# Winning Ways for your Mathematical Plays

> Source: https://ollybritton.com/notes/textbooks/winning-ways-for-your-mathematical-plays/ · Updated: 2024-10-26 · Tags: winning-ways

## Notes
### Chapter 1, "Whose Game"
### Chapter 2, "Finding the Correct Number is Simplicity Itself"
### Chapter 3, "Some Harder Games and How to Make Them Easier"

## Flashcards
### 2022-03-26
What is a game in which the second player to move wins called?::
A zero game.

What does the notation
$$
\\{L | R\\}
$$
mean for the value of a game?::
The left player has a move to a value of $L$, the right player has a move to a value of $R$.

What is the value of $\\{|\\}$?::
$$
0
$$

What is the value of $\\{0|\\}$?::
$$
1
$$

What is the value of $\\{|0\\}$?::
$$
-1
$$

What is the value of $\\{n|\\}$?::
$$
n+1
$$

What is the value of $\\{|n\\}$?::
$$
-(n+1)
$$

What is true about the following surreal number
$$
X = \\{L | R\\}
$$
::
$X$ is greater than all $L$ and less than all $R$.

What is the value of $\\{0|1\\}$?::
$$
\frac{1}{2}
$$

What is the value of $\\{-1|0\\}$?::
$$
-\frac{1}{2}
$$

What has to be true about
$$
\\{L|R\\}
$$
to make a surreal number?::
Any number in $L$ is less than any number in $R$.

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