Game reviews


Our World of Darkness campaign, that we began by accidentally exterminating a native American tribe from history, ended today when we accidentally reset history to a parallel world ruled by a Thousand Year Reich built on justice and honour.

In the process we went from a group of ordinary mortals struggling to understand why we were trapped in a pocket universe with a genocidal spirit, to generals of a supernatural host, leading armies of magical beasts in a war against heaven. My character, John Micksen, went from a washed-up, ageing hippy sitting alone in a bar, to Winter Knight wielding a sword out of legend (Excalibur!) and leading an army of the four courts of faerie.

We did great things while we wound our ugly and complex path to this brutal ending. In the last session alone we caused an angel to fall from heaven, destroyed an army, killed a god, had lucifer sacrifice himself to open a gate into the primal stuff of the universe, and reset the world so that an evil god never existed. As we wound our way across continents seeking the keys to the destruction of the God Machine we did great things, and saw great evil. From the first moment we opened a door in the basement of a psychiatric hospital, to find an infinite space filled with chains and cogs, we knew we were up against something relentless and evil, and our actions had to be bold, powerful and often cruel.

We started small, rescuing children from paedophiles who were smuggling them to an evil corporation; we burned the paedophiles alive and fought a fatal battle with the petty angel they served. We crossed into the land of the dead from an abandoned concentration camp to save the children’s’ souls from undead scientists who were performing hideous experiments, and while we were there we liberated lucifer himself from a thousand years of captivity. We fled destroyer angels who laid waste to whole city blocks trying to find us, hid in anarchist squats in East Berlin and vegan fascist terrorist lairs in Chicago. We dealt in pride and babies with the courts of faerie, so that we could betray a demon to a vampire, in service to a cause we didn’t yet understand. We did a deal with an ancient dragon and crept into hades to kidnap its ruler in trade for a faerie queen; that same god of death we later saved from a hideous experiment that used his essence to resurrect Jesus – and that same queen rode back into the faerie land of winter on the back of a Russian T34 tank, that our demon violinist drove. We carved a kingdom out of faerie, and bought a mansion in Ireland to connect to it using gold stolen from hell. For a while Cerberus itself (an intellectual and arrogant beast if ever there were one!) was our mansion’s guard dog, but of course we had to flee when angels came to destroy our mansion – a destruction John Micksen watched while speaking of lost love with an angel more terrible and beautiful than the sun. “The Winter Knight,” he said, after fleeing from her wrath, “Tires of this shit.”

We tired of many things, because we were constantly fleeing from great powers. We destroyed corporations digging around for the answers we sought – literally, leveled their offices and killed their officers. Anyone who helped us or even met us died – bodyguards, wives, children, allies, friends, political fellow-travelers, anyone who sheltered us, anyone who did business with us, and almost everyone who crossed us. They died in fire, the rubble of apartment blocks razed by enraged angels who sought after us, in the pits of hell or in the snowy wastes of faerie, they died chained to a steering wheel in a flaming gasoline stand or savaged by berserk werewolves on vast fields of battle. Some of them were pounded into red mist by the Winter Knight, some left to experience an eternity of frozen pain in the deepest darks of the wastes of faerie winter. Some were tortured by our enemies, or just disappeared into nowhere by ancient powers we had angered. For every one of our allies or friends who suffered, our anger grew and our list of retributions extended. We were not patient, or careful, but we did all we could to destroy those who crossed us.

We were no match for our foes. An implacable god without emotion, possessed of infinite patience, sought to change the world to suit its cold mechanical whims, and the angels that served it felt no mercy, fear or compassion. They slowly reworked the political landscape of the world to suit the mysterious machine passions of their master, turning America  into a fascist dystopian nightmare, laying waste to whole nations with plague and war, exterminating races and cultures with machine precision that no human could ever master. They sought to tip the balance in every dimension. For a short time the courts of faerie waged war against each other and a strange machine god, and all the seasons were thrown into chaos – until we intervened to restore peace and kidnap a mad faerie queen wed to a despicable machine. But for every victory our terrible foes became more ruthless and more wrathful, so that we were forced to flee, and flee again, always running and hiding.

Some of us died three times. Some of us were infected by the God Machine’s sinister viruses, rebooted, cleansed and returned to us unrecognizable. Some of us were cast down from our powers and left to rot and die, before we rose up again to take on new and greater roles. Some of us tried to strike out for freedom and failed. Some of us had to dig deep and fight hard to uncover the secrets of our past, and strike a path into the future. Some of us lost everything, rebuilt, and lost it all again. We reached our wits’ end, burned our patience, rampaged through our enemies’ lairs in rage and anger destroying everything in sight. We stole a sacred stone from Mecca, and books of gibberish from under the noses of angels that could destroy whole armies. We were epic, and constantly terrified.

All of this came down to a final battle on a dusty plane in the American mid-west, to find a gate that would change the past and the future. Our Demon Violinist opened the gate, while armies fought to end the world, and we reset everything so that all our enemies were extinguished. We triumphed! And the world was restored to an order of peace and justice that could never exist in any boring, cold reality.

Truly, this was a glorious campaign of great deeds, terrifying struggle, mysteries unraveled and paedophiles flame-grilled. It was exhilarating, terrifying, deeply absorbing, sometimes incredibly frustrating, confusing and exhausting. I don’t think it had anything in common with a normal World of Darkness campaign, and the Demon book on which it was all based only arrived for the last session. But it was amazing in its scope, its power and its content. And it ended in glory. It was role-playing at its finest!

In my recent post on principles for RPG systems I put dice pools near the top of the list, because I think they’re fun. Unfortunately, however, I think it’s hard to make a simple dice pool that doesn’t break several of the other principles in the list, and it’s difficult to make a dice pool mechanism that is satisfying. This is because of the way in which dice pools are related to skills and attributes.

Most dice pool systems are basically constructing a binomial probability distribution, with the probability of a single success determined by the success number on the dice in the pool, and the number of trials being the size of the pool. That is, in classic binomial distribution notation, if Y is the number of successes, n is the size of the dice pool and p is the probability of a success on one die (e.g. 5 or 6 on a d6=1/3 probability of success on one die), then

Y~Binomial(n,p)

The resulting number of successes is compared to some target number, that is either set by the GM or determined by the opponent’s attributes and skills. The problem here is that for every point of target number, you need more than one die to have a good chance of getting a success. For example in Shadowrun if the target number is 1 (the easiest non-trivial task) you have a 1/3 chance of hitting it with one die, just under 50% with two dice, and so on. Also you cannot get more successes than your pool, so if the target number is equal to n you can’t succeed.

