Bad mathematics in tabletop games.
- In the Warhammer setting, different factions use different calendars, which contain references to the standard Imperial Calendar to allow for calibration by sufficiently interested fans. Unfortunately, when the same events are compared in different calendars, the dates are all out by one year, as the writers forgot that the first year of a reign starting in, say, 2000, is 2000, not 2001.
- In the current Codex for the Black Templars space marine chapter in Warhammer 40,000, the introduction states that the whole chapter is divided into "crusades", of which there are "usually no more than a few", comprising fifty to several hundred marines. This would be fine if the Templars were a chapter of one thousand, following the Codex Astartes, but the same page — nay, the same paragraph — says that there are between five and six thousand Templar marines. The numbers just can't work with only a "few" crusades, unless a "few" is pretty large or each is over a thousand strong.
- It does work out if you interpret "crusades" as meaning "in active combat". There could be any number of Templar companies doing routine garrison duties or recruitment.
- The same book states that the Chapter does their recruiting from keeps established on conquered or rescued worlds, each with a garrison of a few marines. After ten thousand years of crusading, they should logically have so many of those that at least half of the Chapter must be manning them (and a ludicrous proportion of them must be Apothecaries).
- And after the Horus Heresy, the ten remaining Space Marine Legions were split into a thousand chapters, so each Legion would (on average) be split into a hundred chapters. In the same book, the Ultramarines Legion is claimed to have by far the most offsplit chapters, at twenty-three; implying casualty rates far in excess of anything ever established.
- Post Horus Heresy there were actually nine remaining legions, and the thousand chapters is both an approximation, and valid for "current" time in the 40k universe (M41), not immediately post Horus Heresy (M31). There have been loads and loads of foundings of new chapters in the intervening 10,000 years.
- This is backed by Codex Grey Knights as the other chapters noted its oddness as to their number (666) despite only a few hundred chapters having been founded.
- Plus although the legions had a theoretical strength of 100,000 very few of them were actually up to full strength, especially after taking heavy casualties during the Heresy itself. Additionally the list of Second Founding chapters is not complete, many of the chapters have been destroyed and their name lost to history.
- Space Marine chapters, famously, are composed of a thousand marines each (not counting casualties). Which makes sense — there's ten battle companies, each composed of ten squads of ten men each, for a thousand marines... plus the captains/chaplains/command squads (7 per company, or an additional 70 marines), the Chapter command (roughly 15 marines, counting the honour guard), the armoury, the apothecarion, the librarius (cumulatively another 70 marines), plus the vehicle crew, starship commanders, and pilots. In all, "a thousand" marines, is actually at least 1350 and could potentially be upwards of 1600.
- On the other hand, this very issue (measuring "effectives" versus larger metrics) is a real thing with armed forces. It's quite possible for a real world force nominally described as 1,000 men to mean either "1,000 enlisted combatants plus officers and hundreds of supporting elements" or "about four hundred combatants, three hundred supporting elements, forty officers, sixty sick and two hundred absent or in hospital." See also division slice
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- On the other hand, this very issue (measuring "effectives" versus larger metrics) is a real thing with armed forces. It's quite possible for a real world force nominally described as 1,000 men to mean either "1,000 enlisted combatants plus officers and hundreds of supporting elements" or "about four hundred combatants, three hundred supporting elements, forty officers, sixty sick and two hundred absent or in hospital." See also division slice
- The Rogue Trader RPG's writers apparently forgot about the square-cube law when giving the size and weight of the starships. The smallest vessels are slightly denser than balsa wood, while cruisers and battlecruisers have roughly the density of smoke.
- The explosives in the Inquisitor Handbook of Dark Heresy have some... weird blast radius. Promethium, especially, is ridiculously volatile. During a session, a supertanker filled with five hundred million liters of promethium (that is surely a lot, but, again, this capacity falls easily in the modern super tankers range) blew up. The player asked the Game Master if they were safe at the other side of the harbor, so he made a couple of counts to find it out: imagine the hilarity when they found out that, according to the manual, the resulting explosion had a radius of 1.6 millions kilometers (almost a million miles). To give an idea of the scale, the fireball is about twelve times the size of the sun. Somebody should inform the High Lords Of Terra that the conventional Exterminatus methodologies are largely outdated: why waste an expansive cyclonic torpedo when you can go supernova with a simple ship filled with cheap promethium?
