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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart;\n" }
{MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "P:= Matrix([\n" }{MPLTEXT 1 0 53 "[1   ,  0 , 0  ,  0
  ,  0  ,  0   ,  0  ,  0  ,  0],\n" }{MPLTEXT 1 0 53 "[0   ,  1 , 0  \+
,  0  ,  0  ,  0   ,  0  ,  0  ,  0],\n" }{MPLTEXT 1 0 53 "[1/12, 1/6,
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1/6, 0  ,13/18,  0  ,  0   ,  0  ,  0  ,  0],\n" }{MPLTEXT 1 0 53 "[5/
36, 1/6, 0  ,  0  ,25/36,  0   ,  0  ,  0  ,  0],\n" }{MPLTEXT 1 0 53 
"[5/36, 1/6, 0  ,  0  ,  0  , 25/36,  0  ,  0  ,  0],\n" }{MPLTEXT 1 
0 53 "[1/9 , 1/6, 0  ,   0 ,  0  ,  0   ,13/18,  0  ,  0],\n" }
{MPLTEXT 1 0 53 "[1/12, 1/6, 0  ,  0  ,  0  ,  0   ,  0  , 3/4 ,  0],
\n" }{MPLTEXT 1 0 52 "[2/9 , 1/9,1/12, 1/9 , 5/36, 5/36 ,  1/9, 1/12, \+
 0]\n" }{MPLTEXT 1 0 4 "]);\n" }}{PARA 206 "> " 0 "" {MPLTEXT 1 0 0 ""
 }}{PARA 11 "" 1 "" {XPPMATH 20 "-I'MatrixG6$%*protectedGI(_syslibG6\"
6#/I$%idGF'\")%e'o#)" }}}{EXCHG {PAGEBK }{PARA 0 "> " 0 "" {MPLTEXT 1 
0 53 "sP:=MatrixInverse(MatrixAdd(IdentityMatrix(9),-t*P));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "-I'MatrixG6$%*protectedGI(_syslibG6\"6#/I$%idG
F'\")Ww_$)" }}}{EXCHG {PAGEBK }{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "A:=M
atrix(9):\n" }{MPLTEXT 1 0 21 "for i from 1 to 9 do\n" }{MPLTEXT 1 0 
21 "for j from 1 to 9 do\n" }{MPLTEXT 1 0 31 "A(i,j):= limit(sP(i,j),
\{t=1\});\n" }{MPLTEXT 1 0 5 "od: \n" }{MPLTEXT 1 0 4 "od:\n" }
{MPLTEXT 1 0 2 "A;" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I'MatrixG6$%*prot
ectedGI(_syslibG6\"6#/I$%idGF'\")#pqN)" }}}{EXCHG {PAGEBK }{PARA 0 "> 
" 0 "" {MPLTEXT 1 0 15 "AA:=Matrix(9):\n" }{MPLTEXT 1 0 21 "for i from
 1 to 9 do\n" }{MPLTEXT 1 0 21 "for j from 1 to 9 do\n" }{MPLTEXT 1 0 
48 "AA(i,j):= limit(simplify((1-t)*sP(i,j)),\{t=1\});\n" }{MPLTEXT 1 
0 4 "od:\n" }{MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
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(_syslibG6\"6#/I$%idGF'\")3OL$)" }}}{EXCHG {PAGEBK }{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "M:=Matrix(9):\n" }{MPLTEXT 1 0 21 "for i from 1 to 9 \+
do\n" }{MPLTEXT 1 0 21 "for j from 1 to 9 do\n" }{MPLTEXT 1 0 17 "M(i,
j):= P(i,j);\n" }{MPLTEXT 1 0 4 "od:\n" }{MPLTEXT 1 0 4 "od:\n" }
{MPLTEXT 1 0 4 "#M;\n" }{MPLTEXT 1 0 23 "for k from 1 to 10 do \n" }
{MPLTEXT 1 0 30 "M:=MatrixMatrixMultiply(M,M);\n" }{MPLTEXT 1 0 4 "od:
\n" }{MPLTEXT 1 0 21 "for i from 1 to 9 do\n" }{MPLTEXT 1 0 21 "for j \+
from 1 to 9 do\n" }{MPLTEXT 1 0 39 "if (M(i,j)< 10^(-100)) then M(i,j)
:=0;\n" }{MPLTEXT 1 0 4 "fi;\n" }{MPLTEXT 1 0 4 "od:\n" }{MPLTEXT 1 0 
4 "od:\n" }{MPLTEXT 1 0 10 "evalf(M);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "-I'MatrixG6$%*protectedGI(_syslibG6\"6#/I$%idGF'\")gb0&)" }}}
{EXCHG {PAGEBK }{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "AAA:=simplify(sP(9,
1)/sP(1,1)+sP(9,2)/sP(2,2));#F91+F92" }}{PARA 11 "" 1 "" {XPPMATH 20 "
,$*,I\"tG6\"\"\"\",*!%#f#F&F$\"%_T*$F$\"\"#!%I>*$F$\"\"$\"$0#F&,&!#OF&
F$\"#D!\"\",&!#=F&F$\"#8F3,&!\"%F&F$F.F3#F&F." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "sE := unapply(AAA,t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "f*6#I\"tG6\"F%6$I)operatorGF%I&arrowGF%F%,$*,9$\"\"\",*!%
#f#F,F+\"%_T*$F+\"\"#!%I>*$F+\"\"$\"$0#F,,&!#OF,F+\"#D!\"\",&!#=F,F+\"
#8F9,&!\"%F,F+F4F9#F,F4F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 32 "sE(1);#probability the game ends" }}{PARA 11 "" 1 "" {XPPMATH 20
 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "ET:=subs(t=1,di
ff(sE(t),t));#expected time T to the end of the game\n" }{MPLTEXT 1 0 
14 "mu:=evalf(ET);" }}{PARA 11 "" 1 "" {XPPMATH 20 "#\"$d&\"$l\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "$\"+wvvvL!\"*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 46 "ET2:=subs(t=1,diff(t*diff(sE(t),t),t));#E(T^2)" }}
{PARA 11 "" 1 "" {XPPMATH 20 "#\"&p<'\"%DI" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 19 "ET2-ET^2;#Variance\n" }{MPLTEXT 1 0 43 "sigma:= eva
lf(sqrt(%));#Standard Deviation\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "#\"
'scC\"&Ds#" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+3#eR+$!\"*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats):" }}}{EXCHG {PARA 0 "> 
" 0 "" {MPLTEXT 1 0 30 "statevalf[cdf,normald](2.33);\n" }{MPLTEXT 1 
0 29 "statevalf[cdf,normald](1.65);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$
\"+W#p4!**!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+?`G0&*!#5" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 205 68 "So with 99% (repectively 95%) pro
bability 1000 games at 1 table take" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "(400*mu+2.33*sigma*sqrt(1000.0));\n" }{MPLTEXT 1 0 
33 "(400*mu+1.65*sigma*sqrt(1000.0));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"$\"+$)yjr:!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+/B/2:!\"'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 205 6 "tosses" }}}}
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