Saturday, March 7, 2015

The Mathematical Simplicity of Dungeon!

How many hit points should you have to feel comfortable?  Does it depend on your level?
Would 1 or 2 make you uncomfortable and desire to avoid combat?
One of the features of the pre-3rd edition D&D games was the notion of combat as an abstract concept.  Real combat is anything but abstract, however games have to simulate combat and D&D chose to do it in the abstract.  Believe it or not, MMO logic not withstanding, RPGs are not supposed to be about combat.  Combat can be an important part, but it is only a part.  Interaction is far more important and avoiding combat can be just as rewarding, if not more so, than defeating monsters and taking their stuff.  Sadly combat is one of the most regulated parts in terms of rules and thus it gets much attention in the gaming manuals.  The early combat was very abstract, as I have said.  What this means is that it was not meant to be a blow-by-blow description of a fight with every move calculated and every swing of the sword rolled by the player.  The attack roll was really more of a combat success check.  By this we mean that the roll was a way to determine if any of the various blows, feints, parries, and maneuvers resulted in some measure of success against the foe.  To fully appreciate this we must also appreciate what Hit Points really represent, which is not life but ability to stay in action.  Hit Points combine many things including life, stamina, mental fitness for action, and resistance to pain, among other things.  The whole thing is an abstract; I can't say that enough.
Keeping all of that in mind, a combat round, which is anything up to a minute long as of AD&D 2nd edition, is a way to break out the chaos of a general melee into an ordered set of attack rolls, all meant to determine how each participant did during that minute.  It isn't one guy stands still and takes the swing from another guy and then takes his turn, it is just a way to determine an order of resolutions.  A successful "hit" might not actually touch flesh, even though Hit Points are reduced.  That reduction could be fatigue or a bruising through the armor vice a flesh opening slash of a sword's blade.  When Hit Points are gone (0 by default) the combatant simply cannot stay in action any longer.  The blow that reduced the Hits to 0 was the "killing blow" but whether that was the slash that actually opened an artery or simply the battering of a foe into oblivion is up to the descriptive powers of the DM and players.  Essentially Hit Points could be any amount, what they represent is if one is still in the action, so to speak.
In 1989 TSR released The New Dungeon!, an update of its 1975 game Dungeon! which was a game that boiled a D&D dungeon crawl down to its most basic elements: delve a dungeon, kill monsters, steal their stuff.  The 89 edition was the edition I owned.  Currently there is an edition that was released in 2014, itself an update of the 2012 release.  All told there have been 5 editions.  Each edition is marked by a highly simplified, but I think satisfactory, combat system.
Each class has a corresponding color (e.g. red, blue, green) found on the monster cards.  That color will have a number and that number tells the player what they must get on a throw of 2d6 (the printed number or higher) to defeat the monster.  If the player succeeds the monster is defeated and the player may take the treasure found in the monster's lair.  If the player fails to defeat the monster a second throw of 2d6 is checked against a chart to represent the monster attack success.  This is not done if the player succeeds in defeating the monster.  Depending upon the edition the outcomes were a bit different but in the 1989 edition on a throw of 9 or better the monster missed and nothing happened, on a roll of 7 or 8 the hero was stunned (miss a turn), a roll of 3-6 resulted in a WOUND and a loss of treasure and a roll of 2 meant the hero (player) was instantly killed.  That's a 1 in 36 chance of instant death (2.78% chance).  In the case of a WOUND result (14:36 or 38.89%) the player flipped their character card over to reveal a picture with a W marker to represent the wounded status.
A New Dungeon! character card showing the healthy and wounded statuses and a summary of abilities.

There was no penalty to being wounded save that to suffer another wound meant death.  Effectively the player had 2 Hit Points, but this must be viewed properly, in the abstract.  The classes did not all have the same chance of success.  Let us say that the monster in question is a Giant Spider.

