rjnoe@riccb.UUCP (Roger J. Noe) (08/27/85)
> ... 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
wws@whuxlm.UUCP (Stoll W William) (08/29/85)
> > > > - 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 > > 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. Both of these approaches were taken in the "1000 ways..." book and results were put in the tables in the back. Not bad for a book published before the computer explosion (printed in 1975). I think there are some other tables as well, but I don't have the book in front of me! Bill Stoll, ..!whuxlm!wws