Wednesday, February 04, 2009

Randomness and the Black Swan in RPGs (Part 1)

Raph Koster wrote an interesting post on the connection between games and the ludic fallacy as discussed in Nassim Nicholas Taleb's bestselling book The Black Swan. For those unfamiliar with the book, a black swan is an unpredictable but highly impactful event. Raph ends his post with a question:

"Rather than just bemoan this, I'll instead issue the challenge: what is the fun game that features black swans, phase transitions, and the catastrophic 100-year flood? How do you sculpt a system that does this without chasing away the newbies?"

This is an interesting question, and one which has a simple answer if not constrained to electronic games: pen and paper roleplaying games. The presence of a human game master lends unpredictability, surprises, and ad hoc creativity that electronic games can't hope to match. However, even ignoring the human element, the mechanics of electronic RPGs have been straying ever further away from unpredictability in a misguided pursuit of balance. Since long before I had the Black Swan framework to hang it upon, I have been thinking about the role of randomness in roleplaying games.

Roleplaying games typically draw on randomness for two different major functions. The first is in their action resolution mechanics. The second is in their content generation systems. Both of these got their start in the earliest pen and paper roleplaying games. The earliest electronic RPGs, existing primarily to recreate the tabletop experience, inherited both of these random elements. As electronic RPGs have diverged from their pen and paper roots, the role of randomness has steadily diminished. The results of this process are manifested most clearly in today's MMORPGs and JRPGs. But let's not get ahead of ourselves, even within the early pen and paper tradition, randomness has been afforded varying degrees of importance.

Let us begin by comparing the combat resolution systems of Advanced Dungeons and Dragons and Rolemaster. In AD&D a typical orc has 1d8 hit points and an armor class of 6. A first level fighter with no bonuses will hit an armor class of 6 with a roll of 14 or higher on 1d20(the standard die used for attack rolls in AD&D). At tenth level, the same fighter only needs to roll a 5 or higher to hit the orc. With a standard longsword, the fighter will do 1d8 hit points of damage to the orc if his attack succeeds. So, the first level fighter will hit the orc 35% of the time and it will take anywhere from one to eight successful blows to kill the orc. According to my calculations, the chance the fighter will kill the orc with his first swing is just under twenty percent(0.35 * 0.5625). However, if the fighter had a strength of 18/00(the max a human fighter can have naturally), he would receive a +3 bonus to hit and a +6 bonus to his damage roll. In this case, the fighter would have almost a fifty percent chance to kill the orc on his first attack. Clearly, there is a large random element to combat in AD&D. Bonuses from high ability scores and special abilities and equipment do reduce the relative importance of the random rolls, but these bonuses are usually fairly small. The main constraint to AD&D randomness is that the range of results is clearly defined. If a player's character has 10 hit points and an enemy is attacking him with a longsword, the player knows that his character can't be killed in one blow unless the opponent has some damage bonuses from strength, magic, etc.

In Rolemaster, however, things aren't quite so simple. The attack roll in Rolemaster is an open-ended d100. Normally, results range from 1-100, but on a natural/unmodified roll of 96-100 another d100 roll is made and added to the result of the first roll. This second roll is open-ended as well, so a natural 96-100 will result in a third roll, and so on, ad infinitum. The upper bound of an attack roll in Rolemaster is infinity. Unlike AD&D, the attack roll determines both whether a hit occurred and how much damage was inflicted, with one exception. The final attack roll result, plus the attacker's offensive bonus and minus the defender's defensive bonus, is indexed on a chart for the weapon being used and cross-referenced against the defender's armor type. The result is a number indicating the amount of damage inflicted and possibly a letter indicating a critical hit. Most combat deaths in Rolemaster are either direct or indirect results of critical hits; combatants tend to die in sudden and dramatic fashion and not as much through attrition. There are five degrees of critical hits, A through E, with E being the deadliest. When a critical is indicated, a separate d100 roll is made on the appropriate critical chart. Crticals can result in broken bones, bleeding, blindness, loss of consciousness, and even gruesome death. Even an A critical can kill on a natural roll of 100. Combine the lethality of critical hits with the fact that even the best armor usually can't reduce the probability of a critical hit to zero, and you have a system where any blow can kill. The genius of Rolemaster is that it allows players to manage risk by using any portion of their offensive bonus as a defensive bonus instead. It is rare for players to take a purely offensive stance unless their opponent is stunned.

Now let us draw a comparison between these older pen and paper mechanics and a modern console RPG, Final Fantasy 12. The damage equation for wielding a spear is:

DMG = [ATK x RANDOM(1~1.125) - DEF] x [1 + STR x (Lv+STR)/256]

Notice that the random element ranges from 1.0 to 1.125. Vaan at 50th level, wielding the best weapon in the game(ATK 150) against an enemy with a DEF of 50 yields:

DMG = [150 x RANDOM(1~1.125) - 50] x [1 + 50 x (50+50)/256]

The end result is damage ranging from 2053 to 2438, a fairly narrow range compared to the pen and paper systems. Also notice that successful attacks are the default. Instead, certain equipment like shields provide a chance block an enemy's attack. There is also a small chance to score a critical hit, which results in double damage. As you can clearly see, combat resolution in Final Fantasy 12 is much less random than even AD&D.

To see for yourself how much things have changed since the early days of roleplaying, just compare the combat of a grind heavy MMORPG with the commercial MUD Gemstone IV. Gemstone IV's game mechanics are derived from Rolemaster(in fact, earlier versions of the game licensed the Rolemaster rules and the Shadow World setting). You will not hear Gemstone players using terms like DPS(damage per second) when discussing combat strategy. You often hear complaints from MMORPG players concerning the grind necessary to gain levels, but in fact every MMORPG battle is a microcosm of the level grind. This is especially true of the large raid bosses. You can find a very brief excerpt of a Gemstone IV battle here. I was caught in an invasion of high level plant creatures into my low-level hunting ground and killed. Another player who attempted to rescue me was killed as well. The point of this comparison is that predictability isn't necessarily more fun because it is "balanced", sometimes it is just boring. And if it would be boring in a pen and paper game, then fundamentally, it is probably still boring electronically. It is just dressed up in a such a way that people put up with it.

But even the relatively unpredictable and complex combat mechanics of Rolemaster fall short of the conditions needed for Taleb's black swans. Even without knowing all the bonuses involved, the player can roughly estimate the risks. Looking at the attack charts, the player can see what results are needed to generate critical hits. With transparent mechanics, black swans are by definition impossible because the possibilities are known beforehand. With regard to task resolution mechanics, this isn't necessarily a bad thing. It is the generation of game content which can really benefit from black swans -- like the plant invasion which killed my character in Gemstone IV -- and this shall be the topic of my next post in the series.

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