## Changes from eb485838c87de2760f9936b9daf98673cebe550c to current

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R&N Chapter 6

+ The fundamental concept is **two-player, zero-sum games**
+ The basic solution technique is **minimax search**
+ Minimax search grows exponentially
+ heuristic searches are important (Section 6.3)
+ Video lecture [mp4](multiplayer.mp4)/[ogg](multiplayer.ogg)
provides a few anchor points for the material.
It does not replace the text book.

# Briefing

## Two-player, Zero Sum games

+ **State-machine**
- to-move: state $\to$ player
- actions: state $\to$ {action}
- result: state $\times$ action $\to$ state
- utility: state $\times$ player $\to\mathbb{R}$
+ Minimax algorithm:
- maximises utility for the player currently to move
- **Tree Search**: optimise utility bottom-up
- **min nodes and max nodes**
- exhaustive research
+ Caveats and variations
- Branching factor
- multi-player games - alliances and trust
- co-operative games
- $\alpha\beta$ pruning
- heuristic searches
- Type A and Type B:
- move generation
- move evaluation
+ **Monte Carlo** Tree Search
- Monte Carlo $\sim$ Stochastic Simulation
- Balance Exploitation and Exploration
+ More Caveats
+ Stochastic Games - **Chance Nodes**
+ Partially Observable Games
- the percept sequence is no longer the opponent's move.
+ Limitations - Section 6.7
+ Intractible
+ Approximations and Assumptions
+ Individual moves - no sight of the bigger picture

# Exercise

## Tic Tac Toe

+ [Code from github](https://github.com/hgeorgsch/pai-exercises/tree/main/TicTacToe)

I was not able to find suitable exercises on CodinGame, so instead,
I have provided a simulator for you.  You should

1.  Clone the git repo, git clone https://github.com/hgeorgsch/pai-exercises.git
2.  Change to the TicTacToe subdirectory
3.  Modify the template to implement your intelligent agent.
You should use the minimax algorithm as described for two-player,
zero sum games.
4.  Play the game, using the test scripts: python3 ttt.py
5.  Consult the README file for details.

This assumes that you have git and python3 installed.

## Discussion

From [R&N Exercises](https://aimacode.github.io/aima-exercises/game-playing-exercises/)

+ Exercise 1
+ Exercise 3

## Monte Carlo Tree Search

+ [Can you save the forest - Episode 1](https://www.codingame.com/training/medium/can-you-save-the-forest---episode-1)

# Debrief

All the algorithms we are studied are based on (discrete)
**state machine models** and **tree search algorithms**
in the graph defined by the states and transitions in the
state machines.
It is crucial that we understand the basic structure of these
models and algorithms well, so that we can adapt them to the
different special cases we encounter.

+ exhaustive searches in small state spaces
- BFS
- DFS
+ non-deterministic environments lead to random transitions
+ modelled by and-or trees
+ partial observation leads to belief states
+ in offline search we can jump to arbitrary nodes to restart the search
+ in online searches we need to backtrack by actual actions in the environment