Monopoly dice roller

How to use these dice on the page

The tool rolls two six-sided dice, just like the ones in the box. When they stop, it shows each die separately and the total, which is the number of squares you move.

The Speed Die found in some recent editions is not included: this is the two white dice of the classic rules. Every roll is random and independent of the last one, exactly like real dice.

Monopoly dice rules

Hasbro's classic rulebook is clear about the dice. There are not many rules, but plenty of families play house versions that differ from what the box says.

Rolling and moving

At the start everyone rolls and the highest total goes first. On each turn you roll both dice and move your token that many squares in the direction of the arrow. Then you deal with the square: buy, pay rent, draw a card, pay tax or go to jail.

Doubles: roll again

If both dice show the same number, you move the total as normal, deal with the square and then, keeping the dice, roll again.

Three doubles in a row: go to jail

Roll doubles three times in succession in the same turn and you do not move with the third roll: your token goes directly to jail. When you are sent to jail you do not collect your salary for passing Go, even if the token would have crossed it, and your turn ends there.

Other ways to end up in jail

• Landing on Go to Jail.
• Drawing a card that sends you to jail.
• Rolling three doubles in a row.

If an ordinary roll lands you on the jail square, you are Just Visiting: no penalty, and you carry on as normal next turn.

How to get out of jail

1. Rolling doubles on any of your next three turns. If you do, you move forward the number shown, but that double does not give you another roll.
2. Using a Get Out of Jail Free card, your own or one bought from another player at an agreed price.
3. Paying the fine (50 in current editions) before rolling on either of your first two turns.

If you have not rolled doubles by your third attempt, you must pay the fine and then move the number shown on that roll. While in jail you can still collect rent, buy and sell houses and hotels, and trade.

A very common house rule is to put tax and fine money in the middle of the board for whoever lands on Free Parking. The official rules do not include it: according to the box, Free Parking is just a resting place with no reward.

Two-dice probabilities

Two six-sided dice give 36 equally likely combinations. The most common total is 7, which can be made six ways (1+6, 2+5, 3+4 and the reverse). The extremes, 2 and 12, can only be made one way each.

Of those 36 combinations, 6 are doubles (1-1, 2-2, 3-3, 4-4, 5-5 and 6-6), so the chance of doubles on any roll is 1/6. Because each roll is independent, the chances of rolling them back to back multiply.

Put another way: out of every 216 turns that start with the token free, one on average ends in jail for three doubles. It is rare, but in a long game with four or five players it does happen.

Taking doubles and extra rolls into account, the most likely move in a whole turn is still 7 squares, and the maximum is 35 (6-6, 6-6 then 6-5). On average a token moves just over 8 squares per turn, because doubles add extra rolls.

Getting out of jail: pay or try for doubles?

Each attempt has a 1 in 6 chance of working. The chance of rolling at least one double in three attempts is 1 minus the chance of missing all three: 1 - (5/6)³ = 91/216, or 42.13%. In 57.87% of cases you end up paying the fine on your third turn.

The right choice depends on the stage of the game, and mathematical analyses of Monopoly agree on the general idea:

• Early on, with lots of unowned property, it pays to get out straight away. Every turn in jail is a turn you are not buying.
• Later, when the board is full of other players' houses and hotels, staying in and trying for doubles works as a shelter: you do not move, you pay no rent and you still collect your own.

The get out of jail mode on this page lets you play out the second option: roll up to three times and the tool tells you whether you are out or have to pay.

The most landed-on squares

If every square were landed on equally, each would get 2.5% of visits. That is not what happens, for three reasons: Go to Jail and several cards send tokens to the same place, other cards move you to specific squares, and 7 is the most common total. This is worked out with a Markov chain, the method that has been used for decades to analyse Monopoly, which tracks the probability of a token finishing on each square after a very large number of rolls.

The table below comes from that calculation using the classic US board (the template for every edition), the standard Chance and Community Chest cards and the three-doubles rule. UK names are given alongside. Squares are numbered from Go (0). Two cases are shown: leaving jail by paying straight away, or staying in and trying for doubles.

The results match the analyses published since the 1990s: jail is by far the square where tokens stop most often, the most visited street is the third red (Illinois Avenue in the US, Trafalgar Square in the UK), and Go and the third station follow closely. The brown streets and Park Place / Park Lane get the fewest visits, and Go to Jail sits at zero because nobody stays on it.

By colour set, the split is:

Part of the third red's lead comes from a Chance card that sends you straight to it.

Why the streets 6 to 8 squares past jail matter

Because so many tokens pass through jail, whatever comes just after it gets more traffic. From square 10, the three orange streets are 6, 8 and 9 squares away. Adding the combinations for 6 (5), 8 (5) and 9 (4), a token leaving jail on a normal roll lands on an orange in 14 out of 36 rolls, or 38.9%.

If you leave by rolling doubles, the destination is even narrower, as there are only six possible rolls:

Two of the six doubles finish on the orange set. That is why the oranges, together with the reds, are the most visited streets, and they are also much cheaper to build on than the reds or dark blues. The reds benefit too, but they are 11, 13 and 14 squares away: with a single roll from jail you can only reach the first one, and only with a 5 and a 6.

The opposite case is Park Place (Park Lane in the UK), the first dark blue: Go to Jail is 7 squares before it, and as 7 is the most common total, many tokens that could have reached it are sent to jail first. That is why it is among the least visited streets.

Street names change from country to country

Monopoly was built around the streets of Atlantic City, New Jersey, and each country adapted it with its own names. The structure does not change: 40 squares, the same colour sets in the same order, the same relative prices and the same special squares. So the probabilities on this page apply to any classic edition; you just need to look at the square's position.

Elsewhere in Europe, the most expensive street is the Schlossallee in Germany, the rue de la Paix in France and the Parco della Vittoria in Italy, while the third red is the Opernplatz, the avenue Henri-Martin and the Largo Colombo respectively. Recent and themed editions have renamed many squares, so your box may not match the table. If in doubt, count squares from Go.

History and curiosities

This page is not official and has no connection with Hasbro. Monopoly is a registered trade mark of its owner and is named here only to describe the game.

Practical tips for the dice

• Keep in mind that 7 is the most likely total when you weigh up whether a rival will land on your squares: a token with your streets 6, 7 and 8 squares ahead lands on one of them in 16 out of 36 rolls, or 44.4%.
• If you own the oranges, build early: it is the set that makes the most of the traffic coming out of jail.
• Early on, pay and get out of jail. Late on, when there are hotels all over the board, staying inside can save you a lot of money.
• Doubles do not cancel what happens on the square: land on Go to Jail with a double and you go to jail and lose the extra roll.
• If you play house rules (money on Free Parking, double salary for landing on Go), agree them before you start.