The problem here is that typically your dice pool is constructed in a similar way to your defense target number when it comes to challenged skill checks. For example, if I construct an agility+melee dice pool and try to shoot someone, it will target a difficulty set by their agility+melee dice pool (or something similar). But because each point of target number requires more than a single die to have a chance of success, your attacking pool is not going to be enough to hit, in general. The systems I have played have several ways around this problem, none of which are satisfactory in my opinion. These are listed below.

Shadowrun

Shadowrun gets around the problem of equal target numbers by having both attacker and target roll their dice pool. Because the target pool will generate less successes than a target number based on the attribute/skill combination, this will always produce a lower target number than the attribute/skill combination itself. The problem here is that you have two players constructing then rolling and calculating a dice pool, and comparing results. This has the advantage of giving the player the chance to roll to avoid an attack (which gives them agency) but makes for a lot of rolls, which with large dice pools is trouble. It also introduces a lot of variation, especially at lower levels . You could simplify this by having everyone roll their defense alongside initiative, and then requiring them to keep it, but this would be unsatisfactory to many players, I think.

World of Darkness

World of Darkness (WoD) creates a whole range of problems for itself and then somehow gets around them in a bad way. In WoD your melee attack pool will be an attribute + skill, but your defense pool is just the lowest of two attributes, so it is usually much lower than the attacking pool. This solves the problem of overly-boosted target numbers, but it is deeply unsatisfactory. John Micksen, for example (my WoD Mage) has a defense of 2 (what can I say, he’s clumsy) but he has 3 dots in weaponry, specializing in swords, and he is carrying Excalibur. Excalibur! But his defense is 2! Excalibur is a +5 Holy Sword of Legend, FFS, but he gets no benefit. This is ridiculous: when magically boosted, wielding that sword, Micksen gets 21 dice to attack! But the same Micksen gets a defense of 2, three if he boosts his dexterity above his wits.

However, all is not lost! In WoD, your armour counts on your dice pool. John Micksen’s friend gives him Forces armour 5, so he gets 7 defense. Whew. The WoD rules get around the problem of unfair target numbers by having you subtract your defense from your opponent’s attack pool, and the opponent rolls the result. This seriously reduces the variance of the roll, but it also means that the imbalance of target numbers and attack pools is removed. However, what happens if your defense is greater than your opponent’s attacking pool? In this case, they have no dice left to roll! However, WoD has a rule for this: they roll a single d10 and hit on a 10. That’s right, they have a 10% chance of hitting you with a dice pool of zero.

So let’s imagine this scenario. John Micksen has a ritual casting on himself that gives him +4 strength and dexterity; another that gives him 8s again on his attack rolls; and his friend Andrew has given him Forces 5 armour. John decides he is sick of the paper boy making a noise at the gate of his mansion, so early one sunday morning he staggers out of his faerie-wine induced reverie and, leaving his lithe elven lover entangled in the bedclothes of the master bedroom of their faerie demesne, he wanders up the stairs and into mundane Ireland, picking up Excalibur along the way. He creeps up to the door unheard – this is not difficult, his Dexterity is 6, higher than most mortals (truly Faerie has changed him!), so the stupid paper boy won’t hear him. He hauls open the door[1] and springs forward, yelling obscenities, and takes a swing at the paper boy. “I am the Winter Fucking Knight[2], I do not get woken by paper boys!” he yells, rolling his 18 dice pool (he doesn’t bother wasting a point of willpower on a mere paper boy). The paper boy, however, is a cunning little yobbo and sneaky to boot, so he has a defense of 3,+1 for his woolen jacket, 4 defense for a mere villein! Now John rolls 14 dice, which with 8s again means he should get about 5 or 6 successes. This leaves the paper boy on 1 wound (that is a well-made Irish woolen jacket, not some crappy London fashion accessory!) So, the paper boy grabs his anti-dog club, and jabs it in John Micksen’s face. John Micksen has defense 3 and armour 5, for a total of 8, and the paper boy has a dice pool of 4. Result! The kid has 0 dice! He can’t hit. There stands the Winter Knight, resplendently bare-chested, but shimmering with the power of his friend’s enchanted armour, the snow-flake tattoo that betokens his position as Faerie Champion glittering cold blue light from beneath the silken radiance of the magical armour, armour that has been crafted for him in an arcane ritual by a wizard renowned throughout several planes of existence as a master of the elemental energies that bind the world together.

Oh but wait a minute, the paper boy has rolled a 10 on his one die. His anti-dog club slides through that armour like a hot knife through butter, and jabs John in the ribs, leaving a nasty bruise. The kid pulls a stupid face, yells “‘Ave ‘at, you fuckin’ pervo!” and scarpers up the path and away [well, scarpers as best he can for a kid who has just been stabbed in the face with an Ancient Sword Out of Legend by the Winter Fucking Knight, boosted to superhuman strength and speed].

This ridiculous scenario occurs because the lowest success probability in WoD is 10%, for people with an attacking pool less than their defender’s; followed by 30% for people with at least one die left in their pool. This scenario would have been the same even if John benefited from the +5 of his Ancient Sword that Unites Kingdoms. I think that’s a pretty crap rule. But it’s an inevitable consequence of trying to find a way to give some chance to people with zero pool.

Warhammer 3

Warhammer Fantasy Roleplay 3 (WFRP3) gets around this problem by adapting the Shadowrun approach into a single roll, using a dice pool that is as complicated as possible. Basically, the target’s defense (which is calculated in an arcane and annoying way) is used to add challenge and misfortune dice to the attacker’s pool. These dice can roll failures, which are subtracted from the successes that are rolled by the good part of the pool. The challenge and misfortune dice have different probability distributions to the dice that the attacker puts in the pool (attribute and expertise dice). This system has the excellent property of giving the defender a highly variable target number, along with various side effects and it completely eliminates the problem of balancing defense target numbers against attack target numbers where both are derived from attributes and skills. It is also, as far as I know, the only RPG system I have played (except Rolemaster?) that actively incorporates training into defense (in a variety of overly complex ways, of course). It also only uses one roll. The downside is that constructing and evaluating the dice pool are both complex, requiring a lot of time and effort until you’re really familiar with the system.

Some possible simplifications

The Shadowrun system could be simplified to work in one roll by adding d6s of a different colour to the attacker’s dice roll, and having 5s and 6s on those rolls cancel the 5s or 6s on the attacker’s dice. This is basically the WFRP3 single roll, without the complex dice. Basically this is what WFRP3 needs: a simpler way of constructing and calculating dice pools. You could set up the game table with a large pool of white and red d6s in the middle of the table. The attacker grabs his or her number of whites; the defender grabs his or her number of reds and then passes them to the attacker; the dice pool is then rolled, and the result counted. Alternatively, dice pool construction in WFRP3 could be simplified by leaving the roll of challenge and misfortune dice for the GM; the player only sees the dice he or she rolled, and the GM then calculates the result.

