If you’re a bit of a stat nerd, there are some fascinating facts and statistics you can delve into around Monopoly.
You might love the idea of the shortest game ever, or you could be looking for some tips and info to give you a tactical edge in your own Monopoly games.
In this post, I’ve pulled together some fun, interesting statistics about Monopoly. Enjoy!
What are the odds of rolling doubles in Monopoly?
The odds of rolling doubles in any single roll in Monopoly are 1 in 6, or 16.67%.
The odds of rolling doubles three times in a row in your turn – landing you in jail – is 1 in 216, or 0.46%.
This might sound astronomical, but considering the average dice roll in a game of Monopoly is 7, and there are 40 spaces on a Monopoly board, that means it takes around 5.7 turns to get around the board.
If you have four players, then that means every time all players have completed a circuit of the board, there have been around 20 turns.
So on average, once every 10 laps of the board, someone will roll three sets of doubles in a row and go to Jail.
It won’t happen often but over the course of 2-3 games of Monopoly, you’ll probably see it happen once.
What are the odds of something good happening with a Chance or Community Chest card?
Let’s take a look at what each of the Chance and Community Chest cards do.
First up, here’s a table of the Chance cards…
|Chance Card||Number of Cards||Chance||Good or Bad?|
|Move to a property, railroad, or utility||7||44%||Depends|
|Pay money to the bank or other players||3||19%||Bad|
|Advance to Go||1||6%||Good|
|Go to Jail||1||6%||Usually Bad|
|Get Out Of Jail Free Card||1||6%||Good|
|Go Back 3 Spaces (to either Income Tax, New York Avenue, or Community Chest)||1||6%||Depends|
So, with Chance cards, you can expect a good card 25% of the time, a bad card 25% of the time, and the other 50%, it depends on your situation. So the probability of a good Chance card is roughly equal to the probability of a bad card.
Now, here’s a table of the Community Chest cards…
|Community Chest Card||Number of Cards||Chance||Good or Bad?|
|Pay money to the bank or other players||4||26%||Bad|
|Advance to Go||1||6%||Good|
|Go to Jail||1||6%||Usually Bad|
|Get Out Of Jail Free Card||1||6%||Good|
You can expect a good Community Chest card 68% of the time and a bad card 32% of the time.
So, Community Chest cards are generally better than Chance cards.
However, it’s worth considering that the worst cards (Street Repairs when you have a lot of buildings) can be much worse than the good cards can be good.
What is the fastest that a game of Monopoly can last?
The fastest game of Monopoly can be completed in approximately 21 seconds.
This would be a 2-player game of Monopoly that requires a very specific set of dice rolls, and the correct cards to be drawn during the game. The odds of this happening are 1 in 250 trillion.
Here’s how it works…
- Player One rolls double-6, landing on Electric Company. They let the other player win it
- They roll another double-6 and land on Illinois Avenue. They don’t buy it
- They roll a 9, land on Community Chest, and get the Bank Error card to collect $200
- Player Two rolls a double-2, paying $200 Income Tax.
- They then roll an 11 and land on Pennsylvania Railroad. Player One can’t buy this in auction, they must let Player Two buy it
- Player One rolls double-2, buying Park Place
- They roll double-1, buying Boardwalk
- They roll again, with any roll that doesn’t land on Income Tax or Chance. They collect $200 from the bank
- Before their turn ends, they buy 2 houses on Park Place, and 3 on Boardwalk
- Player Two rolls a 7, lands on Chance. They draw the “Advance to Boardwalk” card, where they can’t afford the rent and go bankrupt.
The exact odds of this exact sequence happening by chance are 1 in every 253,899,891,671,040 games.
Let’s assume each failed game takes an average of 6 seconds – since some games will fail at the first roll, some will fail as the second player takes their turn, and some will fail on the second turn of player one.
To ‘guarantee’ seeing this game you would potentially have to play for 70 billion hours, or 8,051,112 years.
Read more: How To Win Monopoly In 21 Seconds
Can you go to jail on the first round of Monopoly?
