I am new to Reinforcement learning and am currently reading up on the estimation of Q pi(s,a) values using MC soft epsilon soft approach and chanced upon this algorithm. The link to the algorithm is found from this website.

https://www.analyticsvidhya.com/blog/2018/11/reinforcement-learning-introduction-monte-carlo-learning-openai-gym/

def monte_carlo_e_soft(env, episodes=100, policy=None, epsilon=0.01):

if not policy:
    policy = create_random_policy(env)
# Create an empty dictionary to store state action values
Q = create_state_action_dictionary(env, policy)

# Empty dictionary for storing rewards for each state-action pair
returns = {} # 3.

for _ in range(episodes): # Looping through episodes
    G = 0 # Store cumulative reward in G (initialized at 0)
    episode = run_game(env=env, policy=policy, display=False) # Store state, action and value respectively

    # for loop through reversed indices of episode array.
    # The logic behind it being reversed is that the eventual reward would be at the end.
    # So we have to go back from the last timestep to the first one propagating result from the future.

    # episodes = [[s1,a1,r1], [s2,a2,r2], ... [Sn, an, Rn]]
    for i in reversed(range(0, len(episode))):
        s_t, a_t, r_t = episode[i]
        state_action = (s_t, a_t)
        G += r_t # Increment total reward by reward on current timestep

        # if state - action pair not found in the preceeding episodes,
        # then this is the only time the state appears in this episode.

        if not state_action in [(x[0], x[1]) for x in episode[0:i]]: #
            # if returns dict contains a state action pair from prev episodes,
            # append the curr reward to this dict
            if returns.get(state_action):
                returns[state_action].append(G)
            else:
                # create new dictionary entry with reward
                returns[state_action] = [G]

            # returns is a dictionary that maps (s,a) : [G1,G2, ...]
            # Once reward is found for this state in current episode,
            # average the reward.
            Q[s_t][a_t] = sum(returns[state_action]) / len(returns[state_action]) # Average reward across episodes

            # Finding the action with maximum value.



            Q_list = list(map(lambda x: x[1], Q[s_t].items()))
            indices = [i for i, x in enumerate(Q_list) if x == max(Q_list)]
            max_Q = random.choice(indices)

            A_star = max_Q # 14.

            # Update action probability for s_t in policy
            for a in policy[s_t].items():
                if a[0] == A_star:
                    policy[s_t][a[0]] = 1 - epsilon + (epsilon / abs(sum(policy[s_t].values())))
                else:
                    policy[s_t][a[0]] = (epsilon / abs(sum(policy[s_t].values())))

return policy

This algorithm computes the Q(s,a) for all state action value pairs that the policy follows. If pi is a random policy, and after