A million simulated dice rolls tell a designer exactly where tokens spend their time on a looping board. They say almost nothing about who wins, what a city is worth, or whether players will trade. I found where that line sits while checking the property trading game that I make. One million rolls gave the busiest square a margin of error of about 0.05 percentage points. They still left every economic question open.

This piece sorts what the run can answer from what it cannot, then ends with a checklist for the next run.

What was simulated

The run was done on 29 September 2026. It sent one million dice rolls through the game's real rules code, the very code the live table runs. Two empty seats walked a 40-square loop. Both declined every city they landed on, every auction expired, and the starting cash was a trillion dollars so that nobody could go bankrupt. The seed was fixed (202609290929), so anyone with the code can repeat it.

The board is an independent Monopoly alternative: 22 cities spread over eight countries, plus airports, utilities, card squares and four corners.

Of the million rolls, 908,113 ended on a resolved landing. The other 91,887 were prison rolls that ended on no new square. That label comes from the run's own report. My reading is that these are rolls made while already shut in Prison. A trip to Prison on a third double does count as a landing in the run.

What a million rolls can tell you

How sure are the shares? For a square that gets about 2.5% of landings, the standard error over a million rolls is the square root of 0.025 × 0.975 ÷ 1,000,000, or 0.0156 points. A 95% interval is about twice that either side. The report uses Wilson intervals, which behave better near zero. Its widest one, for Prison, spans 5.69% up to 5.78%.

So a gap of 0.1 point between two squares is real. Osaka (3.06%) and Start (2.85%) are separate. Osaka and Paris (3.03%) are not: their intervals overlap, and no honest reading ranks one above the other.

How many rolls are enough? To tell two squares apart at 95%, the sample needs about 1.96² × 2p(1−p) ÷ d² rolls, where p is the share (0.025) and d the gap you care about. For a gap of 0.1 point that is 3.84 × 0.04875 ÷ 0.000001, or about 187,000 rolls. For 0.05 point it is four times that, about 750,000. This treats the two squares as independent, which is a simplification, but it explains why a million is enough to rank squares and a hundred thousand would not be.

Do two programs agree? A standalone model of the same board, written separately, put landings at 90.8088% of rolls. The run through the live rules gave 90.8113%. That is 0.0025 points apart. Agreement like this is the right test for movement code. It tells you nothing about the economy.

Which squares are landed on most? Prison leads, for reasons that need their own arithmetic. Beyond it, the property list is topped by Osaka and Paris. Osaka is the destination of two Surprise cards, so its 3.06% is partly the card deck at work and not geometry. A designer who only plotted a heat map would miss that.

A worked example: paying back a build

Movement data becomes an economic number once you multiply it by rent. Take the three cities of France, each with three houses. The table uses the run's landing shares and the game's rent table. Each rent is what an opponent pays on one visit.

  • Nice; share of rolls ending there: 2.4913%; rent with 3 houses: $550; share × rent: $13.70

  • Marseille; share of rolls ending there: 2.6335%; rent with 3 houses: $550; share × rent: $14.48

  • Paris; share of rolls ending there: 3.0286%; rent with 3 houses: $600; share × rent: $18.17

  • Total; share × rent: $46.36 per visitor roll

Houses cost $100 each in this group, so nine houses cost $900. Divide: 900 ÷ 46.36 is about 19.4 visitor rolls. A turn averages 1.17 rolls because doubles give a bonus roll, so the report's figure is about 16.6 active turns.

What a million rolls cannot tell you

This kind of run is a Monte Carlo simulation in the plain sense: repeat a random process many times and count. It is very good at counting. Game balance, though, is a claim about winners, and winners come from decisions. The same report is careful about this, and so should a designer be.

  • Nobody owned anything, so nobody paid rent. The payback above is rent that a wandering token would owe if a landlord existed.

  • No auctions ran. A price is what a table will pay, and an empty table pays nothing.

  • No trades, so the value of a city to a player holding its neighbours is invisible.

  • No debt. Since 2 October, unpaid rent turns into a debt that a player clears by mortgaging, selling or trading. A trillion dollars of cash makes that rule unreachable.

  • No choices in Prison. Whether a player pays the $50 fine or rolls for doubles will depend, I expect, on how much rent is on the board.

The engine has also changed since 29 September, so I would call these figures a baseline for movement and not a result about strategy.

A checklist for the next run

Before trusting a simulation of a board economy, I would want a yes on each of these:

  • 1. The seeds are fixed and written down.

  • 2. The run goes through the live rules code, and not a copy.

  • 3. Every figure is labelled with its sample size and its interval.

  • 4. A second implementation agrees on the part it can check.

  • 5. The report lists what the run excluded, in plain words.

  • 6. The next run adds one thing at a time: ownership first, then auctions, then trades, then debt.

Sixth on the list is the one I expect to take longest, because the first player who buys a city changes what every other player wants to do.

The property trading game behind this run is free to play online with friends, up to six at a table, at Boardit.

Boardit is not affiliated with or endorsed by Hasbro.

Written for Boardit's maker, Ahmed Moaz, with AI help. The game facts were checked against the game's code.