It’s always reassuring to me to realize that brilliant people can get table-flipping mad when they run into a wall, just like everyone else. When Einstein said “God doesn’t play dice,” it was because he was so irked with the unpredictability of quantum physics that all he could fall back on was the argument that it simply shouldn’t work that way, dammit, and that now he was going to go stick out his tongue for dorm room posters until he cooled off.
But as much as I enjoy the thought of angry Einstein stomping about, I can totally understand his frustration. I see it all the time in gaming, and it often stems from an otherwise completely innocent instinct on the part of GMs: to meet the PCs with an “even challenge.”
To a lot of GMs I’ve known, the exact mathematical underpinnings of the systems they’re running are somewhat arcane, even if they have the rules themselves down pat. It’s the difference between studying physics and studying calculus: one covers applications, the other covers theory, and most GMs are studied in applications and thus rely on the book to help them predict how to give their players a good enough challenge that isn’t too difficult and thereby frustrating.
So it’s only natural that a lot of GMs, when left without an exact table to go by, assume that the best thing is to give the PC a 50% chance of success. Lots of systems seem to support this: base AC is 10 in D&D, standard difficulty in White Wolf is 6, base Target Number in Shadowrun is a 4. Each one is half the die used (10 out of d20, 6 out of d10, 4 out of d6). But then, “50/50” is a literal idiom about fairness, so a 50% success rate is totally fair to give your players, right?
Very, very wrong.
There’s another term for a 50% success rate: a “toss up”, which is British for “coin flip,” which most people would agree is not the sort of odds you want to bank on when determining whether an ogre just caved your face in or not. 50/50 in gaming terms is actually horrible odds, and feels so unpredictable for a player that they might flip a table Einstein-style (Ein-style?) instead of the proverbial coin.
In reality, the sweet spot for PC success is closer to 75-80%.
To most GMs, even most players, that may sound nuts. “80%?? Where’s the challenge in that?” But remember that a 20% fail rate means one-in-five. If you had an 80% success rate of making it to the office without a wreck, you’d total a car every week. Similarly, a mercenary with an 80% chance of shooting a bad guy in his stupid face misses said stupid face every fifth time. That miss may include special ammo or an activated ability that’s now wasted if it doesn’t hit. It’s a surprisingly heavy 20%, especially on something you expect your PC to be good at and be able to do reliably.
Also keep in mind that most systems have a twofold mechanic for success, at least in combat: first “did you hit” and then “how hard did you hit.” An 80% chance to shoot a bad guy in his stupid face doesn’t guarantee that said hit is enough to drop him (heck, if it’s certain versions of D&D, it may not even phase him). But a hit still feels rewarding, even if it’s not a lethal one every time.
The 80% “butter zone” also only applies to things the PC is supposed to be at least somewhat good at. If a wizard gets into a slap fight, 50% or less still matches what the player would reasonably be expecting (unless it’s a Bigby’s Hand slap fight, in which case all bets are off). An orc barbarian doing long-division isn’t typically expecting an 80% success rate at it, but the same barbarian trying to kick in a door or clobber an evil slap-fighting wizard is. Set your difficulties and NPC numbers accordingly.
How you set said numbers accordingly varies a little from system to system, of course. Luckily, a number of systems already honor this concept when you take into account the bonuses of a PC’s training.
For D&D, 80% on a d20 means a roll of 5 or higher. If that sounds low, remember that your out-of-the-box D&D fighter should have no trouble hitting AC 10 on exactly that: [BAB +1] + [16-18 Strength] + [masterwork weapon] = +5-6 to hit. A wizard’s level 1 spell usually starts around DC 14-15 to resist (10 + spell level + casting stat 16-18). Given that most targets’ non-primary saves start at zero (or lower with subpar stats), they have to roll a 14-15 to make the save, meaning the wizard has a 75-80% chance to completely succeed.
Numenéra follows a similar pattern much more simply. The system suggests aiming for “standard” difficulty (2) as your sweet spot. That translates to a roll needed of 6 on a d20: a 75% chance of success. That means most PCs can take on level 3 enemies out of the box, since their assets or Effort will reduce the level back to 2 or lower. As they level and gain more skills, get trained in existing skills or gain more uses of Effort per action, the net resulting difficulty should still approach level 2 for the challenges they face to put it in the butter zone.
Things get a bit trickier when you start dealing with multi-dice systems like Fate, Shadowrun, or White Wolf.
Fate, as Fate often does, makes it simple: there are 9 possible net outcomes on the dice, ranging from -4 to +4. 75-80% success means the PC succeeds on a roll of -2 or better (7/9 possible outcomes), so someone with a Good/+3 skill is aiming at an Average/+1 difficulty.
For Shadowrun, a dice pool of 5 hits your 80% butter zone with at least 1 success (1 out of 5 dice). But PC dice pools are often much larger than 5 in combat or while spellcasting, and the number of successes matters much more for damage scaling. When you can, counteract PC abilities and equipment to get the net TN back to 4 (using visibility modifiers to counter smartlinks, armor to counter weapon power, etc) and keep pace with the size of PC dice pools. If your bad guy has an equal chance to scale damage back to the base weapon damage, the PC still succeeds in dealing some damage on average without either blowing the guy’s head off or failing to hit at all, which should match what the player is expecting.
Things get uglier in White Wolf with the ones-eat rule. Under normal provisions, expect one success every 5 dice against a standard difficulty, just like in Shadowrun. A fighter with 3 dots in Strength and 3 dots in Brawl is likely to roll 1 net success with each attack, which is enough to do base damage (where, thankfully, ones don’t eat successes). That typically translates to a reliable 1-2 damage if there’s no Soak involved. Remember that Lethal and Aggravated damage can’t always be soaked, however. The setting already encourages PCs to “go Agg or go home,” just make sure you provide your PCs with a way to do exactly that, and it should keep things in the butter zone for the most part.
The butter zone sounds deceptively large, but when your PCs are in it, most of the time it will feel to your players like a decent challenge. That’s not to say you have to spend the whole campaign there, but knowing the real baseline tells you when you’re amping up the difficulty so that you can prepare your players accordingly.
And then hopefully you can avoid any frustrated Einsteins. (╯°□°）╯︵ ┻━┻