You can go to jail on your first pass around the Monopoly board. In fact, you could even go to jail on your very first roll, if you’re unlucky.
You can go to jail on your first turn in Monopoly by:
- Rolling three doubles in a row
- Rolling a total of 30 across two doubles and a regular third roll to hit the Go To Jail space
- Landing on Community Chest and pulling the Go To Jail card
So, let’s put that into perspective with some stats. This gets heavy, so skip this bit if you don’t like super-detailed information!
1. The probability of rolling three doubles in a row
There’s a 0.46% chance of rolling three doubles in a row.
Doubles make up 1/6 of the potential combinations you can roll at any one time. 1/6 multiplied by 1/6 multiplied by 1/6 is 1/216.
So, in every 216 games you play, chances are you will roll three doubles in a row on your first turn once. Yikes.
2. The probability of rolling 30 on your first turn
Rolling 30 and landing on the Go To Jail space on your first turn is very unlikely.
These are the ways you can do it:
- Roll double-6, double-6, then a six either through a 1-5, 5-1, 4-2, or a 2-4.
- Roll double-6, double-5, then an eight through a 2-6, 6-2, 5-3, or a 3-5
- Roll double-6, double-4, then a ten through a 6-4, or a 4-6
- Roll double-5, double-6, then an eight through a 2-6, 6-2, 5-3, or a 3-5
- Roll double-5, double-5, then a ten through a 6-4, or a 4-6
- Roll double-4, double-6 then a ten through a 6-4, or a 4-6
Each specific roll has a 1/36 chance of happening, which means to get three specific rolls in a row you have a 1/36 x 1/36 x 1/36 chance, or 1/46,656 chance, or around a 0.002% chance of it happening.
As there are 18 possible combinations above, that means there’s around a 0.038% chance of you rolling exactly a 30 on your first turn. It’s exceptionally unlikely.
3. The probability of getting a Go to Jail Community Chest card on your first turn
This is where it gets complicated. You can reach all three Community Chest spaces on your first turn. As there are so many ways to do it, the chance of this is 0.25%.
You can land on the first one by:
- Rolling a double-1
- Rolling a double-5 then a double-6 to land on Chance, pulling the Advance to Boardwalk space, then rolling a 2-1 or a 1-2
- Rolling a double-6 then either double-5, 4-6 or 6-4 to land on Chance, pulling the Advance to Boardwalk space, then rolling a 2-1 or 1-2
The second one is 17 spaces into the game. You can land on it by:
- Rolling a double-6 and then a 1-4, 4-1, 3-2, or 2-3
- Rolling a double-6, double-1 and then 1-2, or 2-1
- Rolling a double-5 and then a 1-6, 6-1, 2-5, 5-2, 4-3, or 3-4
- Rolling a double-5, double-1 and then 1-4, 4-1, 2-3, or 3-2
- Rolling a double-5, double-2 and then 1-2, or 2-1
- Rolling a double-4 and then a 3-6, 6-3, 5-4, or 4-5
- Rolling a double-4, double-1 and then 1-6, 6-1, 2-5, 5-2, 4-3, or 3-4
- Rolling a double-4, double-2 and then 1-4, 4-1, 2-3, or 3-2
- Rolling a double-4, double-3 and then 1-2, or 2-1
- Rolling a double-3 and then a 6-5, or 5-6
- Rolling a double-3, double-1 and then 3-6, 6-3, 4-5, or 5-4
- Rolling a double-3, double-2 and then 1-6, 6-1, 2-5, 5-2, 4-3, or 3-4
- Rolling a double-3, double-3 and then 1-4, 4-1, 2-3, or 3-2
- Rolling a double-3, double-4 and then 1-2, or 2-1
- Rolling a double-2, double-1 and then 6-5, or 5-6
- Rolling a double-2, double-2 and then 3-6, 6-3, 4-5, or 5-4
- Rolling a double-2, double-3 and then 1-6, 6-1, 2-5, 5-2, 4-3, or 3-4
- Rolling a double-2, double-4 and then 1-4, 4-1, 2-3, or 3-2
- Rolling a double-2, double-5 and then 1-2, or 2-1
- Rolling a double-1, double-2 and then 6-5, or 5-6
- Rolling a double-1, double-3 and then 3-6, 6-3, 4-5, or 5-4
