Topic: Probability calculation
Started by: taalyn
Started on: 4/4/2003
Board: RPG Theory
On 4/4/2003 at 5:34am, taalyn wrote:
Probability calculation
I'm not sure this is the right forum, but I'm not sure what would be the right one.
Anyhoo, can anyone direct me to wensites, discussion, or books that are particularly helpful to calculating probabilities within a gaming context.
Aidan
On 4/4/2003 at 5:44am, John Kim wrote:
RE: Probability calculation
I have an essay with a survey of various dice techniques and a bunch of examples looking at the probability of particular systems. Look at "Dice Mechanics" on my System Design page
http://www.darkshire.org/~jhkim/rpg/systemdesign/index.html
On 4/4/2003 at 5:57am, bladamson wrote:
RE: Probability calculation
I use the brute-force method of writing a little piece of code to generate a file containing percentage probabilities and then use a shell script to pipe it into a graphing program to visualize the results.
It's easier than trying to do it mathematically when you've got wierd mechanics that have open ended rolls and such.
If it would help, you can get my code and hack at it here:
http://ultrasoul.com/cgi-bin/viewcvs.cgi/mt/statistics/statistics.tar.gz?tarball=1
It's a unixy sort of archive, but WinZip will uncompress it.
On 4/4/2003 at 6:08am, taalyn wrote:
RE: Probability calculation
John, no offense, but your sight wasn't a help t all. My mechanic doesn't use dice, so looking at what's been done doesn't help me figure out the probabilities of my system at all. Thanks for the effort though!
Bladamson, I may end up doing exactly that - writing a little prog to go through every possibility and compile it, then export it to excel or somesuch.
But I still think we need a gamer's guide to probability: how to calculate it, how design affects aspects of it: what 'exploding' dice do to your probabilities, how various methods of dealing with difficulties affect it, and so on. The brute method works, but it would be nice to have a clue what X tweak to the mechanix will do to the system as a whole before I spend time crunching. Am I making sense?
Aidan
On 4/4/2003 at 6:31am, bladamson wrote:
RE: Probability calculation
taalyn wrote: Bladamson, I may end up doing exactly that - writing a little prog to go through every possibility and compile it, then export it to excel or somesuch.
But I still think we need a gamer's guide to probability: how to calculate it, how design affects aspects of it: what 'exploding' dice do to your probabilities, how various methods of dealing with difficulties affect it, and so on. The brute method works, but it would be nice to have a clue what X tweak to the mechanix will do to the system as a whole before I spend time crunching. Am I making sense?
Welllll. I can't even begin to visualize the probability curve of your mechanic. Though it may be due to the late hour...
Anyhow. You might turn down the number of iterations the code goes through so it will generate results pretty much in real-time. Then interface it to a graphing package. If you're using *nix, make the code directly output gnuplot commands and pipe it into gnuplot. I apologize for not having any decent Windows suggestions, but I imagine gnuplot is available for windows, but you might have to install Cygwin, which is friggin huge.
Then read from stdin, so you can get input from the keyboard. Use that input to tweak the number of different colored motes in the pool. Then you can fiddle with it until you get the curve you want without having to sit through a million iterations each time. Sure the graph won't be pinpoint accurate, but you can use it to get a feel for how things work. Then up the number of iterations to get the exact results.
On 4/4/2003 at 8:13am, Bruce Baugh wrote:
RE: Probability calculation
The professional statistician who's often one of my playtesters has a cuationary note here.
The fact is that the calculations of pure probability apply with any reliability only in two cases: the mathematical calculation itself, and matters of very large populations. In the typical gaming session the dice get rolled...how often? No more than a few dozen times total. That's way, way, way too few members of a population to expect them to conform to the statistics at all. More strongly, in fact, we can expect them not to.
Very few rulebooks tell players much about this, and it's a shame. Systems which encourage gamers to think in terms of quite fuzzy categories - "nearly always", "half", "a quarter", and so on - are the ones that shape expectations which will actually match their results. Precision of the 87.23% sort is spurious in actual play even though it's not spurious mathematically.
Dr. Wendt says that one of the singlest most demanding tasks facing the consulting firm he works for is explaining to customers that not every bit of accuracy that they can obtain along the way actually means anything in practice. And in gaming we seldom get the advantage of professional mathematicians with extensive experience in applying math to real-world situations. Since I've got one, I exploit him by quoting him a lot. :)
On 4/4/2003 at 9:02am, Thierry Michel wrote:
RE: Probability calculation
Bruce Baugh wrote: Very few rulebooks tell players much about this, and it's a shame.
Well, I imagine that including a short treatise on asymptotic statistics in a rpg would probably detract from the mood-setting efforts. ;)
On 4/4/2003 at 9:08am, Thierry Michel wrote:
RE: Probability calculation
taalyn wrote: Am I making sense?
