Overview
Monopoly is one of the classic American games.It’s played among close friends, loved ones, and trusted business partners.It’s also one of the few times in life where it’s perfectly acceptable to want to systematically annihilate and crush the aforementioned friends, loved ones and partners.Monopoly is one of the classic American games.It’s played among friends, our soul mates and people we barely like.It’s also one of the few times in life where it’s perfectly fine to systematically bankrupt and crush the aforementioned people.
Introduction
So let’s say you guys want to dominate in monopoly and destroy every social bridge you’ve ever had. I am here to help
We will use simple math and propabilities to completely comprehend monopoly.
Monopoly has a major element of chance in it, and the best part about games of chance is that people with Microsoft Excel can basically solve them.
Let’s break down the must-know math behind Monopoly as well as several lessons you can take away from what truly is The Most Dangerous Game.
In this guide, we’ll talk about such concepts as:
- The most important properties in the game
- The crucial “axis” that will change the way you think about the shape of the board.
- Where you should invest.
- How to make moves so that your opponent will keep landing on your properties.
Step 1
Let’s start with the most basic propability in Monopoly: Rolling the dice
All of the randomness in Monopoly is derived from that damned dice roll.
So why not build up to a model of Monopoly board starting here.
So right off the bat, here’s what we know.
We see that the most propable square to land is square seven, which is in this case the Chance card. You also have comparatively higher propabilities of landing on Oriental or Vermont.
You also have a greater than one in ten chance of landing on the Reading Railroad or Connecticut.
Rolling Double-os
Rolling double is a huge distribution change.
- In Monopoly, when you roll a set of doubles, you get to roll the dice again.
- The previous section is an excellent calculator of where someone will land on their next roll.
- If we want to find out where someone will end their turn, which will also help us figure out other propabilities, we need to factor in doubles.
So how often do we roll a double?
Rolling doubles can be really powerful.
It’s technically possible, even if unlikely, to get to the Short Line Railroad by dice alone on your first turn, with a propability of 0.00021%.
This could go on in theory forever.
However, Monopoly has the Speeding rule
This means that you will go to jail after rolling three doubles.
Since the problem gets exponentially harder after calculating the second roll, the next chart factors in rolls, or a 97% propability of all cases.
Here we have the propabilities of ending on a space on the first turn of the game.
Of course, winning Monopoly isn’t that easy.
Monopoly isn’t simple dice rolls and games of chance.
And that’s good news, otherwise we’d all play roullette, and thus why it’s so fun!
If it were just dice rolls around a circle each space would be equally likely and thus boring as heck!
Chance cards, your friends and foes.
In Monopoly, when you land on the Chance space, you draw one of sixteen Chance cards.
Chance cards tell you one of the following five things.
- A get out of jail for free card with a chance of 1/16
- Collect money with 3/16
- Advance to somewhere on the board with 8/16
- You pay money 3/16
- Go to jail maggot! 3/16
So, we instantly see that chance cards dramatically change the game.
In particular,
- In 9 of 16 chance cards, you’re transported from one of the three chance spaces to another space.
This has an effect on the different weights of certain spaces on the board.
Heres where they can send you
This leads to some trouble on the board
You’ll notice that the chance cards send you to the first and second rows much more frequently than they send you to the third and fourth rows, thus decreasing the frequency of you landing on others.
Le community chestos
16 cards, so similar chances.
5 different outcomes
- Get out of Jail 1/16
- Collect le dosh $ 9/16
- Advance somewhere on the board 1/16
- Pay up mister 4/16
- Go to the jail and drop the soap 1/16
Let’s use math (or rather excel) and guess what will happen.
Thus, it would be highly profitable, to exploit the cards and their effects, by buying the Railroads, New York Ave, St. Charles Place, Illinois Ave and Boardwalk and the properties neighboring these areas.
How the Jail works
You have 3 ways to dodge the chance to be the next soap dropper and starring as the protagonist in a comic ( ͡° ͜ʖ ͡°)
- You can use or buy a get out of jail card
- Pay $50 dollars at the start of either of your next 2 turns
- Throw the dice within the next 3 turns in order to get a doubles and get out. If not, sorry but you gotta pay $50 to get out.
If you successfuly roll out of jail, you immediately move that number of spaces.
If you fail to roll the doubles thrice and pay the fine, you move the number of spaces of your last roll.
Oh and because I am the excel whisperer here’s a propability chart.
Now why does the jail matter?
Because every single space that comes after the jail gets landed on more frequently than other spaces.
The jail LITERALLY pulls the players into it by how easy it is to get in at any point on the board.
