## Results:

After 10,000,000 dice rolls, the likelihood of each space being landed on is shown below:

Shown below is the top 20 board spaces from the bar graph above:

While the amount of times a property is landed on does affect the benefit it will bring to you as a player, we also need to consider how much it costs to buy the property, and how much players will pay you every time they land on it.

The probabilities shown above can also be described as the chances of a player landing on that property after every roll. We can use that, along with the rent for every property, to find the expected amount of money you will make on every player’s dice roll if you own said property.

For example, Ventnor Ave (shown above) is at a 2.691% chance of being landed on every roll. The rent with no houses for Ventnor Ave is \$22, which means that every roll results in an expected \$0.59202 for the owner.

The revenue per roll is not the best thing to compare between properties because a property that costs more than Ventnor should yield more revenue, but this is not always the case. If we divide the initial cost of buying the property by the revenue per roll, we can find how many rolls it will take to break-even on a property. For example Ventnor costs \$260 to buy, so the owner should expect to make all of that money back after 439.18 rolls. Properties that take less rolls to break-even would be considered better investments because you could start turning a profit before other players.

We also need to consider how building houses and hotels on properties affects the rolls per break-even. Below is a breakdown of each property on a Monopoly board, given it’s situation regarding houses and hotels (excluding railroads and utilities). The value in each cell represents to amount of rolls it will take on average to make back the money spent on the property.

As you can see, some properties are almost guaranteed to lose you money in the long run. Buying Mediterranean Ave and not putting any houses on it will certainly cost you money over the course of a game. It won’t be a significant amount (only \$60 to buy), but it is still not the best purchase.

All properties without houses take an extraordinary amount of time to break-even, which is why buying houses and hotels is so important.

The plot above shows how buying at least 3 houses for every monopoly you own can greatly…