Another possible simplification is to find a way to make attack rolls have more dice than defense targets. For example, if you could add your level to attack rolls, but not to defense target numbers; or if your defense target for any challenged skill check (including combat) was your attribute divided by 3 (round down) + skill, so that most attack pools are larger than target numbers; and also make sure there is a method for boosting attacks (e.g. Edge/Fate/Willpower) etc. Note that with larger dice pools these boosting methods tend to be a waste of time (see e.g. John Micksen), but if you are striving for more contained dice pools, then it probably would work. Of course, no one likes dividing numbers in play, but most character sheets have a place ot write defense; you could have a “defense” section after each attribute, which tells you the value it applies when being used for a defense target.

Another possible dice pool mechanism I thought of yesterday but haven’t done any calculations on, is one in which there is no target number, but the target’s skill+ attribute determine the minimum number required to hit. For example, if attributes start at 2 or 3 points, and skills at 1 or 2 points, then target numbers would range from 3-5. The attacker could then roll e.g. d10s, and get success on any die that rolls above this number. If the target were above 9, then success would only be possible on rolls of 10. So for example you have a dice pool of 5, and your opponent has a target of 5; you roll your five dice and need to get over 5, which basically means that your outcome will be Binomial(5,0.5), giving an “average” of 2.5 successes. Were your opponent’s difficulty 9, you would need to roll 10s, and the chance of getting 1 success would still be pretty good, but little chance of a big success.

I have also been thinking about a concept of what I call success pools, which incorporate post-attack damage values into a coherent framework for all skills and challenges, and could be used to fine tune some of these dice pool mechanisms. I will have more to say about that later.

I don’t think any of the systems I have described here, or their simplifications, are ideal, though the Shadowrun and WFRP3 mechanisms are pretty good (aside from their cumbersome aspects). Shadowrun is fine until you start calculating damage, I think; WFRP3 is fine if you make sure that the only complexity in it is the dice pool (i.e. you drop most of the rest of the game). But they show the difficulty of making a balanced dice pool mechanism, and how there always seems to be a compromise somewhere on the way when you try to introduce a decent random number generation system based on dice.

fn1: With his ritual on, John Micksen has strength 7, so he doesn’t so much haul the door open as launch it into orbit

fn2: John Micksen has some rage issues.

Fantasy Flight Games have announced the completion of the Warhamer Fantasy Role-playing Game 3rd Edition (WFRP 3) “line,” i.e. they’ve decided to stop producing any material for it and move on. I suspect this is at least partly because it was not very popular or successful – it’s a somewhat unusual form for a role-playing game, and also very expensive. I suspect a lot of people gave up trying to get the whole experience to work, and it didn’t sell as well as it needed to given its huge production requirements.

I played one and a half campaigns of WFRP 3, in English and Japanese, and from my experience I think that in many ways WFRP 3 was a revolutionary and exciting game. It imported a lot of ideas from board-gaming to provide improved ways to manage PC resources, skills and powers, and used a really interesting dice mechanic to generate rich and complex results for PC actions. Unfortunately, the mechanics are complex and fiddly in practice, requiring lots of space, huge amounts of tokens and a lot of fiddling. The dice mechanic is also just that little bit too complex for GMs to intuitively understand, making it hard for them to design and run adventures, and I don’t believe that Fantasy Flight Games ever came  up with a good way of handling monsters and providing GMs the proper resource- and system-management tools and tips they need to make the game work. I think this is likely a killer in a role-playing game – if you can’t make the complexity accessible and manageable to the GM, you alienate the central 20% of the gaming population that are essential to making the game sell (since players won’t bother buying books for games they can’t find GMs to play with!)

After WFRP 3 Fantasy Flight Games released the Star Wars system, which uses a stripped down and simplified version of both the action system and the dice system from WFRP 3. The Star Wars system seems to be much more accessible and easy to play, and has better introductory material, and may be more practical as a novel game system. I haven’t tried it yet but expect to soon. I have also simplified WFRP 3 and GMd a really cut-down system in a different world, and I found that once it is stripped down to just the dice and skill system it becomes a really neat little system. It is my hope that Fantasy Flight Games will use their experience of Star Wars to develop a simplified, stream-lined classic fantasy RPG based on the WFRP system without all the bells and whistles, using all their experience to date. If they do that, I think it could be a really good way to play fantasy.

In the meantime I hope to use the simplified version of WFRP 3 for more adventures in the Compromise and Conceit world, where I think it works as a system. I won’t be buying more WFRP 3 stuff, but I will be continuing to play around with what I think was a very promising and innovative way of gaming. Let’s hope for more reports in the future …

Eerily romantic

Eerily romantic

I have recently been exploring the shadowy and terrifying world of the Neath, in a fascinating and quite engaging game called Sunless Sea. This game is set in a location called Fallen London, an scattering of island archipelagos on a vast underground sea, which was formed at the conclusion of a previous game from the same company, Fallen London. This sunless world is an ocean in a deep cavern, full of horrors and strange stories. The game is viewed from above, essentially on a map, and you play the captain of a steamship who is plying the Neath (the name of the underground ocean) trying to become famous or rich or both. Based in the town of London, you travel between islands trading, picking up stories, fighting pirates, and doing the bidding of mysterious powers. Travel across the darkened seas is fraught with risks, however: in addition to the risk of running out of food and fuel and having to eat your crew, there are also pirates, monsters, and the ever-present growing fear of the darkness. Journeys have to be carefully spaced to ensure you can return to London before the fear mounts and your crew mutiny on you, or the nightmares consume you. There are also mysteries to unravel, and stories involving different organizations and kingdoms.

Strange shops in a strange world

Strange shops in a strange world

The game is viewed from above and there are no animations for battles or encounters, just text-based interaction as shown in the picture above. However, despite the lack of animations the graphics are very stylish and engaging, and very carefully build the sense of terror and weirdness that pervades the game. Drawn a little like a comic, but with a grim wash, and with a writing style that is a mixture of dark humour, Victorian prose, and elegant horror, the narrative really gets you involved in the world. It’s also quite challenging, and if you play it the way it is intended, death will be a common event. As the game progresses and the stakes get higher, the struggle with terror also becomes quite consuming, as you try to balance your need to travel the dark reaches of the farthest-flung islands with the compulsion to keep your terror from overwhelming you.

