How do I calculate the probability of a specific sum of repeated die rolls?
September 28, 2012 10:16 PM Subscribe
I'm looking to learn how to calculate probabilities for a multi-round dice game. I've researched this question some, and it looks like I might need to know how to use the multinomial distribution, but I can't find any good introductions. Please point me to the most layman-accessible educational material on this subject, and help me to help myself.
posted by Richard Daly to Education (6 answers total) 4 users marked this as a favorite
The game I'm playing can be abbreviated like this:
I roll two six sided dice and add them.
I then subtract a (fixed) penalty value, and score as many points as remain.
I cannot score less than 0. If I would score less than 0 points, I score 0 instead.
I repeat this process several times, without altering the penalty between rolls.
How do I predict the probability of any 1 particular cumulative score?
I am not interested in simulating this event and taking a random sample; I want to calculate all possible outcomes and their precise probabilities. Examples follow:
My penalty value is 0, and I repeat the die roll 36 times.
Each roll will produce a number between 2 and 12 inclusive, and my final score will be between 72 and 432. What is the chance that I will score 7 points exactly 6 times.
My penalty value is 11, and I repeat the procedure 40 times.
Each roll will produce a value between 0 and 1 inclusive, and my final total score will be between 0 and 40, and likely closer to 0 than 40.
I wish to predict the chance that I will score a cumulative total of exactly 2 points across the sum of all 40 trials.
My penalty value is -5, and I repeat the procedure 5 times.
Each roll will produce a value between 7 and 17 inclusive (negative penalty). I wish to plot the probability of a arriving at each possible total: 35 through 85.
Again, I think maybe this is a case of the muiltinomial distribution, but everything I can find about it (wikipedia) is confusing and not written as educational but as reference material.
I'm familiar with MS Excel and have a basic Liberal Arts understanding of calculus and probability/statistics, though I'm quite rusty. I'm willing to re-learn what I have forgotten, and also to learn new skills - within reason. If this procedure requires me to learn lots of new math, I would appreciate links or book titles to pursue as well as a general outline of what the fields of study are called, and what I'll need to know to pursue them intelligently (i.e. help me ask questions without sounding ignorant/clueless).
I gather that the program R might be helpful in this, so please feel free to recommend a good introduction to both R and Statistics.
Thanks for any help you're able to give!