#Please do NOT post homework
#Julian Herman, 9/27/21, Assignment 7

#1)
#Runs GRt K times and returns the [ProbabilityOfExitingAwinner, AverageDurationOfGame]
EstGR:=proc(p,i,N,K) local s,d,j,A:
  s:=0:
  d:=0:
  for j from 1 to K do
    A:=GRt(p,i,N):
    if A[1]=1 then
      s:=s+1:
    end if:
    d:=d+A[2]:
  end do:
  return [evalf(s/K), evalf(d/K)]
  end proc:



#3)
#outputs the EXACT pair [ProbabilityOfExitingAwinner , AverageDuration] for any i and N where 0≤i≤N
ExactFairGR:=proc(i,N):
  return [evalf(i/N), evalf(i*(N-i))]
  end proc:

  for i to 19 do
      ExactFairGR(i, 20)
      EstGR(0.5, i, 20, 3000)
  end do;
         [0.05000000000, 19.] [0.04533333333, 18.30133333]

          [0.1000000000, 36.] [0.1000000000, 35.54933333]

          [0.1500000000, 51.] [0.1490000000, 50.83200000]

          [0.2000000000, 64.] [0.1880000000, 62.92200000]

          [0.2500000000, 75.] [0.2493333333, 73.93933333]

          [0.3000000000, 84.] [0.3076666667, 84.60466667]

          [0.3500000000, 91.] [0.3476666667, 92.53266667]

          [0.4000000000, 96.] [0.4133333333, 97.28266667]

          [0.4500000000, 99.] [0.4456666667, 100.2993333]

          [0.5000000000, 100.] [0.5013333333, 98.14266667]

          [0.5500000000, 99.] [0.5553333333, 97.28066667]

          [0.6000000000, 96.] [0.5923333333, 96.14733333]

          [0.6500000000, 91.] [0.6486666667, 90.49733333]

          [0.7000000000, 84.] [0.6956666667, 84.12800000]

          [0.7500000000, 75.] [0.7490000000, 73.29533333]

          [0.8000000000, 64.] [0.8023333333, 62.52666667]

          [0.8500000000, 51.] [0.8520000000, 48.89866667]

          [0.9000000000, 36.] [0.9066666667, 36.26800000]

          [0.9500000000, 19.] [0.9480000000, 20.00600000]



#4)
P := RandSM(10);
StSa(P, 4000);
  [0.1087500000, 0.06925000000, 0.1030000000, 0.08425000000,

    0.1080000000, 0.06900000000, 0.1307500000, 0.09625000000,

    0.1067500000, 0.1240000000]


evalf(StSp(P, 4000));
   [0.1174173778, 0.1174173778, 0.1174173778, 0.1174173778,

     0.1174173778, 0.1174173778, 0.1174173778, 0.1174173778,

     0.1174173778, 0.1174173778]


evalf(StS(P));
  [0.1174173778, 0.07243439021, 0.1033371556, 0.08329597760,

    0.1053143503, 0.06188408639, 0.1280674803, 0.09595685853,

    0.1089925630, 0.1232997602]



#6) EXTRA CREDIT: DID NOT COMPLETE
EstimateProbSum:=proc(p1,p2,p3,p4,p5,p6,N1,N2,K1,K2) local i,j,r,a,s:
  s:=0:
  for i from 1 to K2 do
    a:=0:
    for j from 1 to K1 do
      r:=rand()/(1000000000000.):
      if r < p1 then
        a:=a+1:
      elif r < p1+p2 then
        a:=a+2:
      elif r < p1+p2+p3 then
        a:=a+3:
      elif r < p1+p2+p3+p4 then
        a:=a+4:
      elif r < p1+p2+p3+p4+p5 then
        a:=a+5:
      else
        a:=a+6:
      end if:
    end do:
    if N1 < a < N2 then
      s:=s+1:
    end if:
  end do:
  return evalf(s/K2);
  end proc: