Help:=proc():print(`GR(A)`):end:

with(SolveTools):

#GR(A): inputs the max. capital A,
#outputs the list [E[1],E[2], ..., E[A-1]]
#where E[i] is the expected number of tosses
#until the end if currently at i
GR:=proc(A::posint) local E1,i,eq,var,sol1:

if A=1 then
 RETURN([]):
fi:

eq:={E1[0]=0,E1[A]=0}:

var:={seq(E1[i],i=0..A)}:

eq:=eq union
{seq(E1[i]-(E1[i-1]+E1[i+1])/2-1=0,i=1..A-1)}:


sol1:=Linear(eq,var):

[seq(subs(sol1,E1[i]),i=1..A-1)]:

end: