From 80416f0ab893f2b80a01be4acc13bd03c7a03682 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 20 May 2021 10:09:26 +0200
Subject: add new slides

---
 vorlesungen/slides/9/parrondo/spielb.tex | 83 ++++++++++++++++++++++++++++++++
 1 file changed, 83 insertions(+)
 create mode 100644 vorlesungen/slides/9/parrondo/spielb.tex

(limited to 'vorlesungen/slides/9/parrondo/spielb.tex')

diff --git a/vorlesungen/slides/9/parrondo/spielb.tex b/vorlesungen/slides/9/parrondo/spielb.tex
new file mode 100644
index 0000000..6ad512c
--- /dev/null
+++ b/vorlesungen/slides/9/parrondo/spielb.tex
@@ -0,0 +1,83 @@
+%
+% spielb.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Spiel $B$}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Definition}
+Gewinn $\pm 1$, Wahrscheinlichkeit abhängig vom 3er-Rest des
+aktuellen Kapitals $K$:
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\coordinate (A0) at (90:2);
+\coordinate (A1) at (210:2);
+\coordinate (A2) at (330:2);
+
+\node at (A0) {$0$};
+\node at (A1) {$1$};
+\node at (A2) {$2$};
+
+\draw (A0) circle[radius=0.4];
+\draw (A1) circle[radius=0.4];
+\draw (A2) circle[radius=0.4];
+
+\draw[->,shorten >= 0.4cm,shorten <= 0.4cm] (A0) -- (A1);
+\draw[->,shorten >= 0.4cm,shorten <= 0.4cm] (A0) -- (A2);
+\draw[->,shorten >= 0.4cm,shorten <= 0.4cm] (A1) -- (A2);
+
+\draw[->,shorten >= 0.4cm,shorten <= 0.4cm] (A1) to[out=90,in=-150] (A0);
+\draw[->,shorten >= 0.4cm,shorten <= 0.4cm] (A2) to[out=90,in=-30] (A0);
+\draw[->,shorten >= 0.4cm,shorten <= 0.4cm] (A2) to[out=-150,in=-30] (A1);
+
+\def\R{1.9}
+\def\r{0.7}
+
+\node at (30:\r) {$\frac{9}{10}$};
+\node at (150:\r) {$\frac1{10}$};
+\node at (270:\r) {$\frac34$};
+
+\node at (30:\R) {$\frac{3}{4}$};
+\node at (150:\R) {$\frac1{4}$};
+\node at (270:\R) {$\frac14$};
+
+\end{tikzpicture}
+\end{center}
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{Markov-Kette $Y$}
+Übergangsmatrix
+\[
+B=\begin{pmatrix}
+0&\frac14&\frac34\\
+\frac{1}{10}&0&\frac14\\
+\frac{9}{10}&\frac34&0
+\end{pmatrix}
+\]
+Gewinnmatrix:
+\[
+G=\begin{pmatrix*}[r]
+0&-1&1\\
+1&0&-1\\
+-1&1&0
+\end{pmatrix*}
+\]
+\end{block}
+\begin{block}{Gewinnerwartung}
+\begin{align*}
+E(Y)
+&=
+U^t(G\odot B)p
+\end{align*}
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


From d3b772e811ac42cb912cce367b8e7bee07881084 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 20 May 2021 20:24:26 +0200
Subject: add slides

---
 vorlesungen/slides/9/parrondo/spielb.tex | 25 +++++++++++++++++++++----
 1 file changed, 21 insertions(+), 4 deletions(-)

(limited to 'vorlesungen/slides/9/parrondo/spielb.tex')

diff --git a/vorlesungen/slides/9/parrondo/spielb.tex b/vorlesungen/slides/9/parrondo/spielb.tex
index 6ad512c..f65564f 100644
--- a/vorlesungen/slides/9/parrondo/spielb.tex
+++ b/vorlesungen/slides/9/parrondo/spielb.tex
@@ -15,6 +15,7 @@
 Gewinn $\pm 1$, Wahrscheinlichkeit abhängig vom 3er-Rest des
 aktuellen Kapitals $K$:
 \begin{center}
+\uncover<2->{%
 \begin{tikzpicture}[>=latex,thick]
 \coordinate (A0) at (90:2);
 \coordinate (A1) at (210:2);
@@ -47,11 +48,12 @@ aktuellen Kapitals $K$:
 \node at (150:\R) {$\frac1{4}$};
 \node at (270:\R) {$\frac14$};
 
-\end{tikzpicture}
+\end{tikzpicture}}
 \end{center}
 \end{block}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<3->{%
 \begin{block}{Markov-Kette $Y$}
 Übergangsmatrix
 \[
@@ -61,22 +63,37 @@ B=\begin{pmatrix}
 \frac{9}{10}&\frac34&0
 \end{pmatrix}
 \]
+\vspace{-10pt}
+
+\uncover<4->{%
 Gewinnmatrix:
+\vspace{-2pt}
 \[
 G=\begin{pmatrix*}[r]
 0&-1&1\\
 1&0&-1\\
 -1&1&0
 \end{pmatrix*}
-\]
-\end{block}
+\]}
+\end{block}}
+\vspace{-12pt}
+\uncover<5->{%
 \begin{block}{Gewinnerwartung}
 \begin{align*}
+&&&&
 E(Y)
 &=
 U^t(G\odot B)p
+\\
+p&={\textstyle\frac13}U
+&&\Rightarrow&
+E(Y)&={\textstyle\frac1{15}}
+\\
+\overline{p}&={\tiny\frac{1}{13}\begin{pmatrix}5\\2\\6\end{pmatrix}}
+&&\Rightarrow&
+E(Y)&=0
 \end{align*}
-\end{block}
+\end{block}}
 \end{column}
 \end{columns}
 \end{frame}
-- 
cgit v1.2.1