%% This LaTeX-file was created by <jl> Mon Aug 30 08:55:53 1999
%% LyX 1.0 (C) 1995-1999 by Matthias Ettrich and the LyX Team

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\begin{document}


\lyxnewslide{start}

{\par\centering How to Solve Cribbage\par}

{\par\centering John Langford\par}


\lyxnewslide{outline}

\begin{itemize}
\item How to play the game
\item What's important
\item The approach taken
\item Preliminary results
\end{itemize}

\lyxnewslide{How~to~play}

Who knows how to play cribbage?

\begin{itemize}
\item First player to 121 points wins.
\item Play divided into hands. 
\item Score of hand = score of play + score from hands
\end{itemize}

\lyxnewslide{What's~important}

The choice points are critical!

\begin{itemize}
\item Suit doesn't matter during the play.
\item The play has 4! = 24 possible choices.
\item Suit does matter during the count.
\end{itemize}

\lyxnewslide{Approach~taken}

Approach taken: the theoretical level

\begin{itemize}
\item Guess policy and prove correctness.
\item Policy is assumed to not include randomization.
\item phenotypes (cards without suit)
\end{itemize}

\lyxnewslide{Approach}

Approach taken: the implementation level

\begin{itemize}
\item using Ocaml (+/-)
\item Abuse the RAM: Cache every computation you can.
\item Direct index of combinations
\item Play policy - room for cool work here.
\end{itemize}

\lyxnewslide{Results}

Preliminary Results

Portions are coded up and tested.

\begin{itemize}
\item Choice of optimal hand subset = multiyear computation. 

\begin{itemize}
\item inner loop in C might imply x10 speed
\item Parallelizable, but requires much RAM.
\end{itemize}
\item Choice of play-policy iteration = O(days)
\item 1-suit deck does not converge.
\item Hand subset not considering play does converge.
\end{itemize}
\end{document}
