My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 15th, 2010, 04:41 AM   #1
Newbie
 
Joined: Apr 2010

Posts: 2
Thanks: 0

d20 probabilities

So I have this homebrew Pen and Paper system, and I need to calculate some probabilities.
It is an opposed roll with d20s, so my d20 minus your d20.

I need to calculate the probability of the outcome being: 10 or greater, 5 or greater, 1 or greater, -1 or less, -5 or less, -10 or less.

Now, this could be easily done with a matrix, but I am genuinly interested in knowing the math. Also, it is important that I know how to modify the results easily, so that I might for instance calculate these probablities for a (d20+5)-d20.

Any help would be appreciated.
Zerazar is offline  
 
April 15th, 2010, 07:14 AM   #2
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: d20 probabilities

Let's say you want to get 15 or higher on an opposed roll 1d20 - 1d20. If the first die is a 20, then there are 5 possibilities, 1 through 5. If the first die is a 19, then there are 4; etc. So the total number of ways to get at least 15 is 5 + 4 + 3 + 2 + 1 = 5(5 + 1)/2 = 15. There are 20^2 = 400 possibilities overall, so the chance of getting 15 or better is 15/400 = 3.75%.

Notice that trying to get T on 1d20 + t - 1d20 is the same as trying to get T-t on 1d20 - 1d20 (and 1d20 - t - 1d20 is the same as getting T+t), so that doesn't introduce any more complexity.
CRGreathouse is offline  
April 15th, 2010, 01:30 PM   #3
Newbie
 
Joined: Apr 2010

Posts: 2
Thanks: 0

Re: d20 probabilities

Oh right. I had stared myself blind at the problem. I had made myself think it was much more complicated than that.

Thank you very much, sir.
Zerazar is offline  
April 15th, 2010, 09:17 PM   #4
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: d20 probabilities

Quote:
Originally Posted by Zerazar
Oh right. I had stared myself blind at the problem. I had made myself think it was much more complicated than that.
It's not obvious, but it's certainly not as hard as the "roll X dice drop the lowest Y" problems.

Notice that if you don't need to be as high as the other roll you should calculate the number of times you fail rather than the times you succeed (subtracting from 400, naturally) to be able to use that nice sum formula.
CRGreathouse is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
d20, probabilities



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
composed probabilities and total probabilities RifkiNada Algebra 2 November 24th, 2012 04:32 AM
need a help with 2 probabilities safyras Algebra 8 April 5th, 2011 12:48 PM
help with probabilities safyras Algebra 23 March 22nd, 2011 10:59 PM
Please help with expected probabilities mintsharpie Advanced Statistics 0 December 6th, 2010 02:42 PM
probabilities! deadeyedick Algebra 2 December 19th, 2009 03:57 AM





Copyright © 2017 My Math Forum. All rights reserved.