Abraham Quicksilver
United Kingdom Cheltenham Gloucester

I've spent about 6 hours trying to work this out and by googling and basically failed. What I'm trying to do is come up with a set of tables that say:
For a given To Hit value on a D6 What are the chances of rolling X of those hits when rolling Y number of dice
I.e. If I hit on 4+, what are my odds of getting 2 dice with 4+ when I roll 3 dice (and so on)
I'm pretty sure it's binomial distribution but as this point my probability , maths and excel capabilities ground to halt...
I do not want a dice calculator (i.e the varios online dice rollers) I want to get to charts I can look at.
I'm sure someone has done this somewhere....
THanks in advance


Jeremy Lennert
United States California

The Excel function BINOMDIST() does exactly this; tell it the number of successes you want, the number of dice you're rolling, and the probability of a "hit" on each die (in that order).
EDIT: Example spreadsheet: https://docs.google.com/spreadsheets/d/1lrNguUzb6WFg0zIZ3bjF...
Alternately, anydice.com can output charts for you. To roll 3 dice that hit on 4+, enter
output 3d(d6 >= 4)


Abraham Quicksilver
United Kingdom Cheltenham Gloucester

thanks Jeremy
I've tried binom.dist, but I'm certain I am not getting the correct values from it. Which means I must be putting garbage in, but can't work out what.
anydice I am aware of but would require assembling the chart item by item which seems a bit labour intensive.




I've done a similar thing in google docs. I would have thought Excel had a function for this, but maybe not.
You basically want to do some matrix multiplication. https://en.wikipedia.org/wiki/Matrix_multiplication
Although you are only interested in the terms.
So if you have 2 dice represented as 2 columns of face values, transpose the first die, and multiply by the 2nd die. So a row vector multiplied by a column vector. If you google matrix multiplication or cross product, you should be able to find some tutorials for this. However, since you are only interested in the terms, you may have to figure out a couple things your self.
You can then treat all the terms you generate as another column vector and repeat for as many dice as you need.


Abraham Quicksilver
United Kingdom Cheltenham Gloucester

OK, that just lost me... I have no idea what half those words mean.


Jeremy Lennert
United States California

Here's an example sheet:
https://docs.google.com/spreadsheets/d/1lrNguUzb6WFg0zIZ3bjF...


Paul Zagieboylo
United States Austin Texas

You are right that the binomial distribution is what you want here, and the BINOM.DIST() function in Excel implements it. If you feel you are not getting the right values, either you're using it wrong, or your intuition is wrong. (I would actually bet on the latter; human intuition is not really designed for probabilistic calculations bigger than 2 or 3 dice.) Here's the documentation for the BINOM.DIST() function (the BINOMDIST() function is apparently deprecated, but it looks like it did exactly the same thing):
Excel documentation wrote: BINOM.DIST(number_s,trials,probability_s,cumulative)
The BINOM.DIST function syntax has the following arguments:
Number_s Required. The number of successes in trials.
Trials Required. The number of independent trials.
Probability_s Required. The probability of success on each trial.
Cumulative Required. A logical value that determines the form of the function. If cumulative is TRUE, then BINOM.DIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.
This is exactly the question you asked, just written in a slightly confusing way. You want to know, after rolling N sixsided dice, what is the probability that exactly K of them are successes, defined as rolling at least a value of R. The probability of each individual die rolling a success is just (7R)/6, so that's Probability_s. You want exactly K of them to be successes, so Number_s = K (and Cumulative should be FALSE); and you have N dice, so Trials = N.
I've created a simple Google spreadsheet with my results. The values I can do in my head look right, so I'm confident this ended up correct.
If you want the probability of at least K successes, rather than exactly K successes, the formula should be 1  BINOMDIST(K1, N, (7R)/6, TRUE). Decide for yourself why this is (look carefully at the definition of Cumulative).


Abraham Quicksilver
United Kingdom Cheltenham Gloucester

That's it, thank you so much.
This is what I tried, with binom.dist etc, but I must have just messed something up, after 6 hours I was getting a bit zonked.
I've created the excel version too. I shall upload that tomorrow  its way past mybedtime now, but was excited to get this done.
Once again, thanks




Had to read up on Binomial distributions. Just does to show how much stuff you forget from uni.
My method is super overkill. What I basically did was to generate all possible combinations of N dice. Assuming all dice used in a roll have the same number of sides. You can then plug the results into any sort of system.


Abraham Quicksilver
United Kingdom Cheltenham Gloucester

Thanks to Jeremy who's sheet I saw first and used and to Paul for doing the sheet that let me check my results. THanks to both of you. Both of you did exactly what I did, but yours worked and mine didn't! I think I was suffering from some GIGO coupled with a misunderstanding of how the True/False works in binom and that the end results need to be additive  but apart from that...
You can now download a full Excel version of these spreadsheets from here:
http://aqsgames.com/downloads/tohit.xls


James Arias
United States Sanford FLORIDA

Anydice.com ?