The game has a few flaws, however. First of all it has quite a sedate pace, so if you’re the kind of gamer who needs edge-of-the-seat energetic game play, it will probably bore you. Also, sometimes the mission details are hard to access, and the game doesn’t tell you when you have completed a task (in some cases), so you can feel lost at sea (literally!) when in fact you have met the conditions of a quest. It is also difficult to piece everything together into a coherent story, so sometimes it feels like the game just intends for you to grind, grind, grind – I still don’t have a sense of a unifying story or theme to the game, and I’m not sure if it will hold my attention if it does not have a theme. It is also quite hard to make money, though I have begun too, and the rules aren’t very deeply explained, so you spend a lot of time making pointless mistakes at first, and I suspect some players have given up early on because of this. However, once you’ve died a few times and googled a few things, the peculiarities of the world and its systems will begin to make sense.

With that in mind, I thought I’d produce here a list of tips for how to play, based on what I have learnt so far.

  • Always have good stocks of fuel: at first you will only be making small amounts of money, and may find it difficult to purchase things like weaponry; don’t give in to the temptation to spend your cash on a bigger gun when you don’t have much spare, because if you don’t have much fuel, you will find yourself unable to travel to make more money. Always retain enough fuel to at least be able to do a tomb-colonist run, so you can replenish fuel on the return. And always ensure you have enough fuel for the return journey when you head away from London – it is expensive everywhere else (except Palmerston) and if you run out on the high seas you are in big, big trouble
  • Keep your terror down: It is extremely hard to get your terror down from high levels, and/or expensive, so keep your terror down. The main way to do this is to sail through lighted areas, or close to shore. Sure, the pirate raiding requires that you sometimes sail away from the buoys, but you need to make sure that when you travel you stay in the light as much as possible. Especially on long missions, or missions which are going to themselves raise your terror (and many do!) you don’t need to also be burdened with terror built up through frivolous course-tracking
  • Take the blind bruiser’s gift: the only consequence is that later he will ask you to deliver some souls to a far-away place, and you will make your first big cash of the game when you do that
  • Build up admiralty’s favour: it gets you more lucrative and interesting missions, and access to cheaper repairs
  • Keep visiting Hunter’s Keep: Hunter’s Keep is very close to London, and spending time with the sisters will get your terror down. It may seem boring to drop in on a place where you keep having the same conversations, but that soon changes. Hunter’s keep is one of the first stories to reach its resolution, and if you play your cards right you can emerge from the ruins of the story a lot wealthier than you were at the start
  • Watch your nightmares: When you return to London with terror>50 points it automatically resets to 50 (which, btw, is not good!) but your “nightmare strength” increases. Nightmares on the high seas can lead to trouble, including higher terror and ultimately mutiny. It is extremely hard to get your nightmare strength down, but there is one surefire way: travel to the Chapel of Lights north-east-east of London, and visit the well; you can make a sacrifice here and though you incur a wound, you lose nightmares. Do this twice and you can get rid of almost all your nightmares (though having 2 wounds is very risky)
  • Go bat-hunting: bats are easy to kill, and if you throw their corpses overboard you lose a few points of terror. This is the only relatively reliable way I have found to get terror down a lot, though it is not cheap. Basically if you hang around a buoy near Venderbright (or the island of Tanah-Chook, near Venderbright) you will be regularly attacked by bats, but will gain no terror from your location. If you kill 10 or 20 swarms of bats you will get your terror down by 15-30 points, which is really useful. It will cost you in fuel and supplies, though you can recoup the supplies from bat-meat, so make sure you have spare money and fuel before you do this. I think terror affects your abilities, so it’s good to keep it low
  • Torpedos are useful: keep a few in reserve. I was ambushed by a Lifeberg on my way back from the Avid Horizon, and in a moment of desperation I unleashed some, that did it a lot of damage. I took some hull damage but it kept me alive. They cost a lot, but they can be fired early in the battle and do a lot of damage. Combat in Sunless Sea works by increasing illumination until you can see your enemy enough to shoot them, but for the bigger enemies (like Clay Pirates and Lifebergs) you need illumination 100 to get in a really good salvo against them. Getting to illumination 100 without getting sunk is extremely difficult, but torpedos do damage similar to a powerful gun salvo at illumination 50, so if you get ambushed by something much tougher than you they can be a handy way to get out of trouble
  • Keep visiting the old dude in Venderbright: At some point in Venderbright you will get the option to talk to the head of the tomb-colonists, who gives you a mission to explore and find the colours from 8 or so pages of a book. I found two of these colours but the game didn’t tell me I had them, and it took me ages to visit the old dude again. When I did I got an item worth 500 echoes as a reward. So my advice is, once this mission has been unlocked, visit the guy regularly because you can’t be sure you have achieved one of the goals, and the money is worth it. A lot of people say that trips to Venderbright aren’t worth it, but I don’t agree. Not only can you make a bit of money selling news and colonists, but when you explore you can pick up quite valuable artifacts, and as a stop on the way to places further afield, it’s a good way to make a bit of money and get your terror down a bit. Plus some of the story options (the Bandaged Poissonier, Jonah’s revenge, the old dude with the book) can be valuable for you later. So I recommend continuing to visit here.
  • Always go coral-picking at Port Cecil: a single scintillack is worth 70 echoes.
  • Always collect port reports: they can fund your trips, and the admiralty will pay for them no matter how many times you give them
  • Grab stray chances: someone left a coffin on the docks for me once. I took it, and it opened up a whole new island for me. Take any chance you are given!
  • Avoid fights with bigger ships: sure, you can defeat the clay pirates, but unless your mirrors stat is very high you will take hull damage, which will cost about 50 echoes to fix, and all you will get in exchange is a few supplies or a bolt of parabola-silk or something – the maximum profit will be 20 echoes. You can make 20 echoes from a steam pinnace with zero risk. Avoid them.
  • Use the alt-f4 cheat: I’m playing on a mac, I don’t know how to do alt-f4 but I can still do control-command-escape or whatever, and kill the game when I die. Once you are a long way into the game, dying is not such a great idea, so be ready to do this – when you die, kill the game or load before you save, so that you can restart from your last port of call. Otherwise, you have a long upward climb ahead of you …

I think that’s it. I’m slowly gathering stories and trying to find out where the game goes, and I’m not sure if I will finish it (or if it can be “finished”, per se) but I’m enjoying the experience of this new world. I think it would also make a disturbing and evocative role-playing world. If you’re into cthulhu-esque horror and don’t need fancy graphics to make your games fun, I strongly suggest this game. It can be a bit irritating at first, but once you get up and running it’s a really rich and pleasant experience!

