Monopoly starts by rolling 2 dice, which may seem fairly simple. But there are thousands of things that could happen on the very first turn of the game – you could even own a whole set! Let’s look at the most likely outcomes and some other fun possibilities.
I intended to write something about the maths and probabilities of the game as a whole but as soon as I started making some calculations I realised that the first turn of the game, in which player 1 rolls 2 dice and moves, holds so many possible outcomes that it warrants an entire post itself.
The rules of the first turn are quite simple:
- Roll 2 dice and move that many spaces.
- Resolve any actions on that space e.g. buy the property, pick up a Chance card.
- If you rolled a double (the dice matched) then repeat steps 1 and 2.
- 3 doubles in a row sends you to jail.
I am going to be using the London edition of monopoly, which of course is not dissimilar to every other version, but the names will all be different. Here’s a picture of the Board. You may wish to right click and open it in a new tab/window to refer back to it easily.
The first roll has 11 possibilities involving moving 2 to 12 spaces with varying probabilities. That’s where the easy maths ends because you could land on a Chance or Community Chest space and be moved somewhere else on the board with a certain probability. You may also have rolled a double so your turn carries on.
3 of the 16 Community Chest cards move you to another position – Old Kent Road, Jail, Go
7 of the 16 Chance cards move you to another position – Back 3 spaces, Pall Mall, Marylebone, Trafalgar Square, Jail Mayfair, Go
Enough of the blurb and on to the interesting stuff. Remember that although I may phrase things as if they are strategies that you have a choice about, it’s actually entirely luck. You can’t choose to roll a particular number with the dice!
Here’s a breakdown of where you’ll end up after all has been resolved.
- You can end up on 37 of the 40 squares on the Board. The 2nd Chance square, Park Lane and Super Tax cannot be reached by any means
- Pentonville Road is the most likely place to end up (12.01%)
- You have a 1.84% chance of ending up in the jail before anyone else has even started playing!
Most people want to buy lots of properties at the beginning of the game, so the Cards and Doubles that help you visit multiple locations in one turn can be very useful. Here are the probabilities of visiting each of the squares at some point during the first turn.
Here’s the number of properties you can expect to land on during your first turn
Two-thirds of the time you’ll end up with one property, but don’t surprised if you end up with none. Praise your luck if you get 2 or even the improbably 3!
Getting a set on your first go
You can actually own an entire set by the end of your turn. It is only possible with the Brown set and the Utilities (both only require 2 properties)
Brown set – likelihood is 0.0049% or 1/20593
All the possible routes require you to start by rolling a double 1, picking up a Community Chest Card that sends you back to Old Kent Road and of course buying it.
From there, you have 3 routes:
BrownSetRoute1: Roll another double 1 and buy Whitechapel. Of course your 3rd roll can be anything.
BrownSetRoute2: Roll a double 3 and pick up a Chance Card that sends you to Mayfair. Roll a 1 and a 3 to land on Whitechapel and buy it. Note that double 2 will send you straight to jail as it’s a 3rd double.
BrownSetRoute3: Roll a double 3 and pick up a Chance Card that sends you to Go. Roll a 1 and a 2 to land on Whitechapel and buy it.
Utilities set – likelihood is 0.0228% or 1/4391
This is a much simpler route than the Brown set.
Roll a double 6 and buy the Electric Company. Roll another double, and then on your 3rd go roll whichever number is required to land on Water Works.
Get Rich Quick Scheme
Your chance of going past Go twice (and therefore picking up £400 total) is 0.0019% or 1 in 52355. To do this you must land on several Card spaces and pick up ones that move you around the board.
All routes start with rolling a double 1 to get to the Community Chest.
GoTwiceRoute1: Pick up a Community Chest that takes you to Go. Roll a 7 total (either directly, or after a double 1/2) and pick up a Chance that takes you to Go.
GoTwiceRoute2: Pick up a Community Chest that takes you back to Old Kent Road. Roll a double 3 and pick up a Chance that takes you to Mayfair. Roll a 3 or 8 total and pick up a Community Chest/Chance that takes you to Go.
GoTwiceRoute3: Pick up a Community Chest that takes you to Go. Roll a double 6 then a 4+6 and pick up a Chance that takes you to Go, Marlyebone or Pall Mall.
2 properties then jail
The chance of this is 1/526 or 0.19%. Imagine that it is all going so well after rolling a double, buying a property, rolling another double and buying another property. But then the 3rd roll bites back hard either by rolling another double to invoke the 3 doubles rule or by landing directly in Jail. There are of course a lot of routes to do this, so I won’t list anything specific!
The best possible turn
I think the best possible outcome would involve picking up the Brown set as described before. A few of the ways of doing this are comparable in my opinion.
1. “BrownSetRoute1” above gets you the brown set on the first 2 rolls and then use your third roll to land on Pentonville and buy it. This is the most likely square for everyone else to land on, so gives the best chance of preventing them from getting property and also for you to collect a bit of rent.
The chance of this is 1/186624 or about 0.00054%
2. If you like buying Mayfair then “BrownSetRoute2” above gives you that opportunity. You also pass Go to pick up an extra £200.
The chance of this is 1/5971968, or about 0.000017%
For both of these options you can also buy hotels on the Brown set for a total of £500 – pretty awesome to have hotels up before anyone else has made a move in my opinion! Imagine if they then roll a 3 on their turn…
The worst possible turn
There’s a clear winner for this one I think. Roll a double 1 and pick a Chance that makes you pay hospital fees of £100. Roll another double 1 and pay Income Tax of £100. Roll another double and go straight to jail (or roll a 3 and pick up a Chance that sends you to jail). £200 down and in jail…oh dear.
The chance of this happening is 0.0008% or 1/124416 – don’t worry about it too much!
A final note
This article doesn’t actually help you to play better in any way, as the first turn is entirely based on the luck of the dice.
I’m not personally a big fan of the game, but dice are always interesting for me! In brief I find it’s a formulaic luck game for 5-10 turns, followed by 2 minutes of mad trading then a long drawn out process while whoever has the marginally better properties very slowly wins. I had fun looking at what could happen on the first turn anyway!