diff --git a/document.tex b/document.tex
index d23d748..1731c48 100644
--- a/document.tex
+++ b/document.tex
@@ -74,6 +74,7 @@ wangwenhao11@nudt.edu.cn).
 \input{main/nonergodicity}
 \input{main/paradox}
 \input{main/theorem}
+\input{main/2048prove}
 
  
 
diff --git a/main/introduction.tex b/main/introduction.tex
index 0d41064..892171f 100644
--- a/main/introduction.tex
+++ b/main/introduction.tex
@@ -35,6 +35,10 @@ While the game is simple to understand, it requires strategic
 \cite{bangole2023game}
 
 
+\includegraphics{pic/2048epsilon-greedy}
+\includegraphics{pic/maze-eps-greedy}
+
+
 
 
 
diff --git a/pic/maze-eps-greedy.pdf b/pic/maze-eps-greedy.pdf
new file mode 100644
index 0000000..e567d43
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diff --git a/pic/migongeps-greedy.pdf b/pic/migongeps-greedy.pdf
deleted file mode 100644
index 7535168..0000000
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