"And Thorpe makes the turn in the lead... Ian
Thorpe is heading
for an Olympic gold... no, he seems to have forgotten how to swim...
he's sinking... and who's that on the outside lane..? It's Eric the
Eel, he's in the lead..."
Now in a "heroic" game it's fine for the Finnish
World Champion to
roll a one, and only make it fifty metres off the end of the skijump
ramp, only to watch as Eddie the Eagle rolls a twenty and flies a
hundred and twenty metres to the gold medal.
But real life isn't like that.
Which is basically why I have problems with the
idea of using D20 for
nonheroic games.
Before I continue, I should point out that what
I'm about to say is
in no way original. I've seen dozens of people on various message
forums say that they don't like D20 because it has a poor probability
curve. But they never explain what they mean by that, and it occurred
to me that people who haven't, as I have, studied Statistics (I
failed it at A level, and hence have partial knowledge of it) might
not have any idea what they mean by "probability curve".
So I figured I might as well try to explain, just
so that we all know
what we're arguing about. (And if some of you already know this, and
figure I'm being patronising... fuck off!)
To do this, I'm going to use two dice rolling
mechanisms, both
simplified versions of ones used in actual games. The first is, of
course, D20. You roll a D20, add your skill to it, and it must be
equal to, or higher than, a difficulty number. If you roll a 1 you
have automatically failed. If you roll a 20 you have automatically
succeeded.
The second system is based on the one that Steve
Jackson Game's GURPS
{http://www.sjgames.com/gurps/} uses. In this one, you roll three
sixsided dice, add them together, and then add your skill on. The
total must equal or exceed a difficulty number. If you roll 3 (three
ones) you have automatically failed. If you roll 18 (three sixes) you
have automatically succeeded.
Firstly, what do we mean by a probability curve?
Well imagine if you did a bar graph showing how
likely you were to
roll a particular number on a D20. It would be flat, since you have
an exactly 5% (one in twenty) chance of rolling each number.
But if you did the same with the second method
(3D6) you would get a
bellshaped curve (what they call a bell curve) like the diagram
below shows:
With 3D6, you have a 12.5% chance of rolling a
10, but only a 0.5%
chance of rolling an 18 or a 3 (actually it's 0.46%, just to stop
people nitpicking). If you're wondering why this is, it's because
there are many different ways of rolling 10 on 3D6 (6+2+2, 6+3+1,
6+1+3, 5+2+3 etc.) but there is only a single way of rolling a 3 or
an 18 (1+1+1 and 6+6+6).
But what does this actually mean, and more
importantly  why does it
matter?
Okay, let's use our two methods to resolve a
particular test. Let's
say that it's navigating a canoe down a whitewater river using a
"canoe" skill.
We have three blokes, Andy, Barry and Charlie.
Andy is a novice at
canoing, so we'll give him a skill of 0. Barry is at an intermedate
level, so we'll give him a skill of 5. But Charlie is an expert at
international standard, so we'll give him a skill of 10.
And we're going to send them down four rivers,
rated easy, moderate,
hard and very hard and see if they get to the end without capsizing.
We give these four rivers difficulty ratings (the number you must
equal or exceed) of 6, 11, 16 and 21.
How do they get on?
Here are their chances of success with the "D20"
method:
 Andy  Barry 
Charlie 
Easy  75%  95%  95% 
Moderate  50%  75%  95% 
Hard  25%  50%  75% 
Very Hard  5%  25%  50% 
Let's look at some of the implications of that
table.
Firstly, even on the easy run there is still a
significant (5%)
chance for both Barry and Charlie to fail, which seems especially
unfair if Charlie is supposed to be an expert. After all, even Andy
only has a 25% chance of failure. So for ever five runs on the easy
river that Andy muffs it, Charlie will screw up once.
Let's look at the hard run. This is so hard that
an international
standard expert like Charlie has a 1 in 4 chance of capsizing. And
yet it is also so easy that a complete novice like Andy has a 1 in 4
chance of making it down without capsizing. In fact, there is a 1 in
16 chance that Andy will make it down on a run where Charlie
capsizes.
(Now do you understand my bit about Ian Thorpe
and Eric the Eel?)
And when you move to very hard, you find that
although Charlie is
more likely to make it than Barry (50% against 25%) it's not as
though he's on a different level of ability. Barry isn't going to
watch him in action and think: "that guys just on a different planet
to me..."
I could go on, but I think you get the drift.
This dice mechanism
fails to handle wide ranges of ability, and is essentially too
random. Yes, you can give people high or low levels of skill. But
sooner or later, you end up with either "fail unless you roll 20" or
"succeed unless you roll 1" in which case it hardly matters whether
you have +15 or +25.
So, how well does our "3D6" mechanism handle it?
Here are the
chances:
 Andy  Barry 
Charlie 
Easy  95.3%  99.5%  99.5% 
Moderate  50%  95.3%  99.5% 
Hard  4.7%  50%  95.3% 
Very Hard  0.5%  4.7%  50% 
Well, Andy is pretty good on the easy and
moderate rivers, but is
pretty hopeless on the hard and very hard ones. Meanwhile, Barry and
Charlie are pretty similar on the easy and moderate rivers, without
much chance of them screwing up, but on the hard and very hard ones,
Charlie's superior skill becomes very apparent.
Which is why I think that this sort of dice
mechanism is better for
"realistic", skill based games. If I'm playing a space pilot with
twenty years of experience, and I'm racing against someone with two
hours of training, I should beat them *nearly* every time. Yeah,
there is a very slight chance that I might make a mistake, but it
should be pretty damn unlikely.
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