Pokémon GO

Wenjie ZHENG

 

Metagaming

 Data Science

Today's talk

  • Pokémon GO
  • Metagaming
  • Data science

Pokémon GO

  • Augmented reality
  • Mobile game
  • Most popular in 2016

Catch a Pokémon

Gym Battle

Metagaming

  • In-game info => gaming
  • Out-of-game info => metagaming

In-game

  • Combat power (CP)
  • Hit point (HP)
  • Moves
    • Power
    • Energy consumption

Out-of-game

  • Attack
  • Defense
  • Stamina
  • Moves
    • Duration
    • Energy generation

Information in Pokémon GO

Topics

  1. Pokémon tier list
  2. Strongest attacker/defender
  3. Gym battle team choice

1. Pokémon tier list

Three measures

\text{attack}
attack\text{attack}
\text{attack} \times \text{defense}
attack×defense\text{attack} \times \text{defense}
\text{attack} \times \text{defense} \times \text{stamina}
attack×defense×stamina\text{attack} \times \text{defense} \times \text{stamina}

A

B

C

1. Pokémon tier list

1st
2nd
3rd

B

C

B

C

Before

After

1. Tier list (Count in DPS)

1st
2nd
3rd

B

C

B

C

After

Before

2. Strongest attacker/defender

Payoff matrix

2. Strongest attacker/defender

Before

After

Before

After

PCA on attackers (before)

2. Strongest attacker/defender

PCA on attackers (after)

2. Strongest attacker/defender

PCA on defenders

2. Strongest attacker/defender

3. Gym battle team choice

\begin{aligned}\min_{x_{ij}} & \sum_{i}c_{i}\sum_{j}x_{ij}\\ \text{s.t. } & \begin{cases} \sum_{i}a_{ij}x_{ij}\ge1 & \forall j\in\text{gym}\\ \sum_{j}x_{ij}\le1 & \forall i\in\text{inventory}\\ x_{ij}\ge0 & \forall i,j\\ x\text{'s row sparsity}\le6 \end{cases} \end{aligned}
minxijicijxijs.t. {iaijxij1jgymjxij1iinventoryxij0i,jxs row sparsity6\begin{aligned}\min_{x_{ij}} & \sum_{i}c_{i}\sum_{j}x_{ij}\\ \text{s.t. } & \begin{cases} \sum_{i}a_{ij}x_{ij}\ge1 & \forall j\in\text{gym}\\ \sum_{j}x_{ij}\le1 & \forall i\in\text{inventory}\\ x_{ij}\ge0 & \forall i,j\\ x\text{'s row sparsity}\le6 \end{cases} \end{aligned}

Linear Programming

Difficult constraint

Gym battle team choice

\begin{aligned}\min_{x_{ij},z_{i}} & \sum_{i}c_{i}\sum_{j}x_{ij}\\ \text{s.t. } & \begin{cases} \sum_{i}a_{ij}x_{ij}\ge1 & \forall j\in\text{gym}\\ \sum_{j}x_{ij}\le z_{i} & \forall i\in\text{inventory}\\ \sum_{i}z_{i}\le6\\ x_{ij}\ge0 & \forall i,j\\ z_{i}\in\left\{ 0,1\right\} & \forall i \end{cases} \end{aligned}
minxij,ziicijxijs.t. {iaijxij1jgymjxijziiinventoryizi6xij0i,jzi{0,1}i\begin{aligned}\min_{x_{ij},z_{i}} & \sum_{i}c_{i}\sum_{j}x_{ij}\\ \text{s.t. } & \begin{cases} \sum_{i}a_{ij}x_{ij}\ge1 & \forall j\in\text{gym}\\ \sum_{j}x_{ij}\le z_{i} & \forall i\in\text{inventory}\\ \sum_{i}z_{i}\le6\\ x_{ij}\ge0 & \forall i,j\\ z_{i}\in\left\{ 0,1\right\} & \forall i \end{cases} \end{aligned}

Zero-One Linear Programming

Pokémon GO, Metagaming and Data Science

By Wenjie Z