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Die Rolls
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Old 31 Jan 2008, 19:49   #1 (permalink)
Nox
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Default 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.
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Old 31 Jan 2008, 19:51   #2 (permalink)
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Default 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
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Old 31 Jan 2008, 19:55   #3 (permalink)
Nox
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Default 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.
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Old 31 Jan 2008, 20:01   #4 (permalink)
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Default 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 ^_^
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Old 31 Jan 2008, 20:05   #5 (permalink)
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Default 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:
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Old 31 Jan 2008, 20:14   #6 (permalink)
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Default 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.
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Old 31 Jan 2008, 20:30   #7 (permalink)
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Default 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%) ???
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Old 31 Jan 2008, 20:51   #8 (permalink)
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Default Re: Die Rolls

Quote:
Originally Posted by Nox
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%) ???
Keep in mind that statistics will only ever tell you what you'll see on average. Rolling six 6-sided dice will, on average, get you at least one 6 every time (i.e. 100%).
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Old 31 Jan 2008, 20:52   #9 (permalink)
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Default 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.
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Old 01 Feb 2008, 03:06   #10 (permalink)
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Default Re: Die Rolls

Quote:
Originally Posted by Timjim
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
Not quite. That would mean that you are guaranteed to get a 6 if you roll 6 dice, but you're not. It's likely, but not certain. What you want is 1 minus [(the odds of not rolling a six) to the (how many rolls) ].

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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