Conquest Calc

What is Conquest Calc?

Conquest Calc is a Monte Carlo simulator for Risk-style board games that equips players with the probabilities of success for their campaigns. Instead of calculating the exact probability for every scenario, Conquest Calc plays your specified campaign thousands of times. It then displays the frequencies of the various outcomes as probabilities. Armed with probabilities, players can make more informed decisions as they form and enact their strategy for world domination.

For the purposes of Conquest Calc, a campaign is a series of plays in a Risk-style board game where a player attacks one or more countries in series from a single country.

How do you use Conquest Calc?

Enter the current situation for your campaign in the left column.

Using the Attacking Country field, specify how many armies you have positioned in your attacking country. Alternatively, specify how many armies you are planning on attacking with if you would like to leave more than one troop behind to occupy the country.

Using the Defending Country #1 field, specify how many enemy troops are in the first country you plan on attacking. Use the remaining defending country fields, specify the number of troops in each subsequent country you plan on attacking. Make sure to perserve the order of attack for your campaign. If your campaign consists of less than five enemy countries, then leave the remaining defending county fields with a value of zero.

Choose the number of simulations you would like to run for your calculation using the Simulations field. This is the number of times that Conquest Calc plays out your campaign before returning your probabilities of success. The more simulations used, the better the results. However, after a certain point the probabilities change only by a few decimal places with additional simulations. Also, the more simulations you specify, the longer it will take to receive your results.

Conquest Calc assumes that you will leave only one troop behind for each country defeated.

How do I interpret the results?

The results of the simulation are displayed in the right-hand column.

The Toolbar

The Probability value in the bottom toolbar represents the most simple chances of success. It is the probability that you will defeat all countries specified with at least one troop to occupy each of the conquered countries. The Mean value in the bottom toolbar is the average number of troops available to occupy the last defeated enemy country for all the simulations run. The SD value in the bottom toolbar is the standard deviation of troops available to occupy the last defeated enemy country for all the simulations run.

The Grid

The grid displays the probability and cumulative probability distributions of ending the campaign with different amounts of troops available to occupy the last defeated country. The Probability column in the grid shows the probability of ending the campaign with that exact number of troops available to occupy the last defeated country. The Cumulative column in the grid shows the probability of ending the campaign with at least that number of troops available to occupy the last defeated country.

Is using Conquest Calc Cheating?

That is ultimately up to your and your fellow players to decide. I don’t think using Conquest Calc to arm yourself with probabilities is any more cheating than coaches strategically drafting players, running plays or constructing a batting lineups based on statistics. After all, a batting average is an estimated probability of a player’s chances of scoring a run based on his past experiences at bat. Conquest Calc does the same thing: it calculates the chances of winning a campaign based on experience playing the game.

How does Conquest Calc compare to other similar applications?

There are a few Risk-style board game probability calculators available on the internet. However, most of them only allow you to determine the probability of success of the attacking country defeating a single defending country. Often times a decision to attack is based on the probability of defeating multiple countries, not just one.

For instance, if the odds of defeating the three remaning countries in a continent that do not belong to you are good, then you may be willing to stretch troops a little thin. However, if you are only able to take one or two of the countries, then it may not be worth the losses.

This leads to another problem with other calculators: the definition of success. Most of the time the true definition of success is not defeating a country with only one remaining troop to occupy it. More often, you need to be able to defeat the countries with enough remaining troops to defend the newly won country from enemies.

Conquest Calc provides probability and cumulative probability distribution of each outcome in terms of remaining troops. This is much more useful information for strategic planning and decision making.