[muffinhead]

As a first year undergrad math student, I thought it would be fun to come up with a mathematical model for gm. By making a few simplified assumptions, i have a model which I believe to be reasonbly accurate. I might explain how I came up with it later on.

Anyways combining everything together and cutting a long explanation short, Here is my proposed model.

The expected profit (E) from a set of properties before economic collapse can be estimated by:

E = [ 0.8 * H * N * S * (P-1) / 10P ] - C

Where:

H = The amount of money you receive when someone lands on the property
N = The number of properties in the group eg for yellows N=2, for cyan N=3, for black N=4
S = The amount of money you recieve for passing go at a certain moment in the game
P = The number of players in the game
C = The total cost for buying the set ( eg for cyan its the amount you paid for the 3 properties plus the amount it cost to place houses.)

Assumptions made:

The E value is the amount of expected profit before economic collapse, so overall profit will be a little higher.
The E value includes the amount of money you will receive as well as the amount of money you take away from your opponent.


Lets do a quick example:
You buy 2 yellows for 1100 each and start money = 200 in a 4 player game is the moment u fully upgrade ur houses on the yellows.

then C = 2000+ 750 =2750 (half since u get money back when u sell houses)
N = 2
H = 250
S = 200
p = 4

Therefore E = [ 0.8*2*250*200*3 / 40] -2750]
E = $3250
Therefore a good buy at that moment in the game.



So finally whats everyones thoughts? Do you think this would be hepful in a game? Are there any important factors that I have missed? Will this improve ur game?
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[theunknownamus]

This is spectacular. Simply use it combined with independent variables (Bonuses, Chance Spaces, etc.) and you've got a great chart.

[muffinhead]

By assuming profit before economic collapse, the model preety much eliminates any impact that bonus money will have. The only important part which it contributes to is the rate of accession.
I would love to find a list of random cards that are used in the game to determine a more accurate rate of accession. Currently ive estimated the rate of accession decrease due to bonuses and meteor shower to be 10*P (So in 2p the board decreases by 20 each time everyone goes around the board once and 50 in 5p etc) . Do you guys think this is an accurate accession decrease rate? It seems a little high but may actually be accurate.

Personally I believe that the biggest independent variables affecting the current model is going back to start after an auction and jail. Hopfully some day I can factor in those variables. The current model is still a draft where improvements can always be made.
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