Last  week I had the opportunity to play an extended session of D&D 5th Edition, using the pre-generated characters and adventure from the starter kit. We had three players so I played two PCs: an elven wizard called Althiel Moonwhisper (Chaotic Good, indeterminate gender, overly elegant in speech and manner but completely lacking in empathy or social skills); and a human fighter called Xander (Lawful Neutral, fancies himself a noble, but turns into a savage, violent bastard when fighting with his great axe). This post gives a few of my first thoughts about the newest version of our old and faithful system. I didn’t have the rules myself, nor did I read them, so what I report here is based on my experience of the rules as played and as dictated to us by the GM, who assured us he wasn’t house-ruling anything – but we’re a fairly rules-light gaming group so we didn’t kill ourselves trying to answer questions about rules. The rules can be downloaded from here.

First of all, it’s good; and secondly, it’s not really very new. It is essentially a backward step into 2nd edition in feel, using a stripped-down version of the 3rd edition rules and keeping almost nothing from 4th edition. It retains the d20-and-skills structure, ascending armour class and base attack bonus of 3rd edition, but with major simplifications and reorientations to rebalance power. Skills and weapons work on the basis of a d20 roll vs. target DC, modified by an attribute plus proficiency bonus. Proficiencies can exist in weapons and skills, so my wizard had about four skill proficiencies (from memory) and a range of weapon proficiencies (from being an elf). The proficiency bonus at first level for all of us was +2, so depending on attribute bonuses we got total modifiers ranging from +1 to +7 in our core skills, and -2 to +5 outside of them. Proficiency bonuses increase by +1 per 4 or 5 levels, so it’s no longer the case that you’ll have a fighter at 9th level with a +9 Base attack bonus. Essentially attack bonuses scale more slowly than they used to, which keeps them more in line with armour classes. Fighters are the only class that get extra attacks, and I think they also get other attack bonuses and damage bonuses, so the reduced increase in attack bonus is made up for (we thought). Thieves also have less advantage at first level (recall in 3rd edition the skill system meant thieves could get up to a +4 base bonus in a range of skills if they had good intelligence). The skill system has also been stripped down so there is a smaller and more manageable number of skills (only a few more than Warhammer 3, by way of comparison). The reduced importance of the proficiency bonus means that if you need to do something directly covered by these skills, a simple attribute test will do the job. So that makes the GM’s job easier (though maybe this will become more problematic at later levels).

Most of the ideas from 4th edition have been dumped. Things like daily/at will/encounter powers are gone, and the idea of short/long rests introduced. There are no “recoveries” but fighters can recover d10+lvl HPs once between short rests, and once a day a wizard can recover some spell slots in a short rest.  The short rest is a really good idea, enabling parties to partially regroup once in a day, which seems consistent with how I can imagine adventuring groups actually working (and, incidentally, we really needed this short rest). This short rest/single recovery approach keeps the basic idea from 4th edition of being able to regroup and recover some of your damage, without making it so flexible and powerful that the challenge drops out of the game, and does open the possibility of a group of PCs taking on a fairly lethal adventuring task without a cleric, and having some options other than skulking around and running away, since if a brave assault goes pear-shaped they have something to fall back on.

The biggest system change I could see was in the way magic works. In overall style it is a flexible mix of 3rd and 4th edition, but consistent with the feeling of 2nd. Wizards have spell slots, arranged by level, and they are quite restrictive (my first level wizard had 2). They can memorize something like their lvl+Intelligence bonus in spells per day, and these can be of any level they know. They can then shuffle these between slots as they like. For example, my wizard had 6 spells in his/her book, but could memorize 4; he/she could use 2 slots a day, taken from any of these 4 spells at will. This gives flexibility without borking the idea of spell slots, and without quite going all the way into power points. Any spell can be cast out of combat as a ritual without using a slot, so Althiel didn’t bother memorizing detect magic. This gives wizards flexibility as utility casters, but doesn’t suddenly give them the ability to do anything in combat. The best improvement, though, was to give wizards cantrips at will, and to make the combat cantrips more powerful. This essentially means that a wizard has a basic attacking power that does 1d8 damage and hits on an intelligence check vs. AC, but which doesn’t scale with level. It was also cute to see that the Sleep spell and been reset to 2nd edition power: it affected 5d8 hps of enemies, which was just great when we entered the goblin caves, and really brought back that feeling of the wizard as once-per-day artillery. These change meant my wizard could participate in every combat effectively, but without the destructive power of rogues or fighters, so he/she could deploy bigger spells without fear of being completely useless once they were used. The short rest recovery option got him/her back one slot, which meant that Althiel could be useful three times in the day. This makes playing a wizard fun from first level, without making them indestructible artillery. There is no sense of controller/striker/tank as was often complained about in 4th edition: wizards and clerics have gone back to their utility roles, and although the rogue’s backstab is more frequent than in 2nd edition (it works whenever an enemy is engaged with someone else), it is not a multiplier, just a +d6 per couple of levels, and the rogue is very much a glass cannon – ours died in the third combat. In fact our rogue wasn’t so useful – trying to explore a goblin cave complex with a halfling rogue who can’t see in the dark is pretty challenging, and we couldn’t find any evidence that the rogue was particularly good at finding or disarming traps (there is no disarm traps skill!) I think the rogue would be more useful at higher levels, and for scouting in a more suitable environment (the rogue’s stealth skill was quite awesome).

The system has also responded to the way people actually play in some minor but polite ways: any PC can sense that an item is magic by touch, we could check the use of potions by sipping them, and in general the rules on actions and movement were a little looser than in the horrors of 4th edition. Battlemaps are no longer essential, though the rules are still structured around them. Movement rates were relevant in our battle map, but we didn’t spend long periods of time fiddling around with the details of movement. Combats were over relatively quickly, without huge amounts of fiddling, though this will likely change at later levels. This edition of D&D also seems to have dropped the hideous complexity of feats, one of 3rd edition’s clunkiest and most unbalancing aspects. Each class gets a few bonus powers and special abilities, but feats don’t really enter into the development of the class. As I understand it you get a feat at 4th, 8th etc. level but you have to forego an ability score modifier to get it. That enables players to avoid a huge set of complex and frustrating decisions that can really unbalance the game (though at the cost, I guess, of some degree of character diversity at low levels), and makes character creation faster. Also I think when feats do arise they’re going to be big game-changer moves. D&D and AD&D both had relative conformity within character classes (all members of the same class were very similar at first level) and this version of D&D has returned to that, but with a little bit more diversity through skills and unique starting abilities based on package choice – the core rules we used specify only one domain for clerics, but each cleric domain will have slightly different spell choices and some difference in abilities, which was most noticable in the fighter (which had five different starting types available, each with its own skill – Xander was a defender, meaning he gained +1 to AC when wearing armour). I think this idea of broad brushes with small changes in detail that are primarily fluff – due to small differences in skill, and background character descriptions – is more consistent with older brands of D&D, but doesn’t make characters as completely cookie-cutter as they were in those older systems. So, again, a nice balance between the complexity and chaos of 3.5, and the wargaminess of 2.

