Friday, May 18, 2012

3d6 sucks in Risus

Following a really rocking' game of Risus Primeval last night, some discussion came up concerning the dice mechanics. This prompted me to run some numbers this morning. Oh, the numbers I crunched. My brain is sore, and it mostly just confirmed my suspicions, but at least now I can actually make non-anecdotal arguments to defend my position concerning the character generation system.

In Risus, a character typically starts with 10 dice to be divided amongst their skills (known as clichés), with a limit that no skill may start with more than 4 dice.  So, you see a lot of 4/4/2 or 4/3/3 builds, spotted by the infrequent oddball builds like 4/2/2/2 or 4/3/2/1 or even 3/3/2/2. I'm here to tell you that anything other than 4/4/2 sucks horribly, and should be avoided at all costs.

Risus features two types of rolls. Generic rolls vs a static target number to see if you succeed at some standard task, and then there's combat. 

Let's look at the non-combat rolls first.

According to the rules, rolls have a difficulty of 5, 10, 15, 20 or 30 (20 or 30 just sounds crazy to me, given that the hard-cap for a PC whose maxed out a trait is 4 dice at character creation and 6 dice after much XP spending).

Difficulty 10 is meant for things that should be challenging for a professional, and 15 is for "really inventive or tricky stunts".   Then the GM is vaguely instructed to sometimes lower this if a given cliche is particularly appropriate, but only a handful of examples are provided and no real advice on adjudicating it. In my experience, this means most GMs don't really adjust the numbers much. Even if they do, as a player reading the rules you feel really motivated to get at least 3 dice in anything you ever want to do, because the rules state that 3 dice represents professional-level skill. Sounds like you want 3 dice, right?

Wrong. Here's the first wrinkle. Most GM's never have you roll against the lowest difficulty, which is specifically 5 in Risus. Someone at the table is going to have 4 dice in something (in fact, in my experience, nearly every PC has 4 dice in something) pertinent to the roll. The first time the GM sets a "5" difficulty, people grab their 4 dice and someone asks "why are we even rolling this?"  There's a social pressure then to not roll vs difficulty 5 on 4 dice, as it just feels too silly. Most GMs pretty much default to difficulty 10 for average tasks worth dicing for, because it  feels fair regardless of whether you got 3 or 4 dice to roll, and is a lot more interesting than difficulty 5.   Perhaps some other number would be better, but 10 is nice and round, it shows up in the rules, and really who wants to deal with a sliding scale of improvised values in the middle of a fight?

So now 10 is your routine average difficulty, even though that's not really what the rules say.
  • Chance of succeeding at difficulty 10 on 3d6: 63%
  • Chance of succeeding at difficulty 10 on 4d6: 90%
So 4d6 is a good deal better than 3d6 at routine standard tasks, but 3d6 is still plenty respectable. 3d6 feels professional.

Of course, in a typical gaming scenario, not everything is routine. GM's frequently want to make something a little tougher than average. Players also frequently come up with crazy ideas, and it's very normal for the GM to respond to that by raising the difficulty up one step. Officially, one step up in difficulty in Risus is a 15.  But as it turns out, a 15 is terribly hard to score on 3d6:

  • Chance of succeeding at difficulty 15 on 3d6: 9%
  • Chance of succeeding at difficulty 15 on 4d6: 44%

So the 4d6 character is still reasonably proficient, but about half as likely to succeed as they were on a difficulty 10 challenge. Most GMs (and most players who have a 4-die stat) could live with that.

The PC rolling 3d6 however, is nearly guaranteed to fail at that test that's just 1 difficulty level above "normal".  Already 3d6 is starting to suck, and we haven't even gotten to our first fight scene.

If the GM realized how low the odds were on getting that 15, they probably wouldn't use it as a difficulty very often.  Chances are the GM hasn't realized how hard the 15 will be. Most people aren't that good at intuiting actual odds, that's how casino's make money after all. We remember the big successes more than the day-to-day failures. While gamers are often more math-savvy than the general public, we've all been kind of brainwashed by years of D&D optional character generation rules teaching us that a 15 stat isn't all that unusual.  Don't believe it.

Combat in Risus has a somewhat infamous death spiral. If you fail a roll, your dice pool shrinks for the rest of the fight.  Combat uses contested rolls, so each round one side of the fight grows weaker, while the other maintains their strength.  It's in such a combat that 3d6 clichés really become a liability.

Two hypothetical characters (or players), Alison and Brad, are about to have a duel.  Alison has a relevant cliche rated at 4 dice. Bradley's cliche is only 3 dice. What are the possible outcomes of the first round? Most of us would correctly deduce that Alison's got better than even odds, but how much better?

