Taming the Chaos: probability and the heroes

Some time ago, I was discussing critical hits and misses in RPGs with a friend. We talked about how criticals, badly handled, can ruin a game.
He set me on the trail to writing this post - but being the kind of sciencey person I am, I couldn't just spew back out all he'd said. I had to go look for the facts and logic myself - which in turn led me to find other opinions...

To start with, in a survey that I ran on some RPG forums, I found that responders said they liked character skill or player choice to be the most significant part in success or failure, not the dice roll.

On the other hand, in another survey, responders said that they like the extra randomness of critical hits and misses.

So here I'll look at what we can do to marry these two apparently conflicting preferences.

Critically Random

Critical hits and misses are a staple of a great many RPGs. You rolled the biggest number on the die, so you get more than mere success - and the inverse for critical failures.

Players love criticals, because they reward those big rolls, and punish the low rolls - but are they opening up a wealth of excessively random results, where the die result overrides the skill of the character?

Yes, I believe I can show that to be the case.

Critical misses: the more you try the worse you fail
With critical failure rules, whenever you roll the dice to determine your character's success at a task, you run the risk of a critical failure.
The more often you roll, the more likely you are to screw up in this way. This punishes the player characters more than the non-player characters, because the PCs are the focus of the game. You're making all the rolls.
Further, lots of game systems have ways for powerful characters to take more actions during their turn. The more actions you can take, the more you can achieve, meaning that you are generally more effective.
Similarly, some games use dice pools, whereby you roll more dice of the same type to represent your increasing power, and count the number of dice that beat a given target number. It's common in those games to have a critical failure happen when the number of your dice that come up with the minimum result (usually 1) exceed the number that succeed. But it is also common in such games for the success number to be moveable - a routine task might need you to roll a 5, but a difficult task might need a 6, for example.

But both these systems also give you more chances to critically fail, because you're rolling the dice - and taking that risk - more often.
It shouldn't be a consequence of increased power to run a greater risk of catastrophic failure than some unskilled dweeb, should it?

Critical hits: GM loses control
Critical hits give some special result as a reward for a good roll on the dice. Where this can be problematic is that the game's progress can be altered in the extreme by a single random outcome.

For example: In 3rd edition D&D, using only the Players Handbook (let alone the plethora of Splatbooks that add so many options that the creators can't keep track of them), it is possible to create a 1st level (that is, a fresh start up) half-orc barbarian character who can deal 66 damage on a successful critical hit. (Our Strength 20 half-orc is using a Greataxe, is in a berserk frenzy [barbarian Rage], and has rolled maximum damage on a critical hit.)
To put that in context, a routine hit from the same character (no critical, no Rage, rolling average damage) would deal 13 damage. Hell, a maximum damage roll without the critical is 22.

Why's that important? Well, a normal bad guy for this 1st level barbarian is likely to have 10 hit points or so. So the barbarian can kill one of these routinely - whether they get a critical or not. Clearly this is the barbarian's job.
But the heroes aren't supposed to just beat down every encounter they meet. Sometimes - usually for the sake of plot - they need to meet something so overpowering that they ought to run. The Dungeonmasters' Guide even tells us to do this. So an overpowering challenge (challenge rating 6, to use the jargon) that the players are supposed to flee from is likely to have 50 to 80 hit points - a young white dragon, for example, has 76.

With one very lucky hit, the 1st level barbarian can reduce this supposedly overpowering monster to a mere 10 hit points - low enough for the rest of the player party to finish it off with little risk.

Similarly, RoleMaster and its derivatives, (including Middle Earth Role-Paying (MERP) and SpaceMaster, and all), had long tables of critical hit results. Often these were amusing ("arrow pierces both ears; hearing impaired" followed by some extreme damage multiplier for skewering the target's skull) - but ultimately they created the same problem: through random chance, dangerous foes could be destroyed with a single attack.

Conversely, this can easily go the other way: an encounter that was intended to be routine, or even a pushover can explode in the players' faces. That lowly hobgoblin that the mid-level party have cornered stands a non-zero chance of killing one of the player characters in a single hit.

At this point, whether it's the players who are winning big or loosing out, our GM has lost control of the game.

The overpowering encounter has been defeated, or the hero on whom the story-line has been pinned is dead. The game is most likely to grind to a halt while the GM tries to think of a new story line - or they'll be tempted to alter the supposedly overpowering encounter to add another monster to take the dead one's place, or somehow claim that the dead PC lives.

Very unsatisfactory.

What Do We Do About It?

If randomisation can ruin the game, what do we tend to do about it? Anecdotally, it seems, we cheat.

Fudging the rolls
When random rolls go against the story, the GM is tempted to cheat. This special cheating is called "fudging", and most games even explicitly advise the GM to do it.
To me, this ruins the fun. If I know that the GM is fudging to keep PCs alive, to push the story forward, then all sense of risk is lost. I feel like Superman before anyone figured out Kryptonite was bad for my health. As a player, I've quit out of few games over the years where cheating in my favour has kept me alive - and I know other players who feel the same way.

I've also found that GM fudging regarding dice rolls is a significant issue with the wider gamer world. In my survey, I found that about a third of responders volunteered that they considered GM rolls to be subject to doubt, and that they resented or otherwise felt negatively about that. The other two thirds gave no opinion - which considering it wasn't a question I'd asked in the survey, we can't really take as a positive result for GM trust.

Doing away with fudge
If fudging the rolls is a source of dissatisfaction, how can we do away with it?