This edition of D&D has also introduced the dice mechanism of advantage and disadvantage, which replace +2 bonuses/-2 situational modifiers. This system requires the player to roll two twenty sided dice and take the larger or the smaller of the rolls, respectively. Andrew Gelman’s blog has a discussion of how much difference this makes to outcomes – suffice to say it’s huge – but it is a nice way to enhance attacks and I think will retain its power across levels (as opposed to a +2 bonus, which loses value at later levels in 3rd edition, especially for fighters). There are other small changes too, but overall it feels like a fast-flowing, relaxed and less finicky version of 3rd edition, dialed back perhaps to the freewheeling feeling of 2nd edition, without the deep nerdy clunkiness of that old-fashioned game. It has still kept a few of the basic problems that i think make all versions of D&D look a bit dated:

  • Uniform distributions for skill and damage resolution make long chains of bad results and good results inevitable, and make it hard for players to make plans on the assumption that PCs will be able to do well what they are meant to be good at on average
  • The step from 1st to 2nd level still contains that huge power leap as your hit points double
  • It still has that strange incongruity between the combat mechanics and the explanation of how hit points are supposed to work – e.g. at 4th level the fighter gets an extra attack rather than just rolling once and doing more damage, even though combat is supposedly abstracted, so that the d20 roll doesn’t reflect a single discrete attack
  • It has still stuck to the general principle of spell slots, which I still find restrictive and dumb – a system that keeps the richness and diversity of 2nd edition spells, but makes wizards fully functional as spell-users would be much better, in my opinion

Overall though the system is broadly functional again, retaining the best aspects of 3rd edition/d20 but stepping away from the depths of complexity that were beginning to make that system a fractal nightmare (and which have, in my opinion, turned Pathfinder into a form of intellectual interpretive dance rather than a RPG). It has gone back to the simpler days of basic D&D, with the adult feel of 2nd edition but the sense and practicality of 3rd edition. Fortunately, 4th edition has basically been dropped: we can all breath a sigh of relief and put “that little unpleasantness” out of our minds for good.

A word on the introductory adventure too: it is a rich and detailed little gem, starting off with a goblin ambush and opening up slowly into a whole sandbox built around a town undergoing something of a renaissance, but under threat from complex and apparently inter-related forces of human and demi-human evil. It has side adventures, a cast of characters that the PCs need to interact with as more than just purveyors of level-appropriate treasure, and enough detail to form a mini-campaign by itself. It is also linked to the process of learning the rules, so that as you step through stages of the campaign you are introduced to more complex and detailed aspects of the game (e.g., random monsters don’t occur at the beginning of the adventure, so the GM has time to get used to the system before having to handle that most irritating of distractions).

Overall I think this system is a good forward step in the D&D oeuvre, though hardly a radical advance in game design. It’s a return to the solid and respectable traditions we all know and understand, recognizably D&D again but with enough sense to revise some of the old-school version’s weakest points, and enough wisdom to realize that game design really has advanced since the 1970s. I will certainly be trying to play it again, because it rekindles some of the enjoyment I felt when I first returned to D&D through 3rd edition, before its complexity blew into orbit. It will be interesting to see how Pathfinder and the Old-School rip-off world respond to this system – it could be the death knell for both of them …

Aggressiveness: 10. Ferocity: 10.

Aggressiveness: 10. Ferocity: 10. Come visit his country …

As some of my readers know, I have been having fun conquering the world as Japan in Hearts of Iron 2, and that I’m reporting it all cynically in the tone of a Japanese leader forced to war to defend Asia against colonialism. Before I played Japan I had a go as Germany and didn’t do very well – the Soviets declared war on me in 1942 (I can’t think why!) and I got wiped out because my army was busy trying to secure oil in Africa.

Something noticeable about Hearts of Iron (HOI) and its successors is that there is no genocide option, even though some people believe the Holocaust was crucial to German war aims and so should probably be in the game. I understand that there is some debate about whether the Holocaust was a net benefit for the Nazi war machine, but some historians argue that the Holocaust policy developed slowly, piece-by-piece, in response to changing economic and industrial demands, and was actually primarily driven by the need to secure economic resources, especially food. Taking this as the basis for the Holocaust, it’s easy to imagine that a mechanism to represent it could be included in the game, to make it easier for certain countries to develop rapidly in the run-up to total war, or to respond to war needs.

The easiest way would be to incorporate a slider, that runs from 0 to 100 representing just how horrific your intended genocide is. Maybe 5 just means marriage and employment restrictions, while 100 is the fully mechanized destruction of entire races. The process is abstracted, and essentially represents a transformation of money, manpower and transport capacity into a reduction of supply needs and an increase in industrial capacity (or even an increase in supplies). This is pretty much what the historians I linked above argue: that the Holocaust was designed the way it was in the steps it was because it was aimed initially at seizing the economic assets of European Jews, to make production more efficient, and then at restricting their food consumption in order to ensure that other Germans didn’t starve. This is also what Stalin was doing with his “dekulakization” in the 1930s – forcing small, unproductive landholders off of their smallholdings into large collective farms, and because these farms were intended to feed many more people than those who worked in them, the excess population of smallholders would have been an economic deadweight – hence they were sent to the camps to die. Plus of course, when Germany invaded Eastern Europe they expropriated huge amounts of food and money, and essentially instituted a policy of starvation to ensure that no untermenschen used food that could have been feeding Germans. Under this analysis of the Holocaust, it was beneficial for the German war effort. If so, it should be modeled in the game in the interests of historical plausibility[1]. Wouldn’t it be great if when you were starting to lose you could slide your slider up to 100 so that you weren’t vulnerable to blockades? The computer could even use the demographic composition of your empire to give you options about which race to exterminate. We’re all about historical plausibility, right?

