Testing D20

As promised, I finally got some Game Science dice today and immediately set out testing them to see if they're fair, then compared the result against the black D20 that came with my old red box Basic Set and I've had since god-knows-when.  Ready for the results?



Figure 1:  Histograming results initially suggests that the black D20 likes to produce a result of "18."



The inital results are shown in figure 1.  After rolling each die 100 times, I then applied the chi-squared test to estimate the likelyhood of such a result, given the differences between the observed and expected distributions. 

The net result!  The observed distribution of my Game Science D20 is about 80% likely given the expected distribution of a fair die, while the observed distribution of my black D20 is about 5% likely (see figure 2). 

Figure 2:  Chi-squared test probability of the observed distribution given the expected distribution of a fair D20.

If the observed distribution is 80% likely given the expected distribution of a fair die, then I'd bet that the die is fair (or at least as close to fair as is easily observable).  Therefore Game Science die passes the test of fairness fairly well.  The Black D20, however, is a lot more problematic.  I will be testing more of my dice to see if I observe similar results.  In the mean time, however, I think the black D20 will be the designated "hit the bad guys" die. 

Conan The Barbarian

Last summer Conan the Barbarian was released with generally horrible reviews.  Some of the most brutal reviewers were those who loved the original Robert E. Howard stories.  I downloaded and watched it this afternoon and I'm a big fan of the original stories.  Frankly, I didn't think it was all that bad.  I enjoyed it.  I might even watch it again some time.

I think it captured the essense of Conan much better than the Arnold versions.  Even so, it was not a recreation of any of the stories, which I think is mostly what people were disappointed about.  Instead it was Conan pastiche.  That's not to say it was bad.  Conan was such an enduring character that he inspired novels and comic books beyond what Robert E. Howard wrote.  Much of it is quite good in my opinion.  It's a good thing that people wanted to write continuing adventures for Conan long after his original creator died.

While I would love to see a story like The Queen of the Black Coast turned into a movie, I can't help but wonder if there are significant challenges to it, not the least of which is that there are now fans of Conan who have never read any of the stories, or even the comic books. They only know him from the movies.  In order to avoid alienating those fans, you have to include tips of the hat to them too.

That's the rub.  You can't undo a not-so-great rendition of a great character, which has lodged itself in the illiterate mind more firmly than the original source material.  Hence they had to include "the riddle of steel."  None the less, I enjoyed how the bad guys in the new movie's child-Conan scenes were easily recognizable to me as Picts.  I also think the original Conan would be difficult to portray accurately today simply because of the original source material's implied (and not so implied) racism and sexism.  In that sense, it shares a lot with Tarzan. 

I was surprised they went with a giant octopus this time around.  It seems like you can't get through a good chunk of Conan stories without him wrestling a giant snake somehow.  The octopus was good, though.  There were also no Stygians in this one.  The bad guy was of unknown ethnicity, and his daughter was merely a strange witch who moved in  vaguely snake-like way to me.  Acheron, while an ancient evil empire in the Conan series, is not the main source of evil, except in one story I know of.  Stygia is a much more regular source of irritation.  None the less, the sets were spectacular.  I can't think of a more beautiful fantasy movie, with it's spectacular CGI rendered cities and temples.  I feel like they used and didn't abuse CGI in this movie.  Lord of the Rings was good, but this was that multiplied.  I can't help but wonder if it has to do with Lord of the Rings essentially rural flavor, while Conan is a mix of urban and rural locales. 

I liked how they captured Conan's propensity for freeing slaves, womanizing and piracy, as well as implied the tremendous ethnic diversity and vast geographical stretch of Conan's world.  They captured that much better in the most recent movie, than in the Arnold ones.  I also really enjoyed it when he flung his prisoner into the enemy camp with a catapult.