Yes, but how would that differ from an introductory probability course ?
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
On 4/4/2003 at 9:25am, Bruce Baugh wrote:
RE: Probability calculation
Thierry Michel wrote: Well, I imagine that including a short treatise on asymptotic statistics in a rpg would probably detract from the mood-setting efforts. ;)
It would. But it'd be nice if more said things like "Sometimes your group's rolls will be much higher or lower than you'd expect. This isn't bad luck, or a curse, or magic dice. It's just the way probability works. Physical objects like dice rolling on the table don't always behave like ideal mathematical constructs do; the math doesn't have to account for air currents, temperature, the angle of the player's hand as the dice leave, grease on the table, or any of the great many things that can skew the results. Take the surprises in stride. They won't last forever any more than the more typical, average results will."
On 4/4/2003 at 6:52pm, Mike Holmes wrote:
RE: Probability calculation
This was what got posted on the last outcry for help with probabilities.
http://www.indie-rpgs.com/viewtopic.php?t=875
Bruce, while your friends point is true, it's still useful to have an idea of what the mechanics will do. Statisitcal analysis is the only way to accomplish this. I could publish expected variances, and standard deviations and whatnot (ANOVAs anyone?) with each stats post, but I think people understand them fairly intuitively, and don't understand what the advanced stats mean anyhow.
As always, the best thing for getting a feel on your mechanics is playtesting. Which statistics are not meant to replace. Anyone who relies on the stats alone is a fool. Use stats to get in the ballpark and then playtest to perfection.
Mike
Forge Reference Links:
Topic 875
On 4/4/2003 at 8:04pm, bladamson wrote:
RE: Probability calculation
Oh yeah, and here's something else that's handy.
http://www.r-project.org/
Like SAS but free.
On 4/4/2003 at 8:35pm, taalyn wrote:
RE: Probability calculation
Thierry Michel wrote:taalyn wrote: Am I making sense?
Yes, but how would that differ from an introductory probability course ?
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
Right. Just offer the most obvious and efficient option, then. See how you are!
Seriously, though, I think there may be people out there intimidated by the formulae, and that a simple explanation of the most relevant formuae would help a lot. And some explanations of the other effects common in rpg-design. Basically, compile some of this stuff in one place, in accessible language. Maybe I should do it myself...
Aidan
On 4/4/2003 at 10:20pm, Mike Holmes wrote:
RE: Probability calculation
Um, did you see the link I posted above? Not great, but it's a start.
Mike
On 4/4/2003 at 11:09pm, taalyn wrote:
RE: Probability calculation
Mike, I did see it, and it is a great resource. I'm sorry I didn't acknowledge it.
Aidan
On 4/4/2003 at 11:11pm, Paul Czege wrote:
RE: Probability calculation
Um, did you see the link I posted above?
That link is great. I used the hell out of it when I was creating dice mechanics for Nicotine Girls...as you well know.
I'd love to see you package it up as full-fledged article with some of the more specific Excel stuff you taught me via private message. I think it would be a powerful contribution that way. You're not a spring chicken anymore, you know. You need to start thinking about your indie legacy.
Paul
On 4/6/2003 at 12:44pm, taalyn wrote:
RE: Probability calculation
So, I thought I made some progress:
Given:
A balanced caern (equal number of motes of each color)
m: number of motes of each color, number of target motes
a: number of adjacent motes (=2m)
c: number of motes in caern (=7m+3)
h: hand, number of motes drawn from caern
Then:
X: number of possible ways to draw h motes from caern of c motes:
c!/(c-h)!h!
number of ways to get x target motes: same formula - m!/(m-x)!x!
Y: number of ways to get x target and y adjacent motes:
m!a!/(m-x)!(a-y)!x!y!
So, to get probabilities of successes:
sum the #s of ways for possible combinations (i.e. add the # of ways in which you can get 5 success with a hand of 4: ways for 5 asdjacent motes (A), 3A and 1 target (T), 1A2T).
this sum, divided by number of possible ways of drawing 4 motes, should give the probability of drawing exactly 5 successes with a hand of 4.
Or so I thought.
Something's still wrong with the calculations - except for hands 1 or 2,
everything is apparently not possible. What am I doing wrong?
Aidan
On 4/7/2003 at 5:05am, taalyn wrote:
RE: Probability calculation
so, I just did a brute force crunch - just ran 10 million draws, and calculated odds that way. It was much easier.
Aidan
On 4/7/2003 at 6:05am, bladamson wrote:
RE: Probability calculation
hahahaha, yeah, it is most of the time. :)
Still useful to know at least the basis of the theory from the textbook though; helps you design and fix the mechanic, even if it's still easier to brute force the exact figures.