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E-Sim optimal equipment selection
Simulation is concentrated on finding the most efficient equipment set for online game e-sim.

Assignment

 * Project name: E-Sim optimal equipment selection
 * Author: Andriy Zhubryd
 * Software used: Excel
 * Simulation type: Monte-Carlo

E-Sim review
E-Sim is free strategic world simulation. It uses real Earth map, real countries with their official borders. Currently, 58 countries are represented: new countries are added as soon as enough number of real-life citizens of this country register the game. Unfortunately, Czech Republic is represented only on primera server and is fully conquered by Poland. Slovakia successfully exists on the secura server and had conquered Austria and Germany :) Main point of the game is to develop your country's military, economy and politics. It gives people opportunity to test themselves as free entrepreneur, minister or president of the country, disciplined soldier or officer.

Problem description
At first, e-sim military module was very deterministic: soldier's damage in the battle could be calculated precisely. After some time, game's admin decided to make the calculation of damage stochastic to increase uncertainty. They changed basic hit damage from the exact value to uniformly distributed parameter with 20% two-sided interval around previous basic value (for example, 1000 points hit became U(800,1200) hit). Also, they added new parameters, which usually are in most online mmog games: chance of miss, critical hit and avoid of damage (you didn't spend your energy for the hit). Every player had basic values of these parameters and 5 (8 later) slots for special equipment to change parameters, which influence the damage in battles.

Every piece of equipment could be of different quality (from 1 to 5 at the beginning, 6 added later) and have 2 properties, which influence potential damage. These properties were generated upon creation of the item and were chosen randomly, value of property had been chosen randomly from the specific interval (depends on quality and property). Simulation will optimize set of 5 Q5 (quality level 5) equipment items to maximize damage in the battle. We will consider only 5 different properties (value of the rest of them is relatively very low):
 * Reduce miss chance (6-7.5%)
 * Increased critical chance (4-6%)
 * Increased maximum damage (8-10%)
 * Increased damage (4-6%)
 * Chance to avoid damage (4-6%)

Solution of problem
Estimation of the best set of equipment will be done by numerous Monte-Carlo simulations of one-day full fight with different sets of equipment. At the same time, by mathematical calculations we will choose equipment set with maximum expected damage. Also, analysis of added value by each property will help to understand what strategy player should use to maximize the damage. Results can be compared with the most successful soldiers in the game: what properties they choose for themselves.

Andriy Zhubryd 14:14, 14 December 2014 (CET)

Oleg.Svatos 21:01, 14 December 2014 (CET) Looks good. Approved.