# Thread: Quick probability question [RESOLVED]

1. ## Quick probability question [RESOLVED]

How many ten-sided dice do I need to roll for it to become likely to get three 6's? Let's say... a 10% chance, a 50% chance, and a 75% chance?

(I'm thinking of including a kind of "doom pool" mechanic, where a big pile of d10s are rolled every now and then. If three 6's come up, Bad Things happen. Player actions can add or remove dice from the pool)  Reply With Quote

2. ## Re: Quick probability question

I'm not a math wizard, but playing around on AnyDice it seems 10d10 has 5.74% chance to give three 6's, so I feel like 50% and 75% is going to be "way too many to roll." Server issues are preventing me from playing around til I find those numbers though. I could write a program to figure them out if I had to (read: you need more information, no math wizards show up.)  Reply With Quote

3. ## Re: Quick probability question

6 or higher, or 6 exactly? And exactly three of them, or three or more?
Since it's three sixes I'm guessing six exactly.

You roll exactly 6 approximately once for every ten rolls, and 6 or higher 50% of the time.
If it's exactly three sixes, though, the possibility drops again as you add too many dice and start getting more likely to get four or more.  Reply With Quote

4. ## Re: Quick probability question

Three or more sixes-- the important thing is the whole "666" bit.  Reply With Quote

5. ## Re: Quick probability question

I wrote a quick script that did 200,000 tests for a series of 3 through 14 number of D10s, checking if at least 3 were 6s.
If 3 6s were found in a series then 1 point would be added through a series of 200,000 trials, the odds were then calculated as points/200,000.

These were the results. They do vary each time I run the script by about 1% (3d10 goes between 0.11 and 0.09 it seems). These are sort of accurate.

3d10 = 0.1%
4d10 = 0.35%
5d10 = 0.85%
6d10 = 1.56%
7d10 = 2.54%
8d10 = 3.82%
9d10 = 5.34%
10d10 = 7.11%
11d10 = 8.94%
12d10 = 11.19%
13d10 = 13.38%
14d10 = 15.86%

Here's the script
Spoiler

HTML Code:
```<html>
<title>Mastikator is great</title>
<script>
function doStuff()
{
var result = [];

for (var min = 3; min < 15; min++)
{
var res = 0;
for (var i = 0; i < 200000; i++)
{

var nr6 = 0;
for (var j = 0; j < min; j++)
{
var a = D10();
if (a == 6) nr6++;
}
if (nr6 >= 3) res+=1;
}
var odds = res/200000;
result[min] = odds;
}
var data = document.getElementById("data");
for (var awesomesauce= 3; awesomesauce< 15; awesomesauce++)
{
data.innerHTML += awesomesauce+"d10 = "+parseInt(result[awesomesauce]*10000)/100+"%<br/>";
}
}
function D10()
{
return parseInt(Math.random()*10)+1;
}
</script>
<div id="data"></div>
</body>
</html>```  Reply With Quote

6. ## Re: Quick probability question

Answer: way too many to bother. Think of it this way: the earliest you can even get 666, a 3d10 roll, it'll be 1/1000 chance. From there, the chance will very gradually rise with every additional die.  Reply With Quote

7. ## Re: Quick probability question

Hmm. How do the odds change if we use d6s?  Reply With Quote

8. ## Re: Quick probability question

1/216 at 3. To have the most consistency, use d4s.  Reply With Quote

9. ## Re: Quick probability question Originally Posted by Grod_The_Giant Hmm. How do the odds change if we use d6s?
Did the script, changed it to d6

3d6 = 0.43%
4d6 = 1.57%
5d6 = 3.56%
6d6 = 6.18%
7d6 = 9.62%
8d6 = 13.41%
9d6 = 17.67%
10d6 = 22.49%
11d6 = 27.27%
12d6 = 32.16%
13d6 = 37.09%
14d6 = 42.07%  Reply With Quote

10. ## Re: Quick probability question Originally Posted by Mastikator Did the script, changed it to d6
Thanks. You're awesome. I should be able to make my choices now.

(There are a couple mechanisms going into the doom pool size-- a Deadlands-style "fear levels" bit, and something Fate-y with "dark secrets")  Reply With Quote

11. ## Re: Quick probability question

Using a binomial distribution (http://en.wikipedia.org/wiki/Binomial_distribution) in Excel with 6 having a probability of 0.1 and Not-6 having a probability of 0.9. I found:

11d10 --> 8.96%
12d10 --> 11.09%

26d10 --> 48.95%
27d10 --> 51.54%

38d10 --> 74.63%
39d10 --> 76.22%

Using d6s (1/6 and 5/6 probabilities):

7d6 --> 9.58%
8d6 --> 13.49%

15d6 --> 46.78%
16d6 --> 51.32%

22d6 --> 73.48%
23d6 --> 76.27%

My values seem to agree with those from Mastikator's script, so I'm pretty confident I avoided any significant errors.   Reply With Quote

12. ## Re: Quick probability question

Just as a side note, rolling 3d6 and having incredibly bad things happen on 6, 6, 6 seems really fun.
Can you imagine that at character generation?  Reply With Quote

13. ## Re: Quick probability question Originally Posted by Kane0 Just as a side note, rolling 3d6 and having incredibly bad things happen on 6, 6, 6 seems really fun.
Can you imagine that at character generation?
Depends on what "incredibly bad" means. Being possessed by a dormant evil spirit that will act out at inopportune moments, yes, being blinded, no. It'd have to be funny but disastrous curve balls.  Reply With Quote

14. ## Re: Quick probability question Originally Posted by Kane0 Just as a side note, rolling 3d6 and having incredibly bad things happen on 6, 6, 6 seems really fun.
Can you imagine that at character generation?
Ill just leave that here.

Well, of course, when I play it, a 666 usually means great stuff happens because, lets be honest, why would I want to play a birdie when I can play for the Red team.  Reply With Quote

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