Analyzing data in a Monopoly Game?

[Mike P]

This should be fairly straightforward, but I can't figure out how to
approach this.... I'd appreciate any ideas you have.

Goal:

Make recommendations on what a Monopoly player should do with the
houses/hotels, cards and cash they have. (i.e., what should they
mortgage/unmortage, where should they build, etc.)

What I have:

I have created a calculator to figure out the relative value of any
board setup... so any setup I give the script, I can figure out how good it
is. (http://www.psmonopoly.com/calc/propstats.htm). If you try it, the page
will show you the relative value of your setup under RESULTS at the top.

The user has given me their current setup (what they own, what's
mortgaged, what has houses, etc.), how much money they have on-hand, how
much money they want to keep on-hand after the recommendations.

What I'd like to do:

Cycle through every conceivable thing they could do (mortgage a property
here, unmortage one there, build a house here, sell a house there, etc.),
compare the relative values of all the setups, and tell them which would be
their best choice. These options are limited by monopoly rules and what
they have to play with. For example, they have to build evenly, so a user
can't have four houses on one property and the other mortgaged in the same
monopoly. They can't build more houses than they have cash to buy, and they
can only change what they have (i.e., they can't build on a property unless
they own the whole block).

Where I'm stuck:

I haven't the foggiest notion of how to use javascript to loop through all
the configurations.

I assume, once I figure out how to loop through all the user's options, I
can create a two dimensional array, containing specifics of the monopoly
config, and the relative value I calculate for it, then find the highest
relative value, and show them the delta between how the board is set up now,
and how it should (optimally) be set up.

Any thoughts?

[Douglas Crockford]

> Where I'm stuck:

I haven't the foggiest notion of how to use javascript to loop through all
the configurations.

JavaScript is closely related to Scheme, so any sort of AI approach
could be easily accomodated. See
http://www.crockford.com/javascript/little.html

[Lee]

Mike P said:

This should be fairly straightforward, but I can't figure out how to
approach this.... I'd appreciate any ideas you have.

Goal:

Make recommendations on what a Monopoly player should do with the
houses/hotels, cards and cash they have. (i.e., what should they
mortgage/unmortage, where should they build, etc.)

What I have:

I have created a calculator to figure out the relative value of any
board setup... so any setup I give the script, I can figure out how good it
is.

That's not really enough. Maximizing the next move is likely to lead to
dead ends from which there is no "better" move.

Consider the case in the best strategy would be to sell one property
in order to finance the purchase of a hotel. Having the hotel instead
of that property might be clearly favorable, but looking one move ahead,
you're not going to see any advantage to selling the property.

[Mike P]

"Lee" <RE**************@cox.net> wrote in message
news:dj*********@drn.newsguy.com...

That's not really enough. Maximizing the next move is likely to lead to
dead ends from which there is no "better" move.

Consider the case in the best strategy would be to sell one property
in order to finance the purchase of a hotel. Having the hotel instead
of that property might be clearly favorable, but looking one move ahead,
you're not going to see any advantage to selling the property.

Lee, you make a good point. The calculator, as it stands now, uses long
term probability of landing on a square (assuming infinite rolls),
multiplied by the payoff should your opponent land on the square. I think
it's a fairly good measure, though your point is well taken. Monopoly
depends heavily on the dice roll. I'm not currently factoring in where
players are situated on the board, nor am I factoring in how their
opponent(s) are setup. So regardless of what they do, the next roll can
change things significantly... they might lose with the next roll of the
dice.

Still, I have to begin somewhere.... and I believe this is a good place to
start. Any ideas on how to do the data analysis.... or even a better
overall approach?

Thanks!

Mike

[RobG]

Mike P wrote:

"Lee" <RE**************@cox.net> wrote in message
news:dj*********@drn.newsguy.com...

That's not really enough. Maximizing the next move is likely to lead to
dead ends from which there is no "better" move.

Consider the case in the best strategy would be to sell one property
in order to finance the purchase of a hotel. Having the hotel instead
of that property might be clearly favorable, but looking one move ahead,
you're not going to see any advantage to selling the property.

Lee, you make a good point. The calculator, as it stands now, uses long
term probability of landing on a square (assuming infinite rolls),
multiplied by the payoff should your opponent land on the square. I think
it's a fairly good measure, though your point is well taken. Monopoly
depends heavily on the dice roll. I'm not currently factoring in where
players are situated on the board, nor am I factoring in how their
opponent(s) are setup. So regardless of what they do, the next roll can
change things significantly... they might lose with the next roll of the
dice.

Still, I have to begin somewhere.... and I believe this is a good place to
start. Any ideas on how to do the data analysis.... or even a better
overall approach?

Once you define the algorithm, it can be implemented. There are a
number of strategies, and various ways of determining outcomes.

You may be interested in:

<URL:http://hometown.aol.co.uk/monopolycheat/>
Is that what you have in mind?
--
Rob

[Mike P]

"RobG" <rg***@iinet.net.au> wrote in message news:hd******************@news.optus.net.au...

Once you define the algorithm, it can be implemented. There are a
number of strategies, and various ways of determining outcomes.
You may be interested in:
<URL:http://hometown.aol.co.uk/monopolycheat/>
Is that what you have in mind?
--
Rob

Well close :). I've not seen that site before, but I have read through Truman Collins and Durango Bill's work. I'm trying to take their numbers and apply it to actual play situations. Truman Collins speculated that we could estimate game outcome by adding his "long term estimated income" numbers for the current game state of each player. That will give the combined estimated income for that player, at that time. The Monopoly calculator I'm in the middle of writing does just that. A player enters which properties they own, and I determine the combined long-term income. Pretty simple. Comparing the numbers of each players setup will show who's the strongest.

Then I realized, I can take it even further. I can look at what the player's current game state is, and figure out how they can change things around to improve their combined long-term income. I made up a setup, and manually did some "what-if" changes, using the JavaScript calculator I had just written. I thought, suppose a player owned both Blue properties, all three Baby Blue properties, and had $400 in cash. Should they put two houses on Blue or 8 houses on Baby Blue? Playing around with it, I found out that the baby blue option is better.... Beyond that, if a player also mortgaged Park Place (cheaper Blue), they'd get $175 more, allowing them to put Hotels on each of the Baby Blues. That gave the strongest possible long-term expected income, given what they had to play with.

What I'm now trying to do, is have the JavaScript run through all the "what-ifs" for them, and tell them what they should change to optimize their setup (i.e., Houses/Hotels they should buy or sell, properties they should mortgage or unmortgage) to optimize what they have to work with. I'm having trouble figuring out the algorithm to run through all the what-if's. I can determine the outcome, but how do I identify the feasible what-ifs to loop through? It's a little tricky because of monopoly rules. Specifically, they must build evenly, so players can not put four houses on one property until they have three on the others. They can't build up a property unless they own the whole color group, and each property is out of mortgage. If they mortgage a property they get half the purchase price, but they'll pay a 10% premium to unmortgage it. So a $100 property will yield $50 when mortgaged, but will take $55 to unmortgage. How can I figure out all the feasible setups so that I can loop through them calculating their long-term expected income?

Thanks!!!

Mike