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From: rjnoe@riccb.UUCP (Roger J. Noe)
Newsgroups: net.games,net.math
Subject: Re: Re: 1000 Ways to Win Monopoly Games
Message-ID: <504@riccb.UUCP>
Date: Tue, 27-Aug-85 09:27:20 EDT
Article-I.D.: riccb.504
Posted: Tue Aug 27 09:27:20 1985
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> ... I've read the '100 ways to win Monopoly' book
> from the Public Library (plug: visit 'em!) and wasn't all that impressed
> with it.  Most of the stuff they talk about is either common sense or I
> had already figured out with a program I wrote which:
> 
> -	had the complete board internally, including all the cards and the 
> 	actions that each card had (like 'go to jail').  I let it run over
> 	the weekend once and came back to a terrific list of how many times
> 	each property had been landed on after 5 MILLION times around the
> 	board (or some other ungodly huge number like that!) with the same
> 	results that the book were so thrilled about.
> 			-- Dave "Killer Land (slum) lord" Taylor

There's a better way to do that.  First of all, write a program to assemble
the probabilities of getting to each state (defined as combination of square
one is on and how many doubles rolled consecutively so far) given that one
is in each of the other states and assemble these "state-transitional"
probabilities in a square matrix.  Then this square matrix multiplied by the
"steady-state" probabilities of being in each state must equal the same
vector of steady-state probabilities (one probability for each state).  So
subtract the identity matrix from the transitional probabilities and do a
simple Gaussian elimination on this sparse matrix.  Add the resulting values
corresponding to the individual squares and you have the overall probabilities
of being on each square on the board.

I did this years ago (as have others) and took the problem farther, to calcu-
late expected income and return on investment (per token move) for each
property on the board.  Then one can find optimum points of development for
each property group (yes, it's usually but not always hotels) and relative
profitability for each group.  There are some surprises in the results that
no amount of intuition will indicate.  I'll mail these results to anyone
interested.  If there's a ridiculous amount of interest I'll just post it
here.  I seriously doubt anyone wants to look at the programs . . .
--
Roger Noe			ihnp4!ihopa!riccb!rjnoe