MEZARPOLY

The maths of two dice: where will you land in a property game?

30 October 2026 · 3 min read

Everything in a property-trading game starts with two dice. Dice are luck, but luck has a pattern: some totals come up six times as often as others, and some squares are almost safe this turn. We counted every possible dice sequence to map that pattern.

1. Two dice: why 7 comes up most
2. Doubles: roll again, the third one sends you to Jail
3. How far do you move in a turn?
4. Which squares are dangerous?
5. Rolling your way out of Jail
6. Summary
7. How was this calculated?

Two dice: why 7 comes up most

Two dice can land in 36 different ways, each equally likely. Six of them make 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), while only one way each makes 2 or 12. So 7 accounts for 16.7% of rolls, and 2 or 12 for just 2.8%.

Doubles: roll again, the third one sends you to Jail

The chance of a double is 16.7% (one in six). In Mezarpoly a player who rolls a double makes their move and rolls again; a third double in the same turn sends them to Jail without moving. Three doubles in a row happen 0.46% of the time, or once in 216 turns.

That looks small, but games are long. A four-player game lasts about 45 rounds, and over that many turns a player has a 18.8% chance of going to Jail on triple doubles at least once.

How far do you move in a turn?

Counting the extra rolls after doubles, a player moves 8.26 squares per turn on average, not 7. You go round the 40-square board in about 4.8 turns; on the 48-square big maps a lap takes about 5.8 turns. You collect your Go salary less often on big maps, which is one reason those games warm up more slowly.

Which squares are dangerous?

When an opponent's hotel lies ahead, what matters is the chance of landing on that square this turn. This table includes the extra rolls after doubles:

The most dangerous distance is 7 squares: 17.1%. That is a bit higher than the chance of rolling a 7 (16.7%), because you can also land there on a re-roll after a double. You can never land on the square right next to you in one turn, and squares more than 12 away are only in danger after a double.

Cards and the Go to Jail square bend this table a little, but it still helps. If the next 6–8 squares are full of your opponents' expensive properties, keep some cash. And building on squares 6–8 ahead of your opponents pays off.

Rolling your way out of Jail

In Jail you can try for a double each turn, pay ₺50, or use a card. The chance of at least one double in three tries is 42.1%. If the third try fails too, you pay ₺50 and move by the roll. Waiting usually saves money but keeps you off the board for up to three turns. Getting out quickly makes sense early, when there is property to buy; staying put makes sense late, when the board is full of your opponents' buildings (see Which play style wins?).

Summary

• 7 is the most common total (16.7%); 2 and 12 come up only 2.8% of the time.
• A double is one in six; three in a row is one in 216.
• You move 8.26 squares per turn on average; a lap of the 40-square board takes about 4.8 turns.
• This turn you are most likely to land 6–8 squares ahead; the very next square is safe.
• The chance of rolling out of Jail within three tries is 42.1%.

How was this calculated?

The probabilities come from counting every possible sequence of dice exactly, as fractions, not from a simulation: the first roll, a second roll after a double, a third roll after another double (a third double means Jail). The rules come from the game engine on the Mezarpoly server; the game length is the median of 12,000 bot games.

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