We look at the monster card and see that Fighters and Paladins (the red number) need to score only a 4 or better on a throw of 2d6 to defeat the monster (33:36 or 91.67% chance of success) while a Wizard or Thief (the green number) needs to score 5 or better (30:36 or 83.33% chance of success).  It is even harder for the Dwarf and Elf (blue and white respectively) who must score 6 or better (26:36 or 72.22% chance of success).  This combat score holistically takes into account what makes each class what it is.  Fighters wear heavy armor and melee well.  Wizards wear no armor and melee less well than fighters.  Keeping in mind the chance of instant death on a score of 2 on 2d6 should the player fail to overcome the monster we can calculate the danger the player is in in any given combat.  Using our Fighter score of 4 to win we can deduce that the Fighter has a 3:36 chance of failure (8.33%) and a 1:36 chance of instant death only if he fails to win (2.78%) which is actually a 3:1296 chance of being instantly slain (0.23% chance).  Looks like it is worth the risk.

This simple system is reminiscent of the Chainmail fantasy combat table to a great degree.

Once the character is wounded the only change in the probability is that the previous 38.89% chance of being wounded in combat now equals death so you'd take the full 2-6 result into account (since 2 is always death anyway) and that's only 15:36 (41.67%).  The player simply reassesses the risk versus reward in such a situation.  Perhaps retreat is the better option.  But to be fair, if we take a wounded Fighter and put him against a Giant Spider his chance of failure (and thus death) is only 45:1296 (3.47%).  It's still a good risk versus reward.

If we look at all the editions and support articles published in Dragon magazine we can also take magic weapons and armor, as well as some alternate character abilities into account.  Small bonuses of +1 or +2 are much more effective in this system than in a more complex and detailed (such as the flawed 3rd edition) systems.  The gray number on the card image above represent the Lightning Bolt spell that Wizards may use while the yellow number is for the Fireball spell.  Tactically this gives the Wizard the ability to attack at a distance, which prevents the player having to check for the monster should the attack fail, but the numbers are not always better than the green (sometimes they automatically fail) and the Wizard has a limited supply of spell cards.

Now admittedly this is just a board game.  It does not support leveling play where you take a character from neophyte status to world-conquering endgame, but the essence of play could be used in any game.  We measure threats against our chances of success.  That Giant Spider might not be much of a threat to a Fighter or Wizard, but the top tier monsters are a significant threat.  The Red Dragon of New Dungeon cannot even be beaten by a Dwarf or Elf (unless they have a magic weapon, and then they need to throw a 12 on 2d6, which is a 1:36 chance) the Fighter and Paladin require an 11 while Wizard and Thief require a 12.  A Fireball will not work at all (red dragons are immune to fire, heat and flames) but a Lightning Bolt has an 8 (15:36 chance, 41.67%) of success.  If we compared this to a powerful and aged red dragon in one of the editions of the D&D RPG we'd see a monster with massive Hit Points, very good attack values, multiple attacks per round, a breath weapon, maybe spells and a defensive rating (Armor Class) that makes it very hard to hit by all but the highest level characters, and even then they will need to hit it many, many, many times to put it down.  All the while the players will be taking damage.  Does a single roll really change the outcome of the risk?

I am not, strictly speaking, advocating a single roll combat resolution for RPGs.  I understand that there are more hazards in a game than just monsters.  There are traps.  Sometimes the environment wants to hurt you too.  Ever been to a jungle?  Trees actively try to trip you and sprain your ankle.  I'm not kidding.  What I am advocating is the simpler, more abstract concept of combat where you don't have to make 15 rolls of the dice to try to trip an opponent just to get a bonus to kicking him in the junk.  What the 2d6 throw in Dungeon represents is not a single blow of the sword, but the results of the two opponents clashing in a space, perhaps a large room in the case of a dragon, and the statistical outcome of victory and loss.  It requires one to think in terms of risk versus reward and the possession of only 2 conditions (healthy or wounded) is a part of a larger formula that takes into account the attack value as a part of this abstracted conflict resolution system.  In such a case the Wizard does not need to suffer a d4 Hit Die and the Warrior does not need a d10 because holistically this is figured in as part of the number that determines success in combat with Warriors typically (but not always) having the mathematical advantage.  There are a very few monsters (enemy wizards, ghosts, the supernatural things, essentially) that the Wizard has a melee advantage against because of his knowledge of the monster, but for the most part melee advantage is to the Fighter, which is what we've come to expect.

And nobody needs an ever increasing, and frankly ridiculous, amount of hit points that makes a 1d8 longsword look like a toothpick at high levels.

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