If I had one dislike it was the current trend in Hollywood of "equalizing" the roles of women and men by giving women heavy weapons and fight scenes.  I'm not against arming women in movies, or putting women in combatitive roles.  The thing is, you have to consider what kind of woman you're putting in that role.  Just as there are many kinds of men in this world, there are many kinds of women.  There are women (Grace Jones?  Lucy Lawless?) for whom that kind of thing is believable.  But a priestess in a diaphanous gown doesn't strike me as the sort who'd be excited about getting all sweaty flinging around a heavy sword, or for that matter, the kind of person who would be a natural fighting with a heavy piece of steel.  That doesn't make sense.  She's too prissy.  She needed something lighter.  Giving her a dagger worked for me.  Picking up a big sword worked less, but having her actually demonstrate how good she was with it seemed superfluous and silly.  It was especially non-sensical because after discovering her talent for swordplay, she didn't keep a sword with her the rest of the movie, regardless of the dangers she faced.  If that was the case, why have her demonstrate how good she was with it?  The obviously female archer made a little more sense, but it looked to me that the director originally gave her a bigger role in the film and then edited her out.  I liked the witch daughter.  She was fabulous.  I'd want her part in the movie.  She got the best costume, the best makeup and the wildest hair.  Those claws were awesome.

I want to see a Conan director's cut.  I suspect it'd be a better movie.

Joined a Play by Post Game

I recently joined a Play by Post (PbP) game on the Labyrinth Lord forums.  I decided it'd be fun because I usually DM and I need to play more.  I wanted to get excited about my one character.  As luck would have it, the DM rolled me some above average stats, using the 4d6, drop the lowest and arrange in order convention, resulting in statistics which would suggest a fighter-thief if left un-rearranged.  Since he ruled out multi-classing, I chose an elven thief.    I'm excited about my character. 

I'm also excited to participate in a PbP game for the first time, simply because I'm curious about the mechanics.  In this game, the DM rolls all the dice, hence nobody has to rely on the honor system.  While that's fine, it got me wondering if one could make a "cheat detecting" spreadsheet that takes advantage of Bayes' theorem to estimate the probability of someone cheating, given that they rolled what they rolled.  Then, through Bayesian revision, one would gradually update that probability.  Thus, if one cheated, a high confidence level that they were cheating would eventually be achieved, and the offending player appropriately disciplined.

Part of the fun of RPGs to me, is rolling some dice.  I like the feel and sound of them.  Yes, from time to time I have taken advantage of smartphone apps and spreadsheet formulas to fill in when I don't have access to my dice, but using them seems to replace the visceral feeling of dice rolling.  Let's face it, it's not fun to hinge your success on the outcome of pressing the F9 button.  I'm always left wondering if I had reset my system's clock then something else would have happened.

Who is More Fightey? D&D Monsters or AD&D Monsters

Continuing my thinking about morale in the two different systems...

Figure 1: A creature with a morale score of '7' has an almost 60% chance of failing a morale check compared to AD&D's base morale of 50%. 

Since D&D Morale rules mandate the use of 2d6 instead of d% as in AD&D, comparing the two systems requires looking at the distribution of outcomes.  If a relatively cowardly monster in D&D has a morale score of 7 then I would argue that the weakest D&D monsters are slightly less aggressive than in AD&D where their base morale score is 50%.  That's assuming the morale rules are applied under similar circumstances and left unmodified.  The modifiers are where things get complicated, though.

AD&D Morale versus D&D Morale

Continuing my contrasting of the AD&D system to the D&D system...

Something else I've noticed is the radical differences in how morale is treated.  First off, in D&D Morale is explicitly labeled as an optional rule.  In AD&D it isn't, however, the failure to label something as optional should not be taken as an indicator that it's essential due to the insistance in the rule book that one make the game their own.

More interesting, is how everything in AD&D has a base probability of morale failure of 50%.  Wow...

In this sense, D&D can be a much more brutal game than AD&D because certain opponents (e.g. skeletons) are absolutely relentless with their morale score of 12 (i.e. 0% probability of failing morale checks). 

Also interestingly, is that while D&D hints that a DM might modify morale based on the situation, AD&D has a table of suggested morale modifications which takes into account issues such as the death of a leader, encountering a larger force and suffering high casualties. 

I'm not sure which system I like better.  I like how in D&D the assignment of a morale score to each creature reflects it's intrinsic aggressiveness or disinterest in fighting.  I like how in AD&D there's a suggested modifier based on the scenario.  I think if I was going to come out with a "D&D Mine" I'd create some kind of hybrid of the two systems. 