Suggesting such a process sounds kind of sick, doesn’t it? Which is why Paradox Interactive made a specific, explicit decision not to model this in the game. I remember somewhere a statement from Paradox about this, but I can’t find it any more – maybe it was in the Hearts of Iron manual that I no longer have. Anyway, we can find this on their forum rules for HOI3:

NOTE: There will not be any gulags or deathcamps (including POW camps) to build in Hearts of Iron3, nor will there be the ability to simulate the Holocaust or systematic purges, so I ask you not to discuss these topics as they are not related to this game. Thank You. Threads bringing up will be closed without discussion.

NOTE: Strategic bombing in HoI3 will be abstracted and not allow you to terror bomb civilians specifically. Chemical weapons will also not be included in the game. Any threads that complain about this issue will be closed without discussion.

Not only did they decide not to model these things, but they make very clear that they aren’t going to talk about their decision. We all know why: games that model the holocaust are beyond poor taste, and any gaming company that included such a mechanic in their wargame would be toast pretty fast.

It is, however, okay to model genocide in Europa Universalis 3. Yesterday commenter Paul pointed me to this post in which someone trying the game for the first time talks about how uneasy the colonization process makes her feel. I agree with a lot of this writer’s criticisms of the way the Native Americans are portrayed in the game, and I would like to add two.

  1. Terra nullius: by making colonizable land grey and devoid of units or cultural structures of any type, the game essentially buys in to the legal fiction of terra nullius – that no one owned the land or had a use for it before white people came. This legal fiction was overturned in Australia in 1994, and where not openly declared the general principle often underlay the willingness of white invaders to breach treaty agreements (as they did again and again, for example, when dealing with native Americans). In the game, although the natives are known to be there (you get a count in the colony window), they are not represented as unit types and structures the way Europeans are – the land is not owned in the sense that European land is owned, it just has some people on it. Terra nullius is a pernicious and evil concept that does not reflect the actual state of indigenous life, only the racist perceptions of the colonizers, and it’s sad to see it being reflected so clearly in this game
  2. Elision of native struggle: A common phenomenon in western popular and academic depiction of colonization is the minimization or dismissal of indigenous struggle. This is very common in Australia, and until the publication of Blood on the Wattle, popular understanding of Aboriginal history was that they didn’t really fight back, a belief that derives from early 20th century racial ideas of Aborigines as “weak.” Obviously in the US this is not so readily done, but for example the Sand Creek Massacre used to be referred to as the “Battle of Sand Creek,” though there were very few Indian soldiers involved, and popular lore about Custer’s Last Stand doesn’t usually include awareness that he was attacking a civilian camp at dawn when he was beaten. In the game, native struggle is implied in the aggressiveness and ferocity statistics for each province, and the effect they have on colony growth, but it is not actually visible or witnessed through the need to coordinate military actions against active opponents as happens in any European conflict between even the most irrelevant powers – it is a low background noise to your successful colonization, mostly

I think these two points show that the designers of Europa Universalis haven’t just implemented a game with a colonization strategy; they have implemented a game with a colonization strategy that implicitly reinforces common modern misconceptions about how colonization worked that tend to underplay its genocidal and military aspects (see also the way natives are absorbed into your population once it becomes an official province – this takes about 20 years and is in no way reflective of how colonization absorbed real native populations – such absorption took more than 100 years in Australia, for example, and only occurred at all through massive force and state coercion). I don’t really think this is a moral decision, but I also don’t think it’s defensible. There are lots of other ways that the game could have been designed, from making America the same as Asia to having a single Native American “state” and a different conquering mechanism – or, as April Daniels suggests, just a better and richer experience playing the Natives. There is DLC for this, but that’s not a defense, and neither are the butthurt bleatings of the gamers in the comments. It’s also noteworthy that the people attacking Daniels in comments of that blog are tending to subscribe to the same misconceptions that are buried in the game itself – there wasn’t much war, might makes right, smallpox did it not us!, natives really did get merged into the colonial population without a fight! This kind of response just shows that the west hasn’t come to terms with its colonial past yet.

So here’s what happened: Paradox spent years developing a game set in Europe in which they explicitly avoided modeling a genocide that occurred in Europe and that was crucial to the historical plausibility of the game; they also spent years developing a game set in Europe in which they explicitly developed a model for genocide that occurred outside Europe and that is crucial to the historical plausibility of the game. The former decision was probably (to the best of my recollection) made for moral and political reasons; defenders of the latter decision want me to believe it was for game mechanical reasons, even though the model they developed happens to reproduce some common misconceptions about how the native American genocide unfolded. I’m unconvinced. I think the designers didn’t consider one genocide to have the same weight as the other. Which isn’t to say that they consciously made that decision, but neither did all the cowboy movie directors in the 1980s who made multiple movies that included the Sand Creek Massacre, but didn’t ever get around to depicting Babi Yar from the Nazi perspective. Our culture makes some stories acceptable even though they are steeped in evil, and some stories unacceptable. Many people reproduce those stories without thinking, and that is what the designers did. (It’s also worth noting that Paradox is a Swedish company, and Sweden was not a colonial country in recent time; maybe for them the horrors of world war 2 are much closer than the horrors of genocidal America, and everything that happened in that period in those far-flung places is just a story).

I think there are some big questions buried in EU3, which we also need to ask when we play GTA or watch some nasty slasher pic, and April Daniels asked some of those questions in her blog post. Those questions are also relevant to the genocide issue in EU3 but they’re bigger than that. Why do we make games about war and killing at all? Why do we think it’s okay to drive around LA killing cops but we universally object to rape stories? Why are we so complacent about the destruction of whole cultures in Australia and America, but so touchy about mass murder in Europe? And why do some fanboys get so stupidly butthurt when people who enjoy the game (or the movie) analyze it a little more critically than wow!wow!wow!? My Ottoman Empire has begun its colonial project, in Cameroon and Cayenne and St Helena, and I’m playing that part of the project with the same sarcastic amusement with which I describe the Empire’s “reclamation” of knowledge in Northern Italy; I will probably kill a lot of natives if I have to, and convert the rest[3]. I’m not particularly fussed about this. But I’m also aware that this game is racist on many levels, and it includes genocide as a central mechanic. Some people may not be comfortable doing that, and they may want to write about it. I think it’s possible to simultaneously enjoy the game and accept these things, but I also think the game could have done better on this issue. If I’m going to kill natives and steal their land, why should it be different to the way I kill Germans and take their land – is there something the designers want to say here? There is a long, long way to go before people in the west can accept and understand the genocide that made America and Australia possible, and the deep wounds colonialism left on Africa. Until we do, I guess we can expect that games like EU3 will fall short of genuinely trying to describe the histories and cultures of the people who were exterminated.

fn1: though actually a very interesting experiment would occur if paradox were to include the Holocaust as a single historical decision that was actually bad for the German war effort, and secretly spied on players[2] to find out how many clicked “Yes, do it!” even though the decision is negative.

fn2: or used NSA data

fn3: actually since I westernized[4] I’m so far on the “open-minded” slider that I can’t actually generate missionaries, so I can’t convert anyone. I’ve conquered so much of Europe that my culture is more christian than Muslim. What to do…?

fn4: racist much?

