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From: hes@ecsvax.UUCP (Henry Schaffer)
Newsgroups: net.math
Subject: Re: Dice "Odds"
Message-ID: <907@ecsvax.UUCP>
Date: Fri, 13-Dec-85 09:35:38 EST
Article-I.D.: ecsvax.907
Posted: Fri Dec 13 09:35:38 1985
Date-Received: Sat, 14-Dec-85 08:17:19 EST
References: <309@tekigm2.UUCP>
Distribution: net
Organization: NC State Univ.
Lines: 52

> Given that you use two dice in a game and that you are trying to figure 
> the odds of getting a particular combination:  do you use the combinations
> or the permutations to determine the odds?
> 
> 	    Permutations                        Combinations
>         Number        Ways                   Number       Ways
> 	  2             1                      2            1
> 	  3             2                      3            1
> 	  4             3                      4            2
> 	  5             4                      5            2
> 	  6             5                      6            3
> 	  7             6                      7            3
> 	  8             5                      8            3
> 	  9             4                      9            2
> 	  10            3                      10           2
> 	  11            2                      11           1
> 	  12            1                      12           1
>                        ---                                 ---
> 		       36                                  21
> 
   The permutations is the simpler approach, because it provides easier,
more direct computation of the probabilities.  The reason is that the 36
different events are all equiprobable, and so the calculation of
probabilities (or odds) reduces to just counting events.
(The crux of the matter is that you see that there are 36 different
events, even though we reduce them to the 12 different numberical sums.
if you have trouble seeing that there are 36, consider that one die is
white, and one is off-white, and each can come up with 6 different faces.)
> ...
> (One red and two white.)  The first throw determines region by the formula:
> Red   even or odd
> White  total of spots
> 
> It is obvious that the red die has 50% odds of reaching either chart, the even
> chart or the odd chart.  From there it becomes less obvious, so I am appealing
> to those other Mathematicians out there whose schooling is much more recent 
> then mine.  I say that you look at the ways you can get the combinations and 
> the other person is arguing for using the permutations.  ...
> 
> The point being:  does it make any difference to throw an 11 whether one die
> is a 5 and the other is a 6 or the reverse?  Are the odds of throwing an
> 11 the same as a 12 or l/2?  Are the odds of throwing an 10 l/2 of a 12 or
> l/3?
> 
   No it doesn't make any difference which die is a 5 vs a 6 when you throw
an 11 - however since it can happen two different (equiprobable) ways, vs. 
the one way a 12 can result, then the probability is twice as great.

> Thanks,
> --Bill--

--henry schaffer