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Probability of attaining a minimum value when rolling dice
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marc.t.davies@gmail.com
science forum addict


Joined: 31 May 2006
Posts: 52

PostPosted: Thu Jul 20, 2006 2:18 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

Arthur Dent wrote:
Quote:
MTD wrote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n?

I'm not sure what you mean. Rolling a total of N on N dice is (1/6)^N,
that's trivial.
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marc.t.davies@gmail.com
science forum addict


Joined: 31 May 2006
Posts: 52

PostPosted: Thu Jul 20, 2006 2:14 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

Quote:
The subject poses the question I was answering, the probability of
attaining a minimum value when rolling dice.

No, you answer how to calculate the probability of getting THE minimum
value for the total.

He asks for the probability of getting a total of _at least X _,
presumably with the condition n <= X < 6n
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Virgil
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Joined: 24 Mar 2005
Posts: 5536

PostPosted: Thu Jul 20, 2006 7:06 am    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

In article <1153378650.631766.155800@75g2000cwc.googlegroups.com>,
"Proginoskes" <CCHeckman@gmail.com> wrote:

Quote:
Virgil wrote:
In article <1153234669.122030.181660@75g2000cwc.googlegroups.com>,
nick@blackmarble.co.uk wrote:

Hi All

If I roll N 6-sided dice, whats the probability of scoring a total of
at least X?

Sorry if this is really simple, but my maths sucks :)

Nick

If each die has a single face with its smallest value on it and the dice
are "honest", then the probability of getting the lowest total on one
roll of n dice (or n rolls of one die) is (1/6)^n = 1/(6^n).

Evidently you need to read the post before you answer.

--- Christopher Heckman

The subject poses the question I was answering, the probability of
attaining a minimum value when rolling dice.
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Proginoskes
science forum Guru


Joined: 29 Apr 2005
Posts: 2593

PostPosted: Thu Jul 20, 2006 6:57 am    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

Virgil wrote:
Quote:
In article <1153234669.122030.181660@75g2000cwc.googlegroups.com>,
nick@blackmarble.co.uk wrote:

Hi All

If I roll N 6-sided dice, whats the probability of scoring a total of
at least X?

Sorry if this is really simple, but my maths sucks :)

Nick

If each die has a single face with its smallest value on it and the dice
are "honest", then the probability of getting the lowest total on one
roll of n dice (or n rolls of one die) is (1/6)^n = 1/(6^n).

Evidently you need to read the post before you answer.

--- Christopher Heckman
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Proginoskes
science forum Guru


Joined: 29 Apr 2005
Posts: 2593

PostPosted: Thu Jul 20, 2006 6:56 am    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

Keith A. Lewis wrote:
Quote:
"Arthur Dent" <fd4scy@yahoo.co.uk> writes in article <1153239107.272078.318890@p79g2000cwp.googlegroups.com> dated 18 Jul 2006 09:11:47 -0700:

MTD wrote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

I don't think a normal distribution is a good approximation.

Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n?

That's easy.

p(=n) = (6 - |n-7|) / 36 for 1<n<13

p(>=n) = 1 - (n-1)(n-2)/72 for 1<n<=7
= (14-n)(13-n)/72 for 7<n<=13

That's with 2 dice; the OP asked the question for a general number of
dice.

--- Christopher Heckman
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marc.t.davies@gmail.com
science forum addict


Joined: 31 May 2006
Posts: 52

PostPosted: Wed Jul 19, 2006 3:54 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

Quote:
Really? I think a normal distribution with mean 7*N/2 and variance
35*N/12 ought to be pretty reasonable for N greater than maybe about 5
or 6, and not ridiculously wrong even for N = 3 or 4. For larger N I
would expect it to get more and more accurate...

That's what I figured.

Hmm. If I have the time I will try to calculate the error factor.
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bill11
science forum Guru


Joined: 07 Sep 2005
Posts: 311

PostPosted: Wed Jul 19, 2006 12:51 am    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

nick@blackmarble.co.uk wrote:
Quote:
Hi All

If I roll N 6-sided dice, whats the probability of scoring a total of
at least X?

Sorry if this is really simple, but my maths sucks :)

Nick

It is really simple, but very labor intensive.

Suppose that N = 10 and X =35. You would to list every combination of
10 dice that added up to 35. This you would hve to do manualy Then you

would have to permutate every combination to get the total number of
ways
of getting 35 with 10 dice.