Lemme show you why
Because so many spaces send people to the Jail, it’s the axis of the board.
Jail is more important as a space than Go.
People go to jail for speeding a lot more often than you’d expect to.
The propability to do so, is 0.4%
However by looking at how many times people roll that dice in a game of monopoly, it becomes pretty plausible over the course of the game, and by turn 50, it goes up to 20% (0.4 * 50 = 20%)
Thus the spaces after jail are strategically important and excellent investments.
The board is designed to route people through the jail. Use that to your advantage when you build houses.
If you’re in jail, consider if it is a better move out early by bailing or gambling.
How to solve the statistics of Monopoly
We know how to figure out the propability of our rolls to any other space, in relation to where we are, and we know how to calculate the propability of getting teleported to another space by a card.
For that we will one of the core mathematical ideas behind the game. The Markov Chain.
Let’s go to NYC. Let’s say you want to project the eventual population shares of various boroughs of NYC.
We know how many people exit each borough to another one for all 5 regions. So let’s assume that nobody leaves NYC.
In our Markov Chain example, here’s what we know about Manhattan.
In any given year, let’s say:
- 94% of Manhattan residents stay there
- 3% go to Brooklyn
- 1.5% go to Queens
- 1% move to Bronx
- and 0.5% move to Staten Island
Now we know all of these numberinos for every borough.
We can build a matrix of all these numbers starring Keanu Excel.
Then we multiply them, and then the resulting matrix product by propability matrix A again. We doso for hundreds of times.
Eventually the numbers stop changing and we get a matrix with one number for each borough called a “steady state propability matrix.
Now, just like we did with the NYC example, we can figure out the steady state propability of someone landing on any space.
What can we learn thus far?
First of all the red and orange properties are exceptional investments.
The railroads, early in the game, they’re killers.
Properties between Jail and Go To Jail get landed more frequently than properties between Go to Jail and Jail.
On any given turn a player lants on an average of 1.25 spaces.
This is the result of either rolling doubles or hitting a chance or community chest space.
The average net income a player receive from one round on the board is $170, including rents, payments and the Go space. Factor that stat into your willingness to stay in jail.
When should I build?
That’s a very good question.
Let’s see the breakeven time for acquisition & construction.
A major question for players is the question of how long it will take them to recoup their investment. The following chart shows the average number of opponent rolls before the cost of buying and building houses is recouped. Red means faster recouped costs and blue means slower.
Now let’s observe this chart showing the total cost of acquisition and construction for each set of properties. This is section with the best Rate of Investment (ROI) times is still highlited with a black border.
What do we know from this?
While Park Place and Boardwalk are excellent for crushing opponents, early in the game their ROI is rather not ideal.
If anything, my personal tip and strategy, go for all the railroads.
Also always try to build the third house on the orange block of St James, Tennessee and NY.
Three houses is the way to go
So what have we realised thus far?
Rule #1.
Take a chance on these properties
- New York Ave and the orange block
- Illinois Ave and the red block
- St. Charles Place and the purple block
- Boardwalk and the blue block
- Le Railroads
Always attempt to buy the properties and blocks that the chance card sends you to. These have a higher than average rate of being landed on.
Rule #2
Everybody needs a place to crash after a night in jail.
The jail is the axis of the board, and a space which will find everyone to end their turn on, most likely.
Buy up properties that come a bit after jail, especially the orange the red and yellow blocks.
Rule #3
- 1. Jail
- 2. Illinois Ave
- 3. New York Ave
- 4. Go
- 5. B&O railroad
- 6. Pennsylvania Railroad
- 7. Reading Railroad
- 8.Tennessee Ave
- 9. Kentucky Ave
- 10. Free Parking
- 11. WaterWorks
- 12. St James
- 13. Atlantic Ave
- 14. Indiana Ave
- 15. North Carolina Ave
- 16. St. Charles Place
- 17. Second Community Chest
- 18. Ventnor Ave
- 19. Pennsylvania Ave
- 20. Boardwalk
Rule #4
Your opponent will propably move seven spaces, very likely to roll a number very close to 7.
When you plan your construction keep this in mind to bankrupt your friends with rents so crippling that they could be cold depression.
Rule #5
When you build, 3 is the magic number. It’s the most cost effective way to build 3 houses at once and accelerates your return on investment.
Conclusion
Nobody wants to play Monopoly with me because I am a competitive ***** who always ends up bankrupting people… or raging while on the process.
Thanks for reading that wall of text, please like, favourite and uh, give me your feedback! Cheers!