A few buddies of mine started playing a new game:
Kingdom Death: Monster. KDM is a table top rpg-like game where you go out to hunt monsters and manage a settlement. We all got deeply involved equipping our characters and deciding their fates. One point of contention amongst the group was which weapons we should equip our squad with.Each weapon has perks and drawbacks so it makes it difficult to determine if there is such at thing as a “best” weapon for your characters. Each weapon has three major attributes, strength, accuracy, and speed.Strength determines how hard the weapon hits, accuracy determines how easy it is to hit with the weapon, and speed determines how many attacks you can get off with the weapon in a single turn. There is usually a trade off between these three stats. A weapon with high strength might have low speed because it is heavy or hard to use. A quick weapon might provide the opportunity for multiple hits, but might be less accurate than another option.All of these options have to be weighed against the monster you plan to hunt. Each monster has different attributes making weapon choice important. Some monsters are harder to hit, others have a tough hide that requires more strength to break through. So keeping this in mind how do we choose the best weapon?
Like most table top games and rpgs all actions the player takes are determined by dice rolls whether they succeed or fail. When a player wants to attack a monster she rolls a dice and the number will tell her whether she hits the monster or not. Simulating actions this way allows to mathematically determine outcome much easier as I just have to model a dice roll for each attack.Before we go into simulation, I should clearly outline the process of attacking a monster in KDM. KDM takes a unique approach on attacking a monster. There are two main stages to an attack: hit phase and wound phase.During hit phase the player rolls to see if they actually hit the monster. They look at the monster’s evasion stat and their weapon’s accuracy stat. In order to hit the player must roll higher than their weapon’s accuracy stat plus the monster’s evasion stat. For each point of speed the weapon has the player may roll one dice. For example if their sword has a speed of 3, they can roll up to three dice.Once the player determines if they hit or not they go to the next phase: wound phase. Here the play rolls again to see if they wound the monster. They re roll any dice that was greater than their weapon’s accuracy stat plus the monster’s evasion stat from the previous phase. To actually wound the monster, the player must roll higher than the monster’s toughness (or hide) minus the strength of the weapon. Every dice that passes this check wounds the monster.Every roll is done on a 10-sided die. However, in KDM there are two special rolls, 1 and 10. Whenever a player rolls a 1, the hit or the wound fails no exception. Whenever a player rolls a 10, the hit or wound succeeds no exception.
In order to quantify which weapon performs better against certain monsters, I will need to determine the probabilities of hitting and more importantly wounding the monster. This could probably be done with distributions and simple probabilities, however, with the 1/10 rule and the various strength and accuracy check I decided on a different approach. In comes Monte Carlo methods.
Monte Carlo methods simulate your problem multiple times to determine probabilities of success. Essential to the method is randomness. Each trial produces a different result and if the number of trials is decently large it begins to model the distribution of the initial problem. I stumbled upon a great blog post that outlines how to perform these methods using R.The website Count Bayesie outlines different ways to use Monte Carlo methods
here. I highly recommend reading the post as it outlines MC methods pretty clearly and gives real world examples with easy to follow code.Using R, I created a script that would crunch the numbers on each weapon. The script calculates the chance to hit, wound, critical hit, and critical wound (happens when a 10 is rolled). The script will also plot the distributions of each stat and compare them to another weapon. All of the above depends on the monster. Each monster has 3 levels with various stats.The script initially produced tables and graphs, but wasn’t super useful. I converted the script into a shiny webapp below. Now anyone can utilize my monte carlo script to compare any two weapons for any given monster.
There are a few limitations so far. You can only compare 2 weapons at a time.
Weapon special abilities are not taken into account. This means that weapons are only compared on base stats only.The weapon simulator has been updated! It now includes all weapon “perks” and affinities. Try it for yourself! (Gaxe is a good option as the affinities add +1 speed)Enjoy!-Marcello
Like most table top games and rpgs all actions the player takes are determined by dice rolls whether they succeed or fail. When a player wants to attack a monster she rolls a dice and the number will tell her whether she hits the monster or not. Simulating actions this way allows to mathematically determine outcome much easier as I just have to model a dice roll for each attack.Before we go into simulation, I should clearly outline the process of attacking a monster in KDM. KDM takes a unique approach on attacking a monster. There are two main stages to an attack: hit phase and wound phase.During hit phase the player rolls to see if they actually hit the monster. They look at the monster’s evasion stat and their weapon’s accuracy stat. In order to hit the player must roll higher than their weapon’s accuracy stat plus the monster’s evasion stat. For each point of speed the weapon has the player may roll one dice. For example if their sword has a speed of 3, they can roll up to three dice.Once the player determines if they hit or not they go to the next phase: wound phase. Here the play rolls again to see if they wound the monster. They re roll any dice that was greater than their weapon’s accuracy stat plus the monster’s evasion stat from the previous phase. To actually wound the monster, the player must roll higher than the monster’s toughness (or hide) minus the strength of the weapon. Every dice that passes this check wounds the monster.Every roll is done on a 10-sided die. However, in KDM there are two special rolls, 1 and 10. Whenever a player rolls a 1, the hit or the wound fails no exception. Whenever a player rolls a 10, the hit or wound succeeds no exception.