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  1. - Top - End - #1
    Titan in the Playground
     
    Grod_The_Giant's Avatar

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    Default 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)
    Last edited by Grod_The_Giant; 2015-02-03 at 12:17 AM.

    STaRS (and STaRS Lite)
    A non-narrativeist, generic rules-light system, by me. Now officially released!

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    Quote Originally Posted by Grod_The_Giant View Post
    Grod's Law: You cannot and should not balance bad mechanics by making them annoying to use
    Giants and Graveyards: My collected 3.5 class fixes and more.

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    Bugbear in the Playground
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    Default 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.)

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    Barbarian in the Playground
     
    Pinnacle's Avatar

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    Default 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.
    Gamer avatar by kpenguin. I love the tiny little game pad belt.

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    Grod_The_Giant's Avatar

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    Default Re: Quick probability question

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

    STaRS (and STaRS Lite)
    A non-narrativeist, generic rules-light system, by me. Now officially released!

    Grod's Guide to Greatness
    A big book of player options for 5e, by me

    Quote Originally Posted by Grod_The_Giant View Post
    Grod's Law: You cannot and should not balance bad mechanics by making them annoying to use
    Giants and Graveyards: My collected 3.5 class fixes and more.

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    Ogre in the Playground
     
    Imp

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    Default 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
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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>
    Black text is for sarcasm, also sincerity. You'll just have to read between the lines and infer from context like an animal

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    Ettin in the Playground
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    Default 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.
    Last edited by Frozen_Feet; 2015-01-31 at 11:20 PM.
    "It's the fate of all things under the sky,
    to grow old and wither and die."

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    Titan in the Playground
     
    Grod_The_Giant's Avatar

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    Default Re: Quick probability question

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

    STaRS (and STaRS Lite)
    A non-narrativeist, generic rules-light system, by me. Now officially released!

    Grod's Guide to Greatness
    A big book of player options for 5e, by me

    Quote Originally Posted by Grod_The_Giant View Post
    Grod's Law: You cannot and should not balance bad mechanics by making them annoying to use
    Giants and Graveyards: My collected 3.5 class fixes and more.

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    Colossus in the Playground
     
    JNAProductions's Avatar

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    Default Re: Quick probability question

    1/216 at 3. To have the most consistency, use d4s.
    Last edited by JNAProductions; 2015-01-31 at 11:28 PM.
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    Ogre in the Playground
     
    Imp

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    Default Re: Quick probability question

    Quote Originally Posted by Grod_The_Giant View Post
    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%
    Black text is for sarcasm, also sincerity. You'll just have to read between the lines and infer from context like an animal

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    Titan in the Playground
     
    Grod_The_Giant's Avatar

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    Default Re: Quick probability question

    Quote Originally Posted by Mastikator View Post
    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")

    STaRS (and STaRS Lite)
    A non-narrativeist, generic rules-light system, by me. Now officially released!

    Grod's Guide to Greatness
    A big book of player options for 5e, by me

    Quote Originally Posted by Grod_The_Giant View Post
    Grod's Law: You cannot and should not balance bad mechanics by making them annoying to use
    Giants and Graveyards: My collected 3.5 class fixes and more.

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    Dwarf in the Playground
     
    PirateGuy

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    Default 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.

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    Ettin in the Playground
     
    Kane0's Avatar

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    Default 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?

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    Ogre in the Playground
     
    Imp

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    Default Re: Quick probability question

    Quote Originally Posted by Kane0 View Post
    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.
    Black text is for sarcasm, also sincerity. You'll just have to read between the lines and infer from context like an animal

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    Halfling in the Playground
     
    MonkGuy

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    Default Re: Quick probability question

    Quote Originally Posted by Kane0 View Post
    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.

    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.
    Last edited by Rondodu; 2015-02-02 at 05:56 PM.

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