Divide this total by the total number of ways of throwing 10 dice;
6^10 to get the probability of a sum of 35.

regards

---Bill J

..
\
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matt271829-news@yahoo.co.
science forum Guru


Joined: 11 Sep 2005
Posts: 846

PostPosted: Wed Jul 19, 2006 12:34 am    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

Keith A. Lewis wrote:
Quote:
"Arthur Dent" <fd4scy@yahoo.co.uk> writes in article <1153239107.272078.318890@p79g2000cwp.googlegroups.com> dated 18 Jul 2006 09:11:47 -0700:

MTD wrote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

I don't think a normal distribution is a good approximation.

Really? I think a normal distribution with mean 7*N/2 and variance
35*N/12 ought to be pretty reasonable for N greater than maybe about 5
or 6, and not ridiculously wrong even for N = 3 or 4. For larger N I
would expect it to get more and more accurate...
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Virgil
science forum Guru


Joined: 24 Mar 2005
Posts: 5536

PostPosted: Tue Jul 18, 2006 7:54 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

In article <1153234669.122030.181660@75g2000cwc.googlegroups.com>,
nick@blackmarble.co.uk wrote:

Quote:
Hi All

If I roll N 6-sided dice, whats the probability of scoring a total of
at least X?

Sorry if this is really simple, but my maths sucks :)

Nick

If each die has a single face with its smallest value on it and the dice
are "honest", then the probability of getting the lowest total on one
roll of n dice (or n rolls of one die) is (1/6)^n = 1/(6^n).
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Keith A. Lewis
science forum Guru


Joined: 24 Mar 2005
Posts: 478

PostPosted: Tue Jul 18, 2006 6:55 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

"Arthur Dent" <fd4scy@yahoo.co.uk> writes in article <1153239107.272078.318890@p79g2000cwp.googlegroups.com> dated 18 Jul 2006 09:11:47 -0700:
Quote:

MTD wrote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

I don't think a normal distribution is a good approximation.

Quote:
Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n?

That's easy.

p(=n) = (6 - |n-7|) / 36 for 1<n<13

p(>=n) = 1 - (n-1)(n-2)/72 for 1<n<=7
= (14-n)(13-n)/72 for 7<n<=13

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
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F_L_Palmer@yahoo.com
science forum beginner


Joined: 12 Dec 2005
Posts: 4

PostPosted: Tue Jul 18, 2006 4:41 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

nick@blackmarble.co.uk wrote:
Quote:
Hi All

If I roll N 6-sided dice, whats the probability of scoring a total of
at least X?

Sorry if this is really simple, but my maths sucks :)

Nick

Take the expansion of (A + B)^n [= A^n + B*A^(n-1) + ... ]
A= 1/6 B=5/6
The first term is the probability of getting 6, the second term is the
probability of gettng 5. The sum of those terms is the probability of
getting at least five.

Keep going until you reach X.

This is much easier to write when you can use sigmas.
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Arthur Dent
science forum Guru Wannabe


Joined: 19 May 2005
Posts: 203

PostPosted: Tue Jul 18, 2006 4:12 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

MTD wrote:
Quote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n?
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Arthur Dent
science forum Guru Wannabe


Joined: 19 May 2005
Posts: 203

PostPosted: Tue Jul 18, 2006 4:11 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

MTD wrote:
Quote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n?
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marc.t.davies@gmail.com
science forum addict


Joined: 31 May 2006
Posts: 52

PostPosted: Tue Jul 18, 2006 3:52 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...
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Patrick Coilland
science forum Guru Wannabe


Joined: 29 Jan 2006
Posts: 197

PostPosted: Tue Jul 18, 2006 3:38 pm    Post subject: Re: Probability of attaining a minimum value when rolling dice Reply with quote

nick@blackmarble.co.uk nous a récemment amicalement signifié :
Quote:
Hi All

If I roll N 6-sided dice, whats the probability of scoring a total of
at least X?

Sorry if this is really simple, but my maths sucks :)

Hello,


I don't think there is a simple expression for the solution.
Il you call p(x,n) the number you are looking for, this number may be
computed in that way :

p(x,n) =
(p(x-6,n-1)+q(x-5,n-1)+q(x-4,n-1)+q(x-3,n-1)+q(x-2,n-1)+q(x-1,n-1))/6
with initialization : p(x,0) = 1 for x <= 0
p(x,0) = 0 for x > 0

--
Patrick
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