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Grod_The_Giant
2015-01-31, 10:06 PM
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)

Gavran
2015-01-31, 10:25 PM
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.)

Pinnacle
2015-01-31, 10:32 PM
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.

Grod_The_Giant
2015-01-31, 10:36 PM
Three or more sixes-- the important thing is the whole "666" bit.

Mastikator
2015-01-31, 11:07 PM
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



<html>
<head>
<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>
</head>
<body onload="try{doStuff();}catch(e){alert(e);}">
<div id="data"></div>
</body>
</html>

Frozen_Feet
2015-01-31, 11:19 PM
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.

Grod_The_Giant
2015-01-31, 11:27 PM
Hmm. How do the odds change if we use d6s?

JNAProductions
2015-01-31, 11:28 PM
1/216 at 3. To have the most consistency, use d4s.

Mastikator
2015-01-31, 11:43 PM
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%

Grod_The_Giant
2015-01-31, 11:58 PM
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")

GGambrel
2015-02-01, 12:20 PM
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. :smallsmile:

Kane0
2015-02-01, 10:42 PM
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?

Mastikator
2015-02-02, 12:34 AM
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.

Rondodu
2015-02-02, 05:53 PM
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?

Iíll just leave that here. (https://en.wikipedia.org/wiki/In_Nomine_Satanis/Magna_Veritas)

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