Shadowrun uses a skill check system based on dice pools and opposed checks. The basic mechanism for opposed checks is quite simple: each party constructs a pool of d6s based on their combined attribute and skill score, and success occurs on a 5 or 6. The person who rolls more successes wins, and the number of successes decides their degree of success.

When I saw this system I thought that there must be a way to recalculate it as a single dice roll. A dice pool of this kind is essentially binomial distributed, and the sum of binomial distributions is binomial, so I thought that the difference of binomial distributions would also be binomial distributed and it would be fairly easy to obtain analytically a formula for a new dice roll based on the probability of success (1/3) and the number of dice in each pool. In fact the difference of two binomial distributions is not binomial (see my appendix below) and the dice pool mechanism is quite complicated. In the case of dice pools of equal size it creates a symmetric, non-binomial distribution that tends towards normality as the size of the dice pools increases; for uneven numbers of dice it creates an appropriately skewed distribution that has no easy calculation formula. In fact, it is fairly easy to show that for equal numbers of dice in the conflicting pools, the probability of success tends towards 50% as the size of the dice pools increases.

To show this, I wrote a simple program in R that calculates the probability of success for opposed dice pools ranging in size from 1 die in each pool to 30 in each pool. I ran the simulation for 10000 rolls for each dice pool, and calculated the probability of success for each roll. In all cases the dice pool of the opponents are of equal size and the success probability is 1/3, as in the standard rules. Figure 1 shows that as the number of dice increases the chance of success tends towards 0.5. That is, a PC with skill and attribute of 10 each, and modifiers of 10, when doing an opposed check against an exactly equally matched PC, will be successful 50% of the time; whereas the same situation for characters with just an attribute and skill score of 1 will show a vastly reduced chance of success.

Figure 1: Probability of success in opposed checks for equal dice pool sizes

Figure 1: Probability of success in opposed checks for equal dice pool sizes

I’m not sure whether I like this outcome or not. Superficially, given low-skill characters are more likely to fail generally, it makes sense that they should be more likely to fail against an opponent of equal skill. But then, it seems reasonable to suppose that the chance of success when opposed by someone with the same skill as oneself should be constant. Which assumption is better? In WFRP3, difficulty of the check is set by the opponent’s skill but is not random, and usually involves competing against dice with a higher chance of generating failure than one’s own dice have of generating success. Is this a better model? Other dice pool systems probably use a fixed target number – is this better? Maybe a fixed target number can be manipulated to generate a fixed failure rate (if it is based on the contrast of the PC skill and the NPC skill). But then again, this opens the possibility that PCs can do better in opposed than unopposed checks. For example, in Shadowrun, when doing an unopposed check the maximum probability of success for a PC with attribute 1 and skill 0 is 1/3. Presumably when they oppose someone with attribute 1 and skill 0 their chance of success should be less than 1/3? If one accepts this proposition, then Shadowrun is perfectly balanced, and the only question is how long it takes to get to 50% success. This pace can be changed by using different success targets and dice sizes: for example, a success threshold of 7 on d10 slightly reduces the chance of success for any given dice pool.

Note that by the Strong Law of Large Numbers, it is impossible to change the limiting probability for opposed dice pool checks, no matter the threshold probability or the die size. This is because as the dice pool grows in size each dice pool becomes increasingly close to normally distributed; but when subtracting one normal distribution from exactly the same normal distribution there is, of course, a 50% chance of getting a positive number. So as the distributions get more normal, so too does the average chance of success tend to 50%. Increasing the dice size and reducing the success threshold will delay the onset of this 50%, but Figure 1 shows that for most PCs and most campaigns, d6 will suffice.

Given these results, I think that the Shadowrun dice pool system is pretty close to perfect; and there is no easy way to modify it or any similar dice system to get more nuanced results. I will shortly be examining WFRP 3 dice systems to see if they produce more subtle outcomes. Stay tuned!

Appendix: Proving that the difference of two Shadowrun dice pools is not binomial.

When both the PC and their opponent have a total skill of one, the opposed check becomes a challenge of 1d6 vs. 1d6. In this case there are three outcomes: -1 success (opponent wins and PC loses); 0 success (both win or both lose); +1 success (PC wins and opponent loses). For a single success probability of 1/3 the probability of each event can be easily calculated without special mathematics as 2/9, 5/9 and 2/9 respectively. This means that the probability of -1 and +1 are equal. If this distribution is binomial, then it can only occur from a binomial distribution with 2 trials and a probability of p, since this is the only binomial distribution that allows three distinct outcomes. Thus if we calculate the probability of 0 successes or 2 successes under such a distribution and set it equal to the extreme probabilities obtained for the 1 vs. 1 shadowrun check, we can see the conditions under which they are equal. Under a binomial distribution with probability p and 2 trials, the probability of 0 successes is (1-p)^2; the probability of 2 successes is p^2. Comparing with the 1 vs. 1 Shadowrun check, we see that these two probabilities must be equal (as they are in the Shadowrun check). That is, p^2=(1-p)^2. This is only possible if p=1/2. But in the Shadowrun check p=1/3. Thus, by contradiction, the Shadowrun check cannot be binomial. If any one check is not binomial then it follows that we cannot expect a general rule in which checks are binomial. Thus, through contradiction, Shadowrun opposed dice pools are not binomial and no formula can be deduced which will enable calculation of binomial probabilities in Shadowrun.

For general opposed dice pools, the probability distribution is obtained by calculating the cross-correlation of the two binomial probability densities. An equivalent calculation for the Poisson distribution is shown in Wikipedia (the Skellam distribution) and is obviously nasty – it involves Bessel functions, which is an immediate “do not enter” sign. The equivalent calculation for the binomial distribution involves a calculation of products of binomial coefficients, and my combinatorial kung fu is not up to it, but I think at least for opposed checks with equal numbers of dice it can be solved analytically, though not in a way that is useful for gamers. I think such a solution is available in a textbook by Ashkey (?) but I don’t have the book or the will to read it. So more complicated solutions to the problem will be found numerically or not at all. I may revisit this problem in order to compare Shadowrun with WFRP 3. But for now, I’m shying away from it for obvious reasons!

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