- Rolling a double-1, double-4 and then 1-6, 6-1, 2-5, 5-2, 4-3, or 3-4
- Rolling a double-1, double-5 and then 1-4, 4-1, 2-3, or 3-2
- Rolling a double-1, double-6 and then 1-2, or 2-1
- Rolling a double-5, then a double 6 to land on Chance, pulling Advance to St. Charles Place then rolling a 1-5, 5-1, 2-4, or 4-2
- Rolling a double-6, then a double-5 to land on Chance, pulling Advance to St. Charles Place then rolling a 1-5, 5-1, 2-4, or 4-2
The third one is only reachable by:
- Rolling a double-6, double-5 to land on Chance, pulling Advance to Illinois Avenue, then rolling a 3-6, 6-3, 4-5, or 5-4
- Rolling a double-5, double-6 to land on Chance, pulling Advance to Illinois Avenue, then rolling a 3-6, 6-3, 4-5, or 5-4
Each of the above that involves just one roll of the dice has a 1/36 chance. Any that have two rolls are 1/36 x 1/36 = 1/1,296. Any that involve three dice rolls are 1/46,656. And any that require the exact Chance card to be pulled to match also have an extra 1/16 chance of being the right card.
And all of that is just to work out the odds of landing on a Community Chest space. I won’t list out all the calculations, but it ends up at being around 4% on your first turn.
You then need to draw the right Community Chest card, which is another 1/16 chance. So your odds of pulling the Community Chest card to send you to jail on your first turn are actually 0.25%.
If you add that to the odds of rolling three doubles in a row – 0.46% – and the odds of rolling 30 on your first turn without rolling three doubles – 0.038% – then the total odds of you landing yourself in Jail on your first turn are around 0.75% – or once in every 133 games.
Which Monopoly property is landed on the most?
Of the Monopoly properties, the one that is landed on the most, based on averages, is Illinois Avenue in the red set. The most landed-on space on the entire board is not a property though – it is the Jail space.
Here’s a look at the probability of landing on every space on the game, per roll of the dice:
|New York Avenue||Orange||3.0852||4|
|B & O Railroad||–||3.0659||5|
|St. James Place||Orange||2.7924||12|
|St. Charles Place||Pink||2.7017||15|
|North Carolina Avenue||Green||2.6252||19|
|Vermont Avenue||Light Blue||2.321||29|
|Connecticut Avenue||Light Blue||2.3003||30|
|Oriental Avenue||Light Blue||2.2621||32|
|Park Place||Dark Blue||2.1864||33|
|Go To Jail||–||0||41|
How long does it take to make back your money on railroads?
If you own all four railroads, you’ll make back your investment in an average of just 35 rolls. In contrast, owning just one railroad means it will take an average of 281 rolls to make back your money.
To work this out, you need to know the probability of landing on each railroad, and the return on investment for every time a player lands on one of the railroads.
While the probabilities are listed above, here they are again just for the railroads:
- B&O Railroad – 3.0659%
- Reading Railroad – 2.9631%
- Pennsylvania Railroad – 2.9200%
- Short Line – 2.4326%
And then based on that, we can take an average of all four and work out the number of rolls needed to make your full investment back:
|Number of railroads owned||Probability of a player landing on a railroad||ROI each time a player lands on a railroad||Average number of rolls needed to make back your investment|
There’s some hefty statistical stuff in this guide, so I hope your brain hasn’t melted too much! Among all the numbers there are some really cool stats, some of which might give you an edge.
If you’re looking for more help to win your next Monopoly game, don’t forget my guide on Monopoly Trading Rules & Strategies to Win too – it could make the difference in those tricky trade decisions.