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From: wrd@tekigm2.UUCP (Bill Dippert)
Newsgroups: net.games.board,net.math
Subject: Dice "Odds"
Message-ID: <309@tekigm2.UUCP>
Date: Thu, 12-Dec-85 14:14:09 EST
Article-I.D.: tekigm2.309
Posted: Thu Dec 12 14:14:09 1985
Date-Received: Fri, 13-Dec-85 20:47:46 EST
Distribution: net
Organization: Tektronix, Beaverton OR
Lines: 48
Xref: watmath net.games.board:156 net.math:2618

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

What we are trying to determine is in the game of Railbaron, what the odds
are of reaching each city.  To do this requires a throw of three dice.
(One red and two white.)  The first throw determines region by the formula:
Red   even or odd
White  total of spots

The second throw then determines the city 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 problem is further
complicated by the fact that some cities have more then one possible way of
getting picked.  I.e. odd 7, even 3, even 10.  

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?

I am cross posting this to the interested group as well as to the "expert"
group.

Thanks,
--Bill--