Quick probability question [RESOLVED]

**Grod_The_Giant** · 2015-01-31, 10:06 PM (ISO 8601)

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 (ISO 8601)

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 (ISO 8601)

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 (ISO 8601)

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

**Mastikator** · 2015-01-31, 11:07 PM (ISO 8601)

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

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HTML Code:

<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 (ISO 8601)

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 (ISO 8601)

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

**JNAProductions** · 2015-01-31, 11:28 PM (ISO 8601)

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

**Mastikator** · 2015-01-31, 11:43 PM (ISO 8601)

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%

**Grod_The_Giant** · 2015-01-31, 11:58 PM (ISO 8601)

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")

**GGambrel** · 2015-02-01, 12:20 PM (ISO 8601)

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.

**Kane0** · 2015-02-01, 10:42 PM (ISO 8601)

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 (ISO 8601)

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.

**Rondodu** · 2015-02-02, 05:53 PM (ISO 8601)

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.

Thread: Quick probability question [RESOLVED]

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