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From: wrd@tekigm2.UUCP (Bill Dippert)
Newsgroups: net.games.board
Subject: Re: Improved truly fair Rail Baron rules
Message-ID: <300@tekigm2.UUCP>
Date: Wed, 4-Dec-85 10:41:52 EST
Article-I.D.: tekigm2.300
Posted: Wed Dec  4 10:41:52 1985
Date-Received: Sat, 7-Dec-85 21:27:11 EST
References: <1324@cornell.UUCP>
Organization: Tektronix, Beaverton OR
Lines: 92

> From: doug (Douglas Campbell)
> 
> After looking at my previous posting, I decided that my scheme for railroad
> pricing was sound, but that the Northeast rails needed a little fixing...
> ......etc.........
> 
> Just for fun, I printed out the probabilities of going to each city under
> the original and the Seattle rules.  Here are some highlights:
> 
> (Numbers are the percent chance of going to the city)
> 
> 			Top 10
> 	Original			Seattle
>   4.05	 New York		 2.70	 New York
>   3.94	 Los Angeles		 2.55	 Portland, Ore.
>   3.40	 Chicago		 2.51	 Oklahoma City
>   2.89	 Philadelphia		 2.51	 Kansas City
>   2.89	 Boston			 2.33	 Indianapolis
>   2.78	 Seattle		 2.33	 Detroit
>   2.78	 Kansas City		 2.31	 Philadelphia
>   2.62	 Portland, Ore.		 2.31	 Memphis
>   2.60	 Baltimore		 2.12	 Spokane
>   2.60	 Atlanta		 2.12	 Salt Lake City
> 
> 			Bottom 10
> 	Original			Seattle
>   0.69	 Tucumcari		 0.77	 Dallas
>   0.69	 Reno			 0.77	 Chattanooga
>   0.69	 Little Rock		 0.64	 Billings
>   0.69	 Charleston		 0.58	 St. Paul
>   0.62	 Pocatello		 0.58	 Shreveport
>   0.62	 Casper			 0.39	 Tampa
>   0.52	 Shreveport		 0.39	 El Paso
>   0.52	 Chattanooga		 0.39	 Charleston
>   0.52	 Charlotte		 0.39	 Birmingham
>   0.46	 Fargo			 0.39	 Albany
> 
> 			Other
> 	Original			Seattle
>   2.31	 San Fransisco		 1.35	 San Fransisco
>   2.08	 Oakland		 1.54	 Oakland
>   1.74	 Miami			 1.35	 Miami
>   1.16	 Portland, Me.		 1.54	 Portland, Me.
> 
> 	    Where the top 10 went/came from
> 	Original			Seattle
>   1.23	 Oklahoma City		 1.93	 Los Angeles
>   1.06	 Indianapolis		 1.91	 Seattle
>   2.33	 Detroit		 1.70	 Chicago
>   1.22	 Memphis		 1.35	 Atlanta
>   0.77	 Spokane		 1.16	 Boston
>   1.39	 Salt Lake City		 0.96	 Baltimore
> 

Out of curiosity:  how did you calculate the odds to get the cities?  Did
you take into consideration the odds to get to the region first, then the
odds that once in that region you could roll that city?  Or what?

When I did my calculations to get the differences of obtaining SE between
the original rules and the Seattle Rules, I did the following math:

Under the "Seattle Rules" reaching Southeast requires:
     an odd 3
     an odd 10 
     or an even 6


The odds of rolling an odd 3 are [(l/2)(1/6 + 1/6)];
the odds of rolling an odd 10 are {[1/2][(1/6 + 1/6)(1/6 + 1/6)]};
and finally the odds of rolling an even 6 are 
	 {[1/2][(1/6 + 1/6)(1/6 + 1/6)(1/6 + 1/6)]}.

To get the odds of any of these to happen is the sum of these three
probabilities or reducing this down:

	  (1/6) + (1/18) + (1/54) = .24 or 24%

	  This compares to the 7% for the original rules. (Per another 
	  posting, I did not check this out.)

	  All of the above based on the forumulas of probability as 
	  expressed in an "Introduction to Modern Algebra" by Neal H. 
	  McCoy.  (And at least 20 years after receiving my B.S. in Math!)

Are you or is there anyone out there willing and knowledgeable to first 
calculate the odds of reaching each region and second of reaching each 
city within each region?  -- for both the original and the Seattle rules?

Thanks,
--Bill--

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