
31 Jan 2008, 19:49  #1 (permalink) 
Shas'Vre
Join Date: Dec 2007
Posts: 1,111

Die Rolls
I know how to get the percentage chance of rolling one 6 or two 6s or six 6s on a given number of dice but what's the formula to determine the chance of rolling a number at least once? For example if I roll 6d6 what are the chances of rolling at least one 6?
Thanks for the help. 

31 Jan 2008, 19:51  #2 (permalink) 
Shas'O

Re: Die Rolls
Well its a one in six chance of getting one six on one dice, so it'll be 6 times that amount for 6 dice.
There's no official answer, all there is is for every six dice you should at least get one six. I don't know the proper stats etc 
31 Jan 2008, 19:55  #3 (permalink) 
Shas'Vre
Join Date: Dec 2007
Posts: 1,111

Re: Die Rolls
Well I know that on one die it's a 16.66% chance. So would I just multiply the percentage by the number of rolls?
16.66% * 6 = 99.96% chance of at least one 6. 
31 Jan 2008, 20:01  #4 (permalink) 
Shas'O

Re: Die Rolls
Yeah that sounds about correct.. but you can't follow those odds, they'll never work that way.
See I pray to the dice gods ^_^ 
31 Jan 2008, 20:05  #5 (permalink) 
Shas'Vre
Join Date: Dec 2007
Posts: 1,111

Re: Die Rolls
Weird, the board ate half of my last post!
And yeah, there are no small animals left in my neighborhood  the dice gods must be appeased after all. :funny: 
31 Jan 2008, 20:14  #6 (permalink) 
Shas'El
Join Date: Dec 2006
Posts: 2,645

Re: Die Rolls
The odd of getting a 6, as you know, is 1 in 6. More dice does not change the likeliness of getting a 6 on a single die, but does increase your chances of seeing one 6 because you're playing the odds in your favor. So, with 6 dice you are likely to see at least one 6 present, being a 1 in 6 chance and having 6 dice.
Think of it this way, you flip a coin and you have a 50% chance of it coming up heads, right? You flip 2 coins, you still have a 50% chance of one coming up heads, having 2 coins does not change that. 
31 Jan 2008, 20:30  #7 (permalink) 
Shas'Vre
Join Date: Dec 2007
Posts: 1,111

Re: Die Rolls
Yes but the percentage should change. I mean if I roll one die I have a 16.66% chance of a 6 but if I roll 1,000 dice I should have a much higher chance of seeing at least one 6. With a thousand rolls it should be higher than 16.66%. It also doesn't seem right that after the number of dice reaches 6 the percentage effectively never changes. (100%) ???

31 Jan 2008, 20:51  #8 (permalink)  
Shas'Vre
Join Date: Dec 2007
Location: United States
Posts: 1,106

Re: Die Rolls
Quote:
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31 Jan 2008, 20:52  #9 (permalink) 
Shas'El
Join Date: Dec 2006
Posts: 2,645

Re: Die Rolls
It can never be 100%. You are dealing with individual items that have a 1 in 6 chance of coming up the number you want, there's no 100%. It's been too long since I had stats, but look at it this way. If you roll a single die 6 times, what are your odds of getting a 6? The odds are still 1 in 6 on each roll, but because you're rolling it 6 times, odds favor that you'll see a 6 show up at least once, 1 roll in 6 or 1 in 6 odds.
It's still a 16.7% chance of seeing a 6, just the more dice you roll the better your "chances" are. 
01 Feb 2008, 03:06  #10 (permalink)  
Shas'Vre
Join Date: Sep 2007
Posts: 1,958

Re: Die Rolls
Quote:
So: 1  (5/6) for 1 die which is 1 / 6 1  5/6)^2 for 2 dice which is 11 / 36 1  (5/6)^3 for 3 dice which is 91 / 216 if the lousy Windows calculator did the math right. 

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