AD&D Combat Round Versus D&D Combat Round

I recently purchased the re-issue of the 1st edition AD&D core rule books.  I realized in retrospect that I only thought I was playing AD&D back in the day.  Really, I was playing a sort of mish-mash of D&D and AD&D.  One of the things I'm struck by is the differences in the two combat systems.  In D&D there's a combat round checklist, and everything happens in a specific order.  In this respect, it's very much like playing a wargame like Panzer Blitz.  I ended up writing a short MATLAB script for predicting the probability of various outcomes of differently armed and armored opponents.  It doesn't take into account special abilities.  I was hoping that it'd be easily modified for the AD&D game.  Unfortunately, that hasn't proven to be the case due to some of the following differences in the combat systems.

Time:  D&D combat rounds are 10 seconds long.  AD&D rounds are 1 minute long which are further subdivided into ten 6 second segments.

Surprise:  In D&D the DM rolls 1d6 for both sides.  A 1 or 2 indicates that side is surprised.  It's fairly easy for both sides to be surprised and spend a round doing effectively nothing, which, in practice, most of the time means that nobody is surprised since if both sides are surprised and do nothing, the DM just marks off a round on his time record and keeps the game moving.  With AD&D, while both sides can be surprised, it's possible for one side be less surprised.  The degree to which one side or the other is less surprised depends on the difference in their surprise die rolls.  Additionally, if both sides are surprised equally, nobody is surprised, negating the effects of surprise entirely.  Interestingly, in certain cases, extremely surprised parties can be surprised for multiple segments.

Initiative:  In D&D, initiative is determined each round.  In AD&D, achieving surprise is also equivalent to winning initiative, so it's only determined on rounds where nobody is surprised, or all sides are equally surprised.  This means that surprise is more deadly.  Not only is there a potential to get free attacks, but you might get multiple free attacks (in the event of both sides being surprised but there being a large difference in their surprise rolls), and on top of that, you get to attack first each segment after the surprise segments are resolved.  YIKES!  Additionally, initiative is determined at the beginning of the round, hence the advantage of intitiative is carried through all ten segments. 

Surprise in D&D feels to me almost like an optional rule, inserted and often employed at the DM's discretion.  In AD&D achieving surprise is an integral part of combat.  Additionally the advantage of initiative is much more decisive. 

Weapon Speed Factors:  This one has me really perplexed.  Most combats are not 1 on 1 encounters, hence they are not uniformly armed.  I can't help but wonder if these rules were only meant to be employed in the event of a duel.  It makes me think an early D&D player must have been an SCA wire-weenie. 

I can't help but wonder if this would have the effect of making shrewd players very focussed on achieving surprise, since the advantages are so much greater.  I'm not sure a fast weapon matters very much, though, since I can only see it mattering in one-on-one encounters.

Philosophizing About Probability

Over at Digital Orc he posted a video arguing about the distinction between "experimental" probability versus "theoretical" probability.  I disagree with his definitions.  Probability is always theoretical.  What he calls an "experimental" probability is better be described as an estimate of the probability subject to an experimental uncertainty.  From the rules of error propagation, it is actually possible to derive a formula for the uncertainty associated with one's estimation of a probability. 

Exactly how this distinction would be valuable to gamers is unclear to me, except maybe for assessing the fairness of one's dice.  Even then, though, to really do it properly you'd need to invoke Bayes theorem and calculate the probability that the dice are fair given that you rolled some number of successes.

What's valuable to gamers isn't a largely philosophical discussion of the nature of probability.  What's more useful is concrete tactical advice based on mathematical analysis.  That's more difficult, or at least more tedious.  Let's face it, multiplying all the little probabilities together to make the probability tree for a combat round is mind numbingly dull.  I still haven't filled out that darned transition matrix.  Maybe I should just give up and write the Monte Carlo.  Or maybe I should write a program for populating the matrix.  Huuuum...

