Help:=proc()  print(`Emnp(m,n,p)`):
print(`Emp(m,p), P(m1,n1,m2,n3,p)`):
end:


Emp:=proc(m,p):
if m=0 then
  0:
else
 (p*Emp(m-1,p)+1)/p:
fi:
end:



#Emnp(m,n,p): The expected number of
#(loaded)coin tosses needed in a Knock `m Down
#game with m pennies in the H side
#n tokens in the T side, and Prob(H)=p
#if the coin is H (T): remove a penny from the H 
#(T) side (if possible)
Emnp:=proc(m::nonnegint,n::nonnegint,p)
option remember:


if m>0 and n>0 then
 p*Emnp(m-1,n,p) +(1-p)* Emnp(m,n-1,p)+1:
elif m>0 and n=0 then
Emp(m,p):
elif m=0 and n>0 then
Emp(n,1-p):
elif m=0 and n=0 then
    0:
else
  ERROR(`Something is wrong`):
fi:
end:



P:=proc(m1,n1,m2,n2,p):
if m1=0 and n1=0 and m2=0 and n2=0 then
 1/2:

elif m1=0 and n1=0 then
 1:
elif m2=0 and n2=0 then
 0:

elif m1>0 and n1>0 and m2>0 and n2>0 then

p*P(m1-1,n1,m2-1,n2,p) +
(1-p)*P(m1,n1-1,m2,n2-1,p):
elif m1=0 and m2=0 then
   if n1>n2 then
     0:
    elif n1=n2 then
      1/2:
     else
     1:
    fi:

elif n1=0 and n2=0 then
   if m1>m2 then
     0:
    elif m1=m2 then
      1/2:
     else
     1:
    fi:

else
p*P(max(m1-1,0),n1,max(m2-1,0),n2,p) +
(1-p)*P(m1,max(n1-1,0),m2,max(n2-1,0),p):
fi:
end: