#### Mathematics, Rock, Paper, Scissors, Lizard and Spock #### Vince ##### [email protected]

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Scissors cuts paper
Paper covers rock
Rock crushes lizard
Lizard poisons Spock
Spock smashes scissors,
Scissors decapitates lizard
Lizard eats paper
Paper disproves Spock
Spock vaporizes rock
and as it always has...
rock crushes scissors.

$$ A= \begin{pmatrix} 0 & -1 & 1 & 1 & -1\\ 1 & 0 & -1 & -1 & 1\\ -1 & 1 & 0 & 1 & -1\\ -1 & 1 & -1 & 0 & 1\\ 1 & -1 & 1 & -1 & 0 \end{pmatrix} $$

Nash equilibrium

Evolutionary dynamics

$$ \begin{align} f =&\;Ax\\ \phi=&\;fx\\ \frac{dx}{dt} = &\; x (f - \phi) \end{align} $$

Moran Processes

$$ \begin{align} p_{i, i-1}&=\frac{i(N - i)}{N^2}\\ p_{i, i+1}&=\frac{i(N - i)}{N^2}\\ p_{i, i}&=1 - p_{i, i-1} - p_{i, i+1} \end{align} $$

![](https://mathwithbaddrawings.files.wordpress.com/2017/09/20161031143242_000321.jpg?w=584) [math with bad drawings](https://mathwithbaddrawings.com/2017/09/20/the-state-of-being-stuck/)