Dungeons and Geometry

I was recently looking through an archive of early Dungeon magazines, and found a fascinating article in issue No. 6, July/August 1987, which featured a great example of a non-Euclidean dungeon called The Forbidden Mountain by Larry L. Church. If you all can find a copy of that issue, I highly recommend it. The article begins with a discussion of spherical and hyperbolic geometries, and their implication for how a dungeon mapped on an ordinary piece of graph paper would in fact play (see figures 1, 2, and 3).  Next he imagines briefly the possibilities of dungeons in arbitrarily curved space (figure 4), and produces a diagram of a dungeon that is effectively on a Moebius strip (figure 5)!  Gary Gygax was known to have had a great deal of respect for gamers' minds, believing them to have above average intelligence and creativity. It's striking to me that so early in the magazine's history they would put such a sophisticated thought in their magazine.  It speaks to the great deal of respect the magazine had for the intelligence of their readers.  I'm suspect that respect is gone today.

I also can't help but wonder if their inclusion of a non-Euclidean dungeon in the first year of publication suggests that at least among homebrew dungeon designers, such machinations were more common than one might guess from early modules.   

Both H.P. Lovecraft's The Dreams in the Witch House and The Call of Cthulu used non-Euclidean geometry as a device to make their horrors seem alien, with access to unfathomable knowledge which humanity is only able to touch upon. It was a common theme in all his stories.  Since even in his time, the ideas of alternative formulations of geometry were well developed, it's implicit in his stories that humanity had already gone "too far," in its search for knowledge.  The Theory of Relativity was something we were not "meant" to know.  The ability to manipulate space itself would almost certainly be a hallmark of powerful magic or divine intervention. I was also thinking about when I was eleven and learning to play D&D while also teaching myself to program in Ye Old BASIC with Lyne Numbers on my ATARI XE computer.  I remember carefully keying in a program called "Hunt the Wumpus" and taking pride in how I'd made the Wumpus' lair into a Moebius strip.  Dr Who's TARDIS would be impossible without non-Euclidean geometry.

As a dungeon master's tool, geometrical tricks are probably about the dirtiest, least expected trick you can pull.  Particularly with all the advanced graphics tools we have now, there's no reason for us to feel constrained to two or three dimensions.  None the less, it seems that we've all succumbed to the tyranny of our graphics software, which invariably seems to produce a flatter, less, mindbending world.  Non-Euclidean dungeons could be examples of weird "funhouse" sorts of magical effects, or else inspire horror and awe in the tradition of H.P. Lovecraft, were a dungeon becomes a weird arrangement of higher dimensional objects, time and space lose their conventional meaning, and serves to make humans feel weak and pitiful in the face of superior beings from the outer reaches.

Maybe it's just me, but growing up I felt like my friends and I all shared an uncomfortable fascination with the alternative formulations of space and time.  In highschool I read Albert Einstein's The Theory of Relativity, and Rucker's Geometry, Relativity and the Fourth Dimension. In college one of our textbooks was Spacetime Physics by Taylor and Wheeler.  Contemplating non-Euclidean geometries was an important part of my intellectual growth as a young person.  Dungeons and Dragons was one place where people could perform gedankenexperiments  and develop a visceral feel for them.  I suspect the experience was more widespread than is commonly acknowledged.  Maybe it's also just me, but it seemed like non-Euclidean geometry was everywhere then.  Maybe I've just lost touch with geeky kids.  So... my next dungeon will be non-Euclidean.
 

More On Backstabbing

A recent discussion of ways to play out the backstabbing mechanic has led me to review the rules, because they greatly influence the probabilities of success.  The Labyrinth Lord ruleset, as written, is extremely uncharitable to thieves in this one respect.  "[He] must catch an opponent unaware of his presense, using move silently and hide in shadows." The requirement to do both makes a successful backstab exceptionally improbable for low level thieves.  After a complaint from a player I've been trying to get interested in old school play, I've been exploring ways to adjust so that thieves could be a little more exciting to play.  Some of those ideas were discussed here.  I also decided to look it up in my old rule books.

