Help:=proc(): print(`SU(m,p), E(m,p) `): end:

#SU(m,p): simulating an extemeley risk-averse player in the Shepp Urn
#Try:
#SU(m,p);
SU:=proc(m,p) local i,m1,p1,r:
m1:=m:
p1:=p:

for i from 1 while (p-p1)-(m-m1)<p-m do
 r:=rand(1..m1+p1)():

  if r<=m1 then
   m1:=m1-1:
  else
   p1:=p1-1:
 fi:

od:

[m1,p1,i-1]:

end:

 


#Code by Alison Bu, April 16 2020, After Class Assignment
#The expected number of rounds for a super-risk-averse player in the Shepp Urn if
#currently there are m minus balls, p plus balls and there are still k dollars to be made
E1:=proc(m,p,k) local t:
  option remember:
  if k=0 then
    t:=0:
   elif m=0 and p>=k then
     t:=k:
   elif p<k then
     RETURN(FAIL):
   fi:

  if m>0 and p>0 and k>0 then
    t:=m/(m+p)*E1(m-1,p,k+1)+p/(m+p)*E1(m,p-1,k-1)+1:
   fi:
  t:
end:


#The expected number of rounds for a super-risk-averse player in the Shepp Urn if
#currently there are m minus balls, p plus balls 

E:=proc(m,p):
  E1(m,p,p-m):
end:

#E(100,110)
#	 33683086189085193138363517127662830063471100444206895955179886
# 	--------------------------------------------------------------
#  	297474726318397739666969118328344655976262651151936062181333 

#evalf(%)
#                          113.2300771