad they got you to come and blog here Douglas. Really enjoying the subject. Great graphs.

  • Douglas says:

    Dustin: Thanks for reading and for the feedback. I agree that each game system enables a different focus, and each gaming group will respond differently to the mechanics, often even by genre.

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