According the Rules Cyclopedia:

If a thief can sneak up on a victim, completely unnoticed, the thief may backstab - if he is using a one-handed melee weapon, he may strike at particularly vulnerable points of his target's body. (Though the ability is called "backstabbing," the weapon doesn't have to be a stabbing weapon.  A thief can use this ability with a club, for example.)
...
If the intended victim sees, hears, or is warned of the thief's approach, the thief's attack is not a backstab; it is an ordinary attack, doing the damage appropriate for the weapon used.

When no battle is in progress, a backstab attack may require a Move Silently ability check.  The DM will make all the necessary decisions on that matter.

Furthermore, in my old, red box, Mentzer, D&D Player's Manual it describes the backstabbing ability this way:

If a thief can sneak up on a victim, completely unnoticed, the thief may Backstab.  If the intended victim sees, hears, or is otherwise warned of the thief's approach, a Backstab may not be taken but the thief may still attack normally.
...
EXAMPLE: An Apprentice is carrying a sword, and sees an ogre approaching the party.  The player says "I'll Hide in Shadows."  The DM rolls 19 on d%, so the ogre does not see the thief (but the DM does not announce the fact). During the battle, the ogre gets turned around, with its back towards the thief.  The player says, "I'll try to move in for a Backstab!" The DM decides that the ogre doesn't notice the thief's approach (no roll is made; it depends on the situation, and the DM's judgement) and says "The ogre doesn't notice you; roll for a Backstab." The thief player then makes a Hit Roll...

So originally, the issue wasn't necessarily the game mechanics, but rather the DM's discretion. Depending on the situation, a DM might require a Move Silently check, a Hide in Shadows check, both, or none.  While I definitely am a big fan of the Labyrinth Lord rule set, I'm coming to appreciate it's differences from D&D.  In this one little respect, I think Labyrinth Lord desperately needs to be tweaked.  One of the brilliant features of old school gaming is how much is left to the dungeon master.  The way it's worded in Labyrinth Lord specifically, though, is excessively binding and needs to be house ruled. Otherwise, no rational player would backstab until achieving a fairly high level. Not only that, house ruling it would be more in keeping with the original game rules.

Testing Dice Fairness

At my game yesterday, one of my players complained about her terrible dice rolls.  She seemed convinced that they were magically biased against her.  She's a statistician so I suggested she determine empirically whether her dice were likely to be biased by rolling them a lot and then use that to determine the likelihood of their bias.  It's a classic probability problem.  Needless to say she didn't, but it got me thinking.  Given how superstitious gamers are about their dice such a test might actually be interesting to do.

The only people I've seen who seem devoted to dice innovation is a company called Game Science.  I haven't used their dice though.  I think I might buy a set, test them, and compare them to my existing dice.

Mean Time Between Random Encounters

This post is in response to a question someone asked me privately. 


Usually in D&D the likelyhood of a random encounter is stated in terms of a m in n chance every p turns.  For example, in B5 - The Horror on the Hill the likelihood of encountering wandering monsters was stated, "Check for wandering monsters on The Hill every three turns when the party is moving and every six turns if they are stationary (camping). If you roll a one on a ld6, one of the following types of monsters is encountered (see table below): roll a ld6 again to determine the exact creature(s)." Most adventures have some similar statement.


For planning purposes, it might be useful to know the expected amount of time between random encounters.  It's not complicated, though.  In the above statement there's a 1 in 6 chance of a random encounter every 3 or 6 turns.  That means that you expect that out of 6 trials you expect one of them to result in a random monster.  If there's a trial every 3 to 6 turns you expect a wandering monster to appear every 18 to 36 turns. 


That makes wandering monsters pretty rare.  A lot has been said about how using wandering monsters forces the players to pick their battles.  That's only true, though, if wandering monsters are common enough to be a real nuissance.


In The Keep on the Borderlands the wandering monsters statistics are phrased a little differently.  "The passage ways here are very busy, and for every 10’ distance covered by the party there is a 1 in 6 chance that they will encounter a group of goblins (see below).  Check every time the the party travels 30’ (a 3 in 6 chance) until wandering goblins are encountered.."


That means that you have 50% chance of encountering the wandering monsters in the first 30', so you will on average encounter them 15' into the dungeon.  A party that moves 90' per turn will run into them on average in less than a turn!