# Formulas & Simulations

A simulation is conducted to analyze the duel combat gameplay and the relative dynamics between each stance, specifically for boxing. The results are elaborated below. The source file can be viewed and downloaded here.

## Simulation Overview

During a duel combat, 3 random numbers are generated for each player (6 total for 2 players) in each turn to calculate the following parameters:

Accuracy

Defense

Damage

Each random number is generated based on a truncated normal distribution, where the shape of the curve (mean, standard deviation) and the maximum value are directly dictated by the combat stance taken. In the case of Damage, the RNG is influenced by the player's Strength (based on stance) and the relative value of a player's Accuracy and her opponent's Defense.

The simulation utilizes the Inverse CDF method to simulate the RNG and compute the above parameters and subsequent combat results.

## Parameter Results

The simulation shows that each combat stance is directly tied to one parameter which it is advantageous in:

#### Accurate

Advantageous in Accuracy, with max output of 270 (vs. 160 for the other stances).

#### Aggressive

Advantageous in Strength (i.e. max hit), with max output of 130 (vs. 110 for the other stances).

#### Defensive

Advantageous in Defense, with max output of 180 (vs. 120 for the other stances).

Note: Given the truncation of the normal distribution in the RNG, the parameter results resemble uniform distributions between 0 and certain max values.

## Combat Results

The simulation pits each combat stance against each other over 30,000 turns. The results are as follow:

On average, if Player A only uses the Aggressive stance to duel against Player B, who only uses the Accurate stance, it will take Player A 23.3 turns to defeat Player B. Conversely, it will take Player B 24.9 turns (1.6 more turns) to defeat Player A.

Last updated