[net.games.board] Final remarks on city probs., rule changes for Rail Baron

doug@cornell.UUCP (12/11/85)

From: doug (Douglas Campbell)

> From wrd@tekigm2.UUCP (Bill Dippert)
> > From: doug (Douglas Campbell)
> > > From: wrd@tekigm2.UUCP (Bill Dippert)
> > > > From: doug (Douglas Campbell)
> > > > 
> > > > Just for fun, I printed out the probabilities of going to each city under
> > > > the original and the Seattle rules.  Here are some highlights:
> > > >
> > > 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?
> > 
> > There are 72 combinations possible for each region/city roll.  (72 = 6x6x2
> > for the 2 six-sided and the even/odd roll).  The number of combinations that
>
> > result in the following values with 2 dice are listed below:
>
> *****WRONG! YOU ARE CALCULATING PERMUTATIONS AND NOT COMBINATIONS.  FOR
> DETERMINING THE ODDS OF REACHING A REGION YOU NEED THE COMBINATIONS OF THE
> DICE NOT THE PERMUTATIONS.*****
> 
>           "Permutations"                     "Combinations"
>  	Result		Ways               Result         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 
  
Sorry Bill, but an 11 is more probable than a 12.  I am right, and you
are wrong, even if you use all capital letters :-).  Scott Turner's
calculations agreed with mine (he considered San Fransisco & Oakland
as the same city, whereas I did not).

Finally, on the subject of Seattle rules vs. rr price changes vs.
leaving everything alone, let me point this out.  Assuming that
you want to make chance less of a factor (if you don't, stick with
the original rules) the rr price changes are more effective than
the Seattle rules.  Witness the difference between the railroad
prices in the original rules, the changed prices in the Seattle
rules, and the changed prices in the original rules.  The difference
in prices is much greater between the original rules and each of
the changed price schemes.  Thus, even with the Seattle rules, some
rr's are greatly underpriced, and some are greatly overpriced.  Thus,
the problem of races for the good deals still exists in the Seattle
rules.  So, the luck at the beginning of the game still largely
determines the outcome.
					Signing off,
					Doug Campbell