08212018, 12:21 AM  #1 
Join Date: Oct 2011

Condensing Multiple Rolls with a Chart? [Math Help Needed]
I decided I'd like to hack together a quick mass combat system, one for fights between groups too small and individuals too varied for the default mass combat system to work well (e.g. supervillain gangs). I figured that a good first step would be to have a way to simulate multiple rolls with one.
For instance, if someone made 10 attacks with skill 12 in a given timeframe, they would hit (on average) with seven or eight of them, but would hit with all 10 roughly 5% of the time. Since there's a roughly 5% chance of rolling 35 on 3d6, you could make it so rolling 35 means they hit with all ten...and, conversely, that 1618 means they miss with all ten. And so on for every number between 1 and 9 as well. But, of course, I want a way to easily calculate that sort of table for any combination of skill level and number of rolls. Ideally, I'd like a big chart, with 318 on both edges, with the cells containing the percentage of rolls which succeed for a given die roll and skill level. It seems like the kind of thing there should be a simple formula I can plug into each square to figure out; stick in the probabilities for rolling each number on the die, multiply or exponent them in the right way, and fill the table. But I haven't been able to figure out what. Or if that's not an option, I guess other options for notquitemasscombat rules could be helpful. But this is the kind of problem that keeps bugging certain types of people until they have a solution, and I am one of those types...even though probability isn't really my forte. I hope I didn't nerdsnipe anyone. 
08212018, 03:20 AM  #2  
Computer Scientist
Join Date: Aug 2004
Location: Dallas, Texas

Re: Condensing Multiple Rolls with a Chart? [Math Help Needed]
Quote:
Code:
3D6 1 roll 2 rolls 3 4 5 10 15 20 3D6 3 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3 4 0.019 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4 5 0.046 0.002 0.000 0.000 0.000 0.000 0.000 0.000 5 6 0.093 0.009 0.001 0.000 0.000 0.000 0.000 0.000 6 7 0.162 0.026 0.004 0.001 0.000 0.000 0.000 0.000 7 8 0.259 0.067 0.017 0.005 0.001 0.000 0.000 0.000 8 9 0.375 0.141 0.053 0.020 0.007 0.000 0.000 0.000 9 10 0.500 0.250 0.125 0.063 0.031 0.001 0.000 0.000 10 11 0.625 0.391 0.244 0.153 0.095 0.009 0.001 0.000 11 12 0.741 0.549 0.406 0.301 0.223 0.050 0.011 0.002 12 13 0.838 0.702 0.588 0.493 0.413 0.171 0.071 0.029 13 14 0.907 0.823 0.747 0.678 0.615 0.378 0.233 0.143 14 15 0.954 0.910 0.867 0.827 0.789 0.622 0.491 0.387 15 16 0.981 0.963 0.945 0.928 0.911 0.830 0.755 0.688 16 17 0.995 0.991 0.986 0.982 0.977 0.955 0.933 0.911 17 18 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 18 

08222018, 05:29 PM  #3 
Join Date: Oct 2011

Re: Condensing Multiple Rolls with a Chart? [Math Help Needed]
Okay, I am bad at explaining my ideas. So let's try taking a simpler example and seeing if I can explain it better with that.
Let's say that instead of GURPS, we have a game where you roll d4's for success. (Like GURPS, the lower the better.) And we're also rolling a d4 for the simplified roll. If you need to roll a 1 for success, you would expect to succeed about 25% of the time. However, if 100 people like that rolled for success, you wouldn't get 25 people rolling successes at the same time; you would get on average 25% of them rolling successes, but each individual lot would vary. Let's say that there was a 3/4 chance of getting at least 15 successes out of a hundred , a 2/4 chance of getting at least 25 successes, and a 1/4 chance of getting at least 35 successes. Then, when representing this chance of success as a d4, might be something like: 1—5% 2—15% 3—25% 4—35% When rolling a d4 and getting a 2, 15% of those hundred rolls (ie, 15, because we picked nice round numbers) would succeed, and 85 would fail. And if the probabilities are right, on average, about 25% of the rolls would be successes. The quick averagers in the audience will note that this does not actually average out to a 25% rate of success. This is because the probabilities I cited are a load of hooey. I'm trying to figure out what the right probabilities to put in the actual list of probabilities, for both skill 1 and skills 24. Only with GURPS instead of the example system. Does that help people understand the question I'm trying to ask? 
08222018, 06:21 PM  #4 
Banned
Join Date: Jun 2005
Location: Bristol

Re: Condensing Multiple Rolls with a Chart? [Math Help Needed]
A quick fix is to use the ROF rules. First work out the average to hit roll and then add a bonus to x attacks (similar to the ROF rules) and for every one point under that to hit roll is another hit.

08222018, 07:01 PM  #5  
Join Date: Feb 2005
Location: Berkeley, CA

Re: Condensing Multiple Rolls with a Chart? [Math Help Needed]
Quote:
However, I don't recommend doing this, because, while GURPS mostly treats the tests as independent, they aren't. 

08222018, 08:17 PM  #6  
Join Date: Sep 2007

Re: Condensing Multiple Rolls with a Chart? [Math Help Needed]
Quote:
https://www.wolframalpha.com/example...noullitrials/ https://stattrek.com/onlinecalculator/binomial.aspx I'd probably structure the table as a cumulative one, so you could roll percentiles once and then read up to the largest value your rolls beats, and take that as the number of successes in that batch of rolls. 

08232018, 03:37 PM  #7  
Join Date: Oct 2011

Re: Condensing Multiple Rolls with a Chart? [Math Help Needed]
Quote:
Quote:
Hm. Quote:
Quote:
Table of raw numbers, table of percentages. A column from the latter (minus the row for number of trials) is closest to what I'd want to put in column 1 of my hypothetical chart. However...which column? The percentage for rolling a 1 doesn't change much from 10 trials to 1,000 (20%>not quite 24%), but the percentage of successes you'd get for rolling a 4 drops from 40% to barely over 26%. ...Hm. Starting to see some problems with my methodology. Last edited by GreatWyrmGold; 08232018 at 08:31 PM. Reason: Just noticed a typo 

Tags 
math, probability 
Thread Tools  
Display Modes  

