Why run simulations if you can calculate?
Spoiler for Python code:
import sympy
import numpy as np
import matplotlib.pyplot as plt
#probability of L winning
p = sympy.symbols("p")
#checks if L wins without EC (bo5)
def Lwins_noEC(x):
return x[:5].count("L") >= 3
#checks if L wins the bo7
def Lwins_bo7(x):
return x.count("L") >= 4
#checks if L wins with EC
def Lwins_EC(x):
if x[0] == "R":
x = x[1:]
if x[:4].count("L") == 2 and x[4] == "L":
x = x[:4] + x[5]
return x[:5].count("L") >= 3
#probability of an outcome consisting of 7 games
def prob(x):
n = x.count("L")
return (p**n*(1-p)**(7-n)).expand()
#build all 128 possible outcomes of 7 games
res = "LR"
games = ["".join([g1, g2, g3, g4, g5, g6, g7]) for g1 in res for g2 in res for g3 in res for g4 in res for g5 in res for g6 in res for g7 in res]
#add up the probabilities
prob_L_noEC = sum([prob(x) for x in games if Lwins_noEC(x)]) #this gives 6*p**5 - 15*p**4 + 10*p**3
prob_L_EC = sum([prob(x) for x in games if Lwins_EC(x)]) #this gives -6*p**7 + 21*p**6 - 21*p**5 + 7*p**3
prob_bo7 = sum([prob(x) for x in games if Lwins_bo7(x)]) #this gives -20*p**7 + 70*p**6 - 84*p**5 + 35*p**4
no_EC = sympy.lambdify(p, prob_L_noEC)
with_EC = sympy.lambdify(p, prob_L_EC)
bo7 = sympy.lambdify(p, prob_bo7)
x = np.linspace(0, 1, num = 200)
ax1, = plt.plot(x, no_EC(x), "-r")
ax2, = plt.plot(x, with_EC(x), "-k")
ax3, = plt.plot(x, bo7(x), "-b")
plt.legend((ax1, ax2, ax3), ("Without EC", "With EC", "Traditional bo7"), loc = 2)
plt.xlabel("Probability of winning one game")
plt.ylabel("Probability of winning the whole match")
If the initiator has a deck that wins with probability p, they win the whole match with probability, Prob(p) = 7p^3 - 21p^5 + 21p^6 - 6p^7.
Since Prob(p) = 1 - Prob(1-p), the chances are the same if the initiator and defender switch places but keep the same decks, so it's all down to the decks.
In fact this EC's effect reduces a bit the overall RNG, but not as much as a full blown Bo7 (even though it's nearly as much work)
TL;DR EC is fair