Alison's 4 dice are in fact 4 times more likely than Brad's three to win the first round of the fight. I ran the numbers on it this morning, and was a little surprised just how dominating that extra die is.  Here's the results of round one:
  • 75%: Alison (with 4 dice) rolls higher than Brad. Brad drops to 2 dice next round.
  • 19%: Brad (with 3 dice) rolls higher than Alison. Alison drops to 3 dice next round.
  • 6%: The rolls are tied.
Risus doesn't actually address what happens when there's ties on a combat round, so the GM is left to figure out what to do on the ties. Most GMs have both sides reroll, either as a new round or as just a second roll in what is technically the same combat round. If that's the case, the 6% is replaced by:
  • 4.5%: The rolls tie initially. The GM calls for a reroll, and Alison wins it.
  • 1%:  The rolls tie initially. There's a reroll, and Brad wins it.
  • Half a percent: This round of combat takes 3 or more rolls to resolve. It's likely Alison wins eventually.

I've seen a few GMs try other tie-breakers to avoid delays from rare consecutive ties. Usually these tie breakers are either "highest stat wins", or "highest single die wins". Either of those basically make the 6% tie chance into another case of Alison's 4-die stat delivering a win. 

So there's about an 80-20 split in favor of the 4-die character. And that's just round one, where the difference in stats is just 1 die.

Round two now deals one of two situations.

It's 80% likely that Alison won the first round, and is still rolling her 4d6 against Brad's now weakened 2d6.  Her odds of winning the second round have just shot up to 96%.  Brad's hosed.

The other 20% of the time, Brad will have gotten lucky and won the first round. Alison's 4-dice are knocked down to 3. That means both characters are rolling 3 dice. Even though Alison lost once, she's still got a 50-50 shot at winning the second round. If she does, she's retaken the advantage.

So a true break-out of the full results of the 4-dice vs 3-dice fight are basically thus:
  • 80%: Alison trounces Brad without ever taking a hit.
  • 10%: Alison takes an unlucky early "wound", but still manages to win the conflict.
  • 10%: Brad defies the odds and comes out the victor.
And that's assuming that Alison only has the one 4-die skill.  If Alison's build is 4/4/2 vs Brad's build of 3/3/2/2, she can essentially soak up one bad roll without it diminishing her attack strength.

Even if Brad's got the second-best build, 4/3/3, he's still likely to come up short in a fight.  Let's see how that 4/4/2 vs 4/3/3 conflict plays out over several rounds of combat.

Rounnd 1: Alison with 4/4/2 vs Brad with 4/3/3. Both characters roll 4 dice.
50% A wins round 1: Rnd 2 is A4/4/2 vs B3/3/3. A has advantage.
50% B wins round 1: Rnd 2 is A4/3/2 vs B 4/3/3. Even dice next round.

Round 2: Number of dice adjusted by who won round 1.
40%: A wins rnds 1 & 2. Rnd 3: A4/4/2 vs B 3/3/2. A has advantage.
10%: A wins 1, B wins 2. Rnd 3: A4/3/2 vs B3/3/3. A has advantage
25%: B wins rnd 1, A wins rnd 2. Rnd 3: A4/3/2 vs B3/3/3. A has advantage.
25%: B wins rnds 1 & 2. Rnd 3: A3/3/2 vs B4/3/3. B has advantage.

Round 3:
32%: A wins all three rounds. Rnd 4: A4/4/2 vs B3/2/2 A has advantage
8%: A wins 1 & 2. B gets lucky on round 3. Rnd 4: A4/3/2 vs B3/3/2. A has advantage.
8%: A wins rounds 1 and 3. B wins 2 Rnd4: A4/3/2 vs B3/3/2. A has advantage.
2% A wins rnd 1. B wins rounds 2 and 3. Rnd 4: A3/3/2 vs B3/3/3.  Even dice, but breaking in B's favor.
20%: B wins 1. A wins rnds 2 & 3. Rnd 4: A4/3/2 vs B 3/3/2. A has advantage.
5%: B wins rnds 1 & 3. A wins rnd 2 only. Rnd 4: A3/3/2 vs B4/3/2. B has advantage.
5%: B wins rnds 1&2. A wins rnd 3 only..Rnd4: A3/3/2 vs B3/3/3. Even dice, but breaking in B's favor.
20% B wins all 3 rounds. Rnd 4: A3/2/2 vs B4/3/3. B has advantage.

So at the end of three rounds:
  • There's a 68% chance that Alison (who started with 4/4/2 stats) has a strong advantage of being able to roll 1 more die than Brad can.
  • There's a 25% chance that Brad (who started with 4/3/3 stats) has a strong advantage of being able to roll one more die than Alison can.
  • There's a 7% chance that they're rolling the same number of dice next round, but that Brad has a minor long-term advantage that may allow him to outlast Alison.
Even if we count Brad's long-term advantage as being as potent as rolling an extra die immediately (which it's probably not), that still means the 4/4/2 build as having twice the chance of the 4/3/3 build at winning a protracted battle.