- For the "Ace In The Hole" miniadventure included with the Star Ace GM screen, the PCs are supposed to rob a casino blind as revenge for the casino owner putting a bounty on one of your NPC buddies. You're also supposed to leave 5000 chips (game currency equivalent to $5 million US) behind to cover the gambling debt that started this whole mess. The scenario uses random rolls to determine just how much money is in the casino at any given point, but if you assume maximum rolls there's only 700 chips in the whole joint. You can't even make up the other 4300 chips by robbing the 1d10x100 customers, because all gambling is done with house scrip instead of coins. Also, the casino owners have put a 1000 chip bounty out on that NPC's head. It's fairly simple for the PCs to bluff their into the casino office by producing fake evidence that they'd just earned the bounty... which the casino owner isn't able to pay because he doesn't have that sort of cash on hand. The Star Ace game assumes that all currency is "hard" currency; computer credits and the like aren't used.
- In one edition of Warhammer Fantasy Roleplay, it attempts to make the point that magic users are rare by claiming 1 in 1,000 people have some magic ability, 1 in 1,000 of those are true wizards, and out of those, only 1 in 10,000 are cut out to be battle mages. That means a planet like Earth, with a population of seven and a half billion, would have, on average, a whopping 0.75 of a battle mage. Warhammer Fantasy Roleplay, with its medieval-esque setting, would be even worse off.
- Speaking of which, using the completely bonkers equations given in Role Master's first companion to determine one's character's height, weight, bust size, waist size and shoe size (you know, in case you're a very, very anal GM and your dungeon has Boots of Speed in size seven — this is Role Master, after all, the Dwarf Fortress of pen and paper RPGs) you would always end up with a monster who had feet twice as long as his waist or somesuch.
- Likewise, the original 1st Edition AD&D tables for character height and weight failed to link these two characteristics, meaning the shorter your PC was, the fatter they were, and tall characters were built like string beans, if not dental floss. Furthermore, the weight tables for demihumans were way, way too extreme, meaning your dwarf hero could've had the approximate density of osmium.
- Dungeons & Dragons:
- Several ways to hypothetically gain infinite currency involve buying items and selling their parts for more than the initial item was worth. For example, in 3.5E a 10-foot ladder could be purchased for 5 copper pieces, split into two 10-foot poles, then sold for 1 silver piece per pole.
- In the game In the Labyrinth, a full wineskin costs $2, while an empty one costs $3. Bottoms up!
- The numbers for the fireball spell were a little off. The shape was controlled by the caster and the volume was fixed, and the resulting blast tended to be the size of Pennsylvania.
- Old-school D&D generally had horrible math. The way "create food and water" spells scaled, a high level cleric could easily clear a dungeon by flooding it with water, since he would create tens of cubic meters per cast.
- The 1e method of determining PC height and weight was to roll these two traits independently. This, together with poorly-thought-out values for the average weight of demihumans, meant that dwarf adventurers had a bodily density that implied their bones must've been made of osmium, tall humans with an 18/00 Strength were likely to be emaciated, and all shorter-than-average halflings were spherical.
- In fourth and fifth edition, pi is apparently 4, given how radius of spells like fireball is determined in squares. And diagonal movement is the same as horizontal, so sqrt(2) = 1. Math in Greyhawk must be really, really screwy. It's a bit better in version 3.5, where sqrt(2) = 1.5. As later editions starting with third at the latest emphasized miniatures tabletop play more and more over the more abstract "theater of the mind" stylenote , eventually something had to give, and the already somewhat spurious notion of tracking imaginary movement and the various geometries of assorted similarly imaginary effects with ludicrous precision was it.
- This varies by edition; the above is fifth. In 1-2e, pi is equal to pi and the square root of 2 is approximately 1.414 because real measurements were supposed to be used. In first edition, movement was given in inches like a miniatures war game so characters were supposed to move a set number of inches on a physical, gridless table using a tape measure. In second edition, movement was given in feet but there was no set standard scale. 1" = 5' was a sort of default for the common 28 mm scale miniatures, but it wasn't set in stone. In 3rd and 3.5 edition and in Pathfinder, 1" = 5' became Word of God. Area of effects have specific templates leading to less arbitrariness but some strange edge cases, and diagonal movement has a fairly decent compromise for moving on a grid. In those editions, the first diagonal move is measured as 1 square, then the second as 2 squares, and so on.
- A potion has no appreciable weight, and neither does acid, holy water or alchemist's fire. But a potion vial (the sort of thing that they are in) does. Therefore liquids in D&D have negative weight.
- A case where it was applied to the mechanics underpinning an entire class: the difficulty a truenamer must beat to use their powers goes up at least twice as quickly as their actual rank in the Truename skill does — it goes up by 2 per challenge rating of the target opponent, and the truenamer can only add one rank of the Truename skill per level. Meaning that by level 20, a truenamer needs to make up a deficit of twenty skill ranks with magic items and stat increases (in other words, +5 to the key stat for leveling up, +5 to that stat from a really expensive magic item, and then another magic item granting Truename +15) to have the same chance of their power working on a level 20 monster as a level 1 truenamer would when targeting a level 1 monster. And then, when they do use a power successfully, the difficulty goes up. There's a reason optimizers tend to dismiss the truenamer as utterly useless.
- They had the same mechanical problem with 4th Edition. Monster design explicitly had the Defenses of monsters increase by one for every level of the monster. So, a level 30 monster had +29 more to their AC, Fort, Reflex, and Will than a level 1. Problem is, you could only get a natural +1 for every two PC levels, which meant +15 at level 30. You could also increase your stats by a maximum of +7 each from leveling (+1 to 2 stats every 4 levels), with an automatic +1 each from levels 11 and 21. But, each point only increased the stat bonus by 1/2. So, a level 30 PC who put every stat point into their main stat got maybe +5 to the bonus, and along with having a +6 (the best) weapon/implement, PCs were still behind on the curve even if they min-maxed. WotC's clumsy solution to the problem was to create a Weapon/Implement Focus Feat that allowed you to get +1 for every 10 levels. So, you had to take a Feat, put every stat increase into your main stat, and have the best possible weapon/implement just to keep up.
- To join the Fists of Hextor in the early 3E splatbook Sword and Fist, you have to kill a member of that organization. Apparently, membership numbers of that organization can only decline. (The Sith have a similar problem.) Though considering that Death Is Cheap, it might not be as ruinous as it sounds.
- Plenty of stats given out for population sizes, overlapping with Sci-Fi Writers Have No Sense of Scale, seem way too small or too large for medieval cities. The City of Greyhawk, for instance, is the largest city on the continent and has a population of about 70,000. This is about half of what Paris had in 1450, right after being hit by multiple plagues and repeatedly attacked in the Hundred Years War — and this is after Greyhawk's numbers were retconned to be significantly higher. Sometimes this is played with or justified.
- Some of the early Star Wars tabletop RPG material, namely the Imperial Sourcebook, refers in much detail to the Order of Battle for starships. One of these configurations is called a Fleet Bombard, which would include two System Bombards, which in turn include three Bombard Squadrons, which in turn would include two Torpedo Lines, which each usually consisting of two Torpedo Spheres. That means a single Fleet Bombard should have about 24 Torpedo Spheres. Later in the book, however, they talk about how there are only six Torpedo Spheres in operation in the entire fleet.
- Considering the giant pile of bile that is F.A.T.A.L., it should be no surprise that randomly generated body parts can have negative proportions. There's the particular case of the success rolls. First you roll percentile dice to find the number to roll against then roll for success to see if you get a higher number. Someone must have thought the extra roll would add randomness. The result is that the odds are always 50.5%.
- In Werewolf: The Apocalypse, when a Garou and their kinfolk partner conceive, the likelihood that they will produce a Garou child is only 10%, compared to a 90% likelihood that they will produce a kinfolk child. That means that each Garou-kinfolk couple would have to have at least ten children to keep the Garou population stable!
- In universe there is a lot of discussion about watching over kinfolk communities is a major duty of the tribes. This implies that the majority of Garou are born to kinfolk couples rather than Garou parents. The math still implies a much larger kinfolk population that the fluff supports, but the Garou population isn't supposed to be kept stable by direct siring.
- In Iron Kingdoms, casualty figures for Cygnar indicate that its entire population has been wiped out. Twice. Most nations only manage it once.
- BattleTech has mostly avoided this trope due to placing a moratorium on providing hard numbers on things like the energy output of lasers but it still has some issues. For example, the Avalon class Warship's stated dimensions are large enough that assuming its armor has the density of steel, it would have to be the thickness of a Mylar balloon.
- Starfinder has a howler when it comes to ship weight, class, and crew-sizes that immediately led to a frenzy of comments on the message boards followed by a "Yeah, mea culpa, but heck with it" from the devs. Plugging the minimum length and weight and any kind of reasonable radius (for approximating a cylinder) results in a starship less dense by a few orders of magnitude than air at sea level.