Rolling in the open:
The GM can of course, roll all the dice in front of the players. That works fine if our game is under control - but if randomisation can have a negative impact on the game, then rolling in the open doesn't solve this. It can even lead GMs to extreme methods, like practising sleight of hand or loaded dice - and no-one in their right mind wants that.

But if we've got our randomisation in a place where all parties are satisfied with its results, then rolling in the open can be engaging and exciting. Players pay more attention when the GM rolls the dice in front of them.
If you adopt this method, you may need to get your players on board with the principle of dramatic irony - the players may end up knowing (or suspecting) things their characters don't know. If the players can see that you've rolled a tiny number on the dice, but announced a massive number as the result, they know the big bonuses you're adding to that roll, and may treat their antagonist with more fear than he would normally command.
Me, I like to cultivate dramatic irony in my games: giving out scenes where the villains discuss their plans, or shadowy figures stalk the player characters. As long as everyone is on board with the separation of player and character knowledge, it can be good fun to play along with the ignorance.

Players roll all the dice:
D&D's Unearthed Arcana supplement for 3rd edition included this variant rule: Let the players roll everything for themselves.

If the GM's dice rolls are suspect, then stop rolling. Instead of the monsters having a dice roll to attack the heroes, the heroes get a defence roll to avoid the monsters' attacks. Rather than the vile vizier trying to lie to the heroes, the heroes try to sense his motives.
Instead of the GM rolling for the NPCs, you assume that the NPCs' actions are always the average of what they might achieve, and let the players do the randomisation.

The great advantage of this is that the players become proactive, leading the action, even when they're defending against a horde of attackers.

Of course, this involves tweaking the rules of the game. It may take some work on the GM's part - but most RPGs give you some idea of what the average results of typical rolls are going to be. You'll just need to work out the rules of thumb for your NPCs and monsters, and apply them.

Again, this method only really works if the randomisation element in your game is sound.

Taming the Chaos

What can we do to keep the game manageable (assuming we're not going to cheat)?

Change the dice: 
If we change from a d20 to a d12, the chances of getting the maximum or minimum result increase - and vice versa. So to decrease randomness, it might appear that we should increase the number of sides on our dice.

But we can't simply swap dice types around without rescaling the modifiers. A +2 to a roll is a big deal when you're rolling a d10, but relatively insignificant when you're rolling a d100.
If we take the d20 as a base, and change it to a d100 instead, we'll need to multiply all the modifiers in the game by 5.

As long as we make sure that the point at which criticals happens stays as the maximum and minimum results of our die type, we should find that they happen far less often (one 5th of the time).

But is that really solving the issue? A less common chance is still going to happen now and then - and perhaps the increased rarity will work against us, as we become even less inclined to plan for those outside chances.

Do away with criticals?
My first instinct is to certainly get rid of critical failures, they're annoying at best and often counter-productive at worst - but critical success is a reward that players seem to resent losing.
I ran a quick poll of RPG forums again, and found that three times as many people liked critical success rewards than disliked them, and over half of people disliked critical failures.
I also found that a significant number of responders volunteered that they didn't like critical success in skills - combat seemed to be acceptable, but the outlandish outcomes of critical skill success seemed to be a randomisation too far.

While getting all this data in, there were some critical failure rules that were brought up that seems to be well-liked, and certainly appeared interesting.

So if critical hits in combat are well liked, how can we keep them? We need to retain the excitement of reward for a good roll, while ensuring they don't ruin the GM's plans (by killing the heroes, or by the heroes killing supposedly overpowering encounters).

Critical advantage
In the game I run, I make critical success in combat give advantage, instead of massive damage.
When a critical result comes up on the dice, the player (or me, as the GM) can opt for some extra effect. in my rules, I split those extra effects into Attack, Maim, or Move.
The Attack option means that the creature can get a free attack (either a simple attack, or a combat trick, like tripping the defender, or disarming them). The attack must make a new check to make this attack. There are a limited number of attacks in a round, so the player has to judge whether this is worth it.
The Maim option lets the player choose to inflict some injury on top of the damage they are deal, so that the defender starts to bleed each round, or has reduced movement, or some similar effect. The defender gets a check to resist this effect.
The Move option lets the attacker re-position themselves in the fight as a free move.

In play, these options have kept the reward of critical hits, which players like, but have largely retained control of the game. With a single additional hit, a hero is unlikely to kill an overpowering menace - and vice versa.
Also, the variety of options gives players choice

Optional failure
While we're praising options for players, I should mention one of the better critical miss rules that was brought up while I was researching this post.
In a few games, a bad roll on the dice allows the player to take the option of re-rolling - but if that second roll is a failure, something catastrophic happens.

For example: In at least one of the systems, that catastrophic thing is damage to your weapon - the game is a post-apocalypse setting, where materials to repair swords are scarce. Let's look at that in action...

Altair tries to hit the lowly goblin with his staff, and his player rolls a 1. The player can opt to re-roll, but risks breaking or damaging his staff  if he misses with the second roll. The player thinks the goblin is not worth the risk, and decided to simply miss. No critical.
Later, Altair is faced with a foul giant. The stakes are far higher, and every hit counts. Altair's player chooses to re-roll his potential critical miss, as he judges it better to try again and risk breaking the staff.

Conclusion: Chaos Tamed?

The randomness of critical hits and misses can be fun, and need not wreck the precarious balance of the GM's plans.
Options and choice for the players are good - giving bonus choices to increase drama is better than merely adding damage, or a secondary table of random effects. When players can choose how their awesome or terrible dice rolling effects the game, there's more meaningful fun to be had.

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