Title: Theory / Unimportant / Math / Game / Winning ways for your Mathematical plays
Tags: hasSeenConjDef

Name: Blue-Red Hackenbush
Definition: \(G_0=(V,E,\gamma)\) is a graph, whose edges are labelled Red or Blue, and \(\gamma\subseteq V\) called the ground
Page: 2
Chapter: 1
Definition2: At each turn, Left (resp. right), delete a bLue (resp, Red) edge. And every edges not linked the the ground anymore
Definition3: Last player to play win

Name: A zero position of \(G\)
Definition: A position of \(G\) such that, whoever start lose
Page: 2
Chapter: 1
Variables: \(G\) a game

Smaller0: \(G\) is composed of two copies of the same game, where Left can do in what exactly what Right can do in the other one
Greater0: \(G\) starts in a zero position
Page: 3
Chapter: 1
Variables: \(G\) a game
Smaller1: the last player to play wins
Name: Tweedledum and Tweedledee Argument
Construction: 2nd player copy 1rst player play in the other part of the game

Smaller0: each edge of a color \(c\) join the ground through a path of color \(c\)
Greater0: the optimal play is to always play a edge as far as possible from the ground (i.e. such that no other edge disappear after you play)
Page: 4
Chapter: 1
Variables: \(G\) a Blue-Red Hackenbush

Name: Ski-jumps's playground
Definition: A rectangle of \(n\times m\) cases.
Page: 8
Chapter: 1
Definition2: Jumper and slipper on some cases

Definition: The position of a jumper
Page: 8
Chapter: 1
Context: Ski-jumps
Notation: upper-case letter

Definition: The position of a slipper
Page: 8
Chapter: 1
Context: Ski-jumps
Notation: lower-case letter

Question: Ski-jumps turns are
Answer: either you play a piece of your (L or R) in your direction
Page: 8
Chapter: 1
Answer2: if one of your jumper is above a piece of the opponent, you jump below your oppononent, and transform their piece from into a slipper

Question: Ski-jumps winning condition is
Answer: last one to play wins
Page: 8
Chapter: 1

Question: The value of p piece is
Answer: the number of case between this piece, and the end of the game where the piece can goes.
Page: 9, 11
Chapter: 1
Context: Ski jump

Question: The value of a jump is
Answer: 1 if potential jumper is nearer to the central column
Page: 9
Chapter: 1
Context: Ski-jump
Answer2: 1/2 if it is imminent
Answer3: 1/2 if 2 players are the same distance from the central column
Answer4: 0 otherwise

Name: Toads and Frogs
Definition: a rectangular play area
Page: 12
Chapter: 1
Context: Ski-jump
Definition2: Toads for left, Frogs for Right
Conjdef: A game with
Definition3: At each turn, the player move one of his piece in his direction at the distance of one square, or jump over an opposing creature onto an empty square
Definition4: Last player to play wins

Name: A game
Definition: Two players, called Left and Right often, moving alternaly
Page: 14
Chapter: 1
Context: Winning ways for your mathematical plays
Definition2: Several positions, often a finite number, often a starting one
Conjdef: A tuple with
Definition3: Rules
Definition4: complete information
Definition5: no chance moves
Definition6: normal play
Definition7: ending condition

Name: A position
Definition: One state in which the game can be at some particular moment
Page: 14
Chapter: 1
Context: Game

Name: A starting position
Definition: The first position to consider when starting the game
Page: 14
Chapter: 1
Context: Game

Name: A rule
Definition: Moves either player can make from a given position to its options
Page: 14
Chapter: 1
Context: Game

Name: Complete information
Definition: Both players know what is going on
Page: 14
Chapter: 1
Context: Game

Name: Chance move
Definition: A move whose outcome is not certain
Page: 14
Chapter: 1
Context: Game
Example: rolling dices

Name: Normal play
Definition: A player unable to move lose
Page: 14
Chapter: 1
Context: Game

Name: Ending condition
Definition: There are no play of infinite-length
Page: 14
Chapter: 1
Context: Game

Name: Drawn play
Definition: An infinite play
Page: 14
Chapter: 1
Context: Game
Name2: tied play (to avoid)

Name: Tied play
Definition: A play which end without a winner
Page: 14
Chapter: 1
Context: Game
Name2: drawn play (to avoid)

Name: A good move
Definition: A move which win for you
Page: 16
Chapter: 1
Context: Game

Name: A bad move
Definition: A move which lose for you
Page: 16
Chapter: 1
Context: Game

Question: Why can you prefer a bad move (in real life)
Answer: Not to reveal your strategy
Page: 16
Chapter: 1
Context: Game
Answer2: Because you expect opponent also to make a bad move, which will give you a bigger pay
Answer3: To appear as a loser and win more later

Name: Enough rope principle
Definition: Between two losing move, you may prefer the one which is the more complicated to analyze for your adversary
Page: 16
Chapter: 1
Context: Game