Just how big of a deal this advantage ends up being has a lot to do with the GM, and what the stats are of the challenges they throw at the players. PC healing rates are totally a matter of GM Fiat in Risus.

Even with a very generous GM who hands out free heals after every conflict and doesn't put you up against NPCs with lots of dice or back-up stats, there's still never a situation where you'll regret a 4/4/2 build. Some GMs might be easy enough you don't _need_ to go 4/4/2, but there's never a downside to doing it. Risus' clichés are so open-ended (you can use "hairdresser" in combat), and the "penalty" for using an inappropriate skills is so unthreatening (it's actually an advantage), that you should have no trouble coming up with just two big cliches that cover everything you really want the character to do and a minor 2-die stat on the side just for flavor.

The basic rules give no advice on how to handle the implications of the math behind rolls, nor does it give any good advice on how to stat out NPCs. Heck, one of examples in the rulebook casually throws out a horde of rats that roll 7 dice, with not even the slightest mention of the fact that 7-die horde is a TPK waiting to happen.  I just spent this huge article talking about how much better 4 dice is than 3, and I assure you 7 dice would be a damn spot better than that.

A few other numbers that may be useful as data points:

4 dice beats 3 dice 80% of the time.
4 dice beats 2 dice 96% of the time.
4 dice beats 1 die 99% of the time.
3 dice beats 2 dice 90% of the time.
2 dice beats 1 die 90% of the time. 


Anonymous said...

I hadn't really thought through to the conclusion that 4 dice is the only way to go, but the numbers were covered in my old article The Die Also Risus on the gamefest site. An interesting discussion.

Philo Pharynx said...

An interesting analysis. I haven't played Risus, but this is definitely something I'll consider if it ever comes up.
As a rule I don't like using opposed rolls, one winner as your combat mechanic or immediate death spiral. Opposed rolls, one winner implies that there's always a winner and always a loser in each combat round. You never have a case where the two people skirmish but can't get through either's defenses. You also don't get the case where both people end up harming each other. In samurai culture, one of the most honorable ends to a duel is Ai Uchi, where both warriors strike and kill each other simultaneously. It was honorable because it showed that both warriors were exactly matched in skill and bravery. (Note, I'm not against opposed rolls in all case, just the case where each side makes one roll and it's winner take all)
Immediate death spirals lead to situations like the one shown above. If you want to survive, you need to focus your character so that you start with the advantages and hope you get lucky. If you fail a couple of rolls, then you should probably retreat and heal because you'll be starting at a disadvantage. (Once again, I'm okay with death spirals that only start to take effect when you've been significantly hurt.)
Combining the two is a big sign that this a game where fighting is serious and you want to avoid it whenever possible.

Philo Pharynx said...

It would be interesting to see if there's a way to reduce these effects without making combat much more complicated.

Anonymous said...

A while ago I was in a Risus campaign that used house rules for the combat. An analysis of two different rules options can be found in
Personally, I still am not a fan of the system.

Peter Darley said...

Point of order, probably doesn't matter but you have a typo at "Let's see how that 4/4/2 vs 4/4/3 conflict plays out"

rbbergstrom said...

Thanks. 4/3/3 was the intent, of course. I fixed that typo and another one.

spaceLem said...

I had a look at the default Risus mechanic and compared it to the "highest die" mechanic (highest die wins, resolve ties by looking at the next highest die). This considerably softens the difference between different levels (e.g. 4d6 vs 3d6 goes from 79% to 60% chance of success, and 1d6 can beat 6d6 8% of the time).

Obviously combat over several rounds still magnifies those differences, but where in default Risus 4d6 beats 3d6 90% of the time, and 4d6 beats 2d6 nearly 100% of the time, that becomes 76% and 94% respectively with highest die, giving you a fighting chance, or allowing for a mistake when trying different tactics and switching between clichés.

When using highest die, you need to think about the TN difficulties. Following the Silhouette and Far Away Land systems where each additional 6 increases the result by 1 (so 4d6 -> 2,4,6,6 = two 6s = 7), then you can set TNs of 4 up to 9 (6d6 has a 1% chance of getting a 9, which about matches the chances of getting 30 with the default mechanic), but where default Risus TN 15 is 6% for 3d6 and 44% for 4d6, the highest die with TN 6 makes that 42% and 52%, and TN 7 makes that 7% and 13%.

I can provide the complete list of probabilities if you're interested, but I think it goes a long way towards fixing the issues you're having, and making 4/3/2/1 or 4/3/3 far more usable. Also highest die is easier on the brain than adding multiple dice!