Note: This webpage is more user-friendly on larger screens.

Follow these steps to get started!

• At the start of a game, note all of the resource-producing hexes adjacent to your settlements
• Click on the cells in the editable table at the bottom of the page to start entering your current board state. Tally how many of each resource you would receive for each number from 2 - 12.
• If a cell is left blank, the code automatically assumes a value of 0 under the hood. (note: at the beginning, the tally can range anywhere from 0 to 2 for a given resource-dice roll combo)
• As the game progresses and you build more settlements/upgrade them to cities, update the table with your new tallies
• Every time a value is changed in the table, the rightmost column will automatically update with the average number of rolls needed to obtain one of the resource corresponding to each row. Furthermore, the four histograms below the table will update with simulation results for how long it could take to build/obtain the specified object
• Trade with the bank is allowed in the simulations. The default exchange rate is 4:1, and upgrades from ports (3:1 general or 2:1 resource-specific) can be indicated using the labeled checkboxes below the histograms

About Monte Carlo Simulation
The goal of Monte Carlo simulation is to understand a phenomenon by repeating it a large number of times and recording quantities of interest each time. For instance: suppose you are unsure how often a flipped coin will land heads. One way to determine this is to flip the coin 100 times, and record how many of the results were heads. When we aggregate these results and look at their frequencies, this is known as an empirical distribution.

With something more complex, such as a game of Catan, it takes too much time to do this sort of repetition manually. This is where code comes in. If we write logic to represent the relevant (not necessarily all) rules and structure of the game, a computer can record, rinse, and repeat much faster than we could hope to as humans.

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Simulation Setup

• Every time the table is updated, 1000 simulations occur in-browser (i.e. nothing is sent to a server)
• Each simulation describes the following scenario: I start from an empty hand. Two dice are rolled repeatedly to represent turns. With each roll, I collect resources according to what is on the board. Allowing for trade with the bank, how many rolls does it take to get the resources to build a road? A settlement? And so on.
• For the sake of runtime, each simulation stops after 120 rolls
• This setup does NOT account for the robber, use of development cards, or trade with other players
• The simulation results are aggregated into an empirical distribution of turn counts, and displayed as a histogram
• The histograms will appear slightly different in separate instances of simulations for the same board. To see this for yourself, type in a number into the table below, and then press the space bar. This is due to the inherent randomness involved in the simulation process.

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Interpretation
Now, this example is something that most players would understand quickly without simulation. The magic of Monte Carlo is that we can ask more complex questions about the game, with the exact same setup. From the very beginning of a game, we can gain an understanding of what players are in a position to do well at the endgame, by looking at their ability to build cities and buy development cards. We can ask which new settlement placement would yield the most benefits down the road. While our simulation is not perfect, it can still help us make better-informed decisions.