Genshin Impact average copies of a specific 4* character after N banner pulls

import matplotlib as mpl
mpl.use('Agg')
import matplotlib.pyplot as plt
import numpy as np

N = 30
memo = np.zeros((N, 10, 2))
done = np.zeros((N, 10, 2))

class Node:

  win = 0.051
  pityCount = 0
  headGuarantee = False
  winHeadChild = None
  winTailChild = None
  loseChild = None

  def avgPulls(self, n):
    if n == 0:
      return 0

    if done[n - 1, self.pityCount, int(self.headGuarantee)] == 1:
      return memo[n - 1, self.pityCount, int(self.headGuarantee)]

    winHeadAvg = 0
    winTailAvg = 0
    loseAvg = 0

    self.winHeadChild = Node()
    if self.pityCount == 9:
      self.win = 1

    # Win branch
    if self.headGuarantee:
      winHeadAvg = 1/3 + self.winHeadChild.avgPulls(n - 1)
    else:
      self.winTailChild = Node()
      self.winTailChild.headGuarantee = True
      winHeadAvg = 0.5*(1/3 + self.winHeadChild.avgPulls(n - 1))
      winTailAvg = 0.5*self.winTailChild.avgPulls(n - 1)
      del self.winTailChild
    del self.winHeadChild

    # Lose branch
    if self.win != 1:
      self.loseChild = Node()
      self.loseChild.pityCount = self.pityCount + 1
      self.loseChild.headGuarantee = self.headGuarantee
      loseAvg = self.loseChild.avgPulls(n - 1)
      del self.loseChild

    ret = self.win*(winHeadAvg + winTailAvg) + (1 - self.win)*loseAvg
    memo[n - 1, self.pityCount, int(self.headGuarantee)] = ret
    done[n - 1, self.pityCount, int(self.headGuarantee)] = 1
    return ret

print(Node().avgPulls(N))
x = np.arange(1, N + 1)
y = memo[:, 0, 0]
plt.plot(x, y, ".")
plt.savefig('graph.png')