We've all seen it.  Games that are otherwise reasonable, but when subjected to even the slightest scrutiny or playtesting, it becomes shockingly obvious how badly the maths fail, and that the designer hasn't the slightest understanding of even rudimentary probability.  Quite honestly, most games, as games, are pretty damn bad, it was one of the reasons I was so fascinated by D&D3, because, short of that godawfully flat expanse that is D20 probabilities, the math actually was pretty sound over all, at least until sourcebooks got involved.

So let's have some examples then, of what I mean.

The D6 System
This was a game that, in it's initial inception, was almost deceptively brilliant.  The die progression is beautiful (the die + pips system looks like it makes large leaps, but the averages go up by precisely 1 every time), the difficulties well considered, and over all it's an elegant and wonderful system.  

Then someone, somewhere between 1e and 2e, apparently decided they would have none of that, because into this otherwise elegant system, they injected the Wild Die.  

The Wild Die is one of those mechanics, like so many in this category, that sound really good in your head at first, until you do the maths and realize it's complete rubbish, only of course, no one ever did the maths in this case so it coasts by unnoticed until it gets to your gaming table and you realize what rubbish it is.

The basic idea is to inject a critical success/failure mechanic into the game.  Normally, the escalating die codes of a system like this mean a hard target like a specific number isn't going to work, so the designers instead designate one specific dice as "special", so they can keep the same aesthetic of a maximum and minimum value triggering the spectacular result.  It sounds intuitive at first, gamers have seen that sort of thing before, and it cuts down on the amount of adding or maths in play.

The trouble is, this is a D6 we're talking about.  It is a very small range of numbers, so having mapped both 1 and 6 for critical failure and success respectively, we've now mapped a third of our possible outcomes to an unusual result.  That means 33% of all die rolls with the Wild Die in play, will have some sort of anomalous outcome.  It certainly keeps things unpredictable, I suppose, but at that margin not only do our criticals become quickly sapped of excitement through sheer repetition, but it's become so unpredictable we may as well just roll the bloody Wild Die and skip the whole rest of the thing.  

But they didn't stop there, oh no.  They added additional effect on the math of the roll itself that comes into play that 33% of the time.  For 1's, you also subtract both the 1 and the highest regular die from play.  For 6's, they explode, meaning you roll again and add, and they explode continuously on respective results.  Now, probability being what it is, this isn't particularly likely to stretch out too long, but it still slows down play, and now that well calculated difficulty table is all but meaningless (and I might note, was never recalculated after the change either).

The end result is an otherwise elegant system, rendered almost completely random by the extraneous bolting on of an unnecessary and ill considered mechanic.  I'm inclined to wonder if this is one of the events that led to Greg Costikyan becoming such a bitter, mean old sod.  

RIFTS
Rifts on the other hand, was mostly a mess from the start.  The original Palladium system upon which it is based was never anything more than a kludgy houseruled D&D variant, but for what it was, it worked, and has it's own old school charm in a sense.

But it couldn't stop there of course.  Palladium is the recycling center of roleplaying developers, everything gets reused again and again, so of course when the desire came to do their new massive kitchen sink post-apocalypse game, of course the original fantasy D&D variant again got pressed into service.  

There are many bizarre results of trying to force a homebrewed AD&D variant to handle everything from power armor to tanks to interdimensional deities, but one in particular that stands out more than anything to me, is the to hit roll.  

Like D&D before it, rolling to hit is done on a D20.  In the original version, still extant in vestigial forms scattered through some books, the target would have an AR based on the time of armor they had, and you would have to roll over that number with applicable to hit modifiers, basically like D20 but with fixed AC values based on gear.  In addition, if you somehow rolled less than a 4, you automatically failed, basically the games critical failure mechanic.

Then Rifts came along, and as part of upping the stakes if this new setting, it used the MDC system from Robotech, only rather than confining it just to vehicles, it was used for bloody everything, including personal armor.  And MDC had no AR, it wasn't necessary according to the developers, because it itself was automatically immune to all non MDC damage.  

The thing was, that to hit roll was still there.  And with the higher power level of the new setting, it was trivially easy to wind up with a number so damn high that success was basically all but guaranteed anyway, "less than 4 rule" or no, and while defensive rolls were allowed, they'd become so damn high that a mere d20 frequently wasn't enough variation to affect the outcome.  

The entire process of rolling to hit had been reduced to little more than a pointless extra ritual, but for that tiny little chance of failure there.  It'd become almost akin to MMO and JRPG systems, where you no longer term it a "to hit" chance, but you invert the concept and have a "miss chance" instead, but here only because of that vestigial little rule of 4 left over from long ago.  The whole system could just as easily take the leap to just taking turns rolling for damage.  

Storyteller
I'm getting a bit long-winded here, but I feel this board will prod me fiercely if I don't throw mention of ST's godawful "botch" rule.  In an attempt to add critical failure to the otherwise pretty straightforward dice pool system, the rules declare that any roll of 1 on the die cancels out a success.  If you have more 1's than regular successes, it's considered a critical failure, and something bad happens to you.

Of course, the way the math adds up, the more dice you get, the more likely you are to roll a fistful of ones and wind up failing horribly instead.  At least one friend I knew had a Werewolf who'd become infamous in my WW circle at the time, because despite doing everything the system allowed to twink out his character, thanks to that little glitch in the probabilities, he pretty much failed catastrophically at everything he ever did.  On paper, he was the most powerful Werewolf that ever lived, if only he could stop jabbing his own glaive into his arms.  


So what examples can you think of, audience?  What games seemed fine on the surface, and then ran smack dab into the "What were they thinking?" wall?

Whether by fault or design, overpowered magic users at higher levels in 1E AD&D.

There's no mandatory requirement for mathematical literacy for rpg designers.  As long as somebody is buying the product, why should they even give a damn?

Quote from: ggroy;323264There's no mandatory requirement for mathematical literacy for rpg designers.  As long as somebody is buying the product, why should they even give a damn?

I don't think it's too onerous a burden to expect a game designer to remember concepts I learned in high school math, especially when they're pretty important skills for making a system that actually works.

Quote from: J Arcane;323268I don't think it's too onerous a burden to expect a game designer to remember concepts I learned in high school math, especially when they're pretty important skills for making a system that actually works.

If I ever become a rich games producer every designer working for me will have mandatory statistics classes.

Quote from: J Arcane;323268I don't think it's too onerous a burden to expect a game designer to remember concepts I learned in high school math, especially when they're pretty important skills for making a system that actually works.

They actually teach probability in high school math these days?

Quote from: ggroy;323277They actually teach probability in high school math these days?

They did when I was in school in the 90s, and most designers are older than I am.

Quote from: J Arcane;323278They did when I was in school in the 90s, and most designers are older than I am.

They didn't cover probability when I was in high school.  Though I did attempt to figure out some basic probability, largely in trying understanding how things like lottery tickets, card games, dice, etc ... worked.

What is the line "there are three kinds of liars: liars, damn liars, and statistics." Sometimes the problem of mathematics probabilities in games isn't a fact of the math itself, but of the desires of the designer vs the actual play experience. The fact that they want an outcome that seems much lower/higher in regular play than the rules desribe.

I think its pretty important to understand the numbers aspect of any game you create--and that doesn't include "how much you handwave to get the results you want."

Wonder how many rpg designers use the formula:

average number of attacks to kill a single target = (number of health units)/(probability of hitting target)

where for each instance the attacker hits the target, it does one health unit of damage.

ie.  For a monster with 2 hit points, and an attacker which has a 50% probability of hitting the monster and doing 1 hit point of damage, it takes on average 4 rounds to kill the monster.

Quote from: ggroy;323302Wonder how many rpg designers use the formula:

average number of attacks to kill a single target = (number of health units)/(probability of hitting target)

where for each instance the attacker hits the target, it does one health unit of damage.

ie.  For a monster with 2 hit points, and an attacker which has a 50% probability of hitting the monster and doing 1 hit point of damage, it takes on average 4 rounds to kill the monster.

I definitely think the 3e and 4e designers probably have.  

Most other games, not so much.  I'm not sure how much thought beyond vagaries goes into specific monster design in other games, and many simply leave it entirely up to the GMs by not having much if any specific antagonists at all, which is fine by me and better than getting a system that claims to tell you what it will take to kill a thing but doesn't.  The closest older editions had for example, was hit dice, which meant basically fuck all, which is why CR was invented in the first place.

The thing that gets me about the OP examples though, is these aren't something as specifically detailed as a monster's stats, I can sort of be forgiving there because that shit's a lot of work if you've got a lot to go through.  

But these are core mechanics of the game, which should, in any system, be the tightest, best tested, best analyzed parts of a system, because they're basically the core program loop on which every other piece of data runs.

Quote from: J Arcane;323268I don't think it's too onerous a burden to expect a game designer to remember concepts I learned in high school math, especially when they're pretty important skills for making a system that actually works.

I keep rereading this post. I'm not to sure that understanding maths is very important for creating a system that works but rather what designers think will make their games more exciting during play. Sometimes what they come up with makes math sense but isn't very interesting whereas sometimes it dosn't make any math sense but plays brilliantly. Of course sometimes it just sucks.

Regards,
David R

The botches rules in Old WoD games... so true. I've seen the "mega dice pool with umpteen million botches" scenario come up quite a few times. This is not like this in New WoD games anymore. You basically get dice added or taken away from dice pools as modifiers to the difficulty of the action now (the die difficulty to beat being always 8 on a single die now). If your dice pool is reduced to zero or less, you still have a "chance die", and if you roll it and get a "1", you botch.

Goddamn, I hated that botch rule in Storyteller.  I was a player in a painful Mage game for a brief time, and it was plainly idiotic.  It was utterly unnecessary for the system to work.

I also hated plenty more about the system - like how there were four very complex rolls with floating dice pools and difficulty numbers required to smack someone upside the head - but the botch thing just pissed me off.

-O

You could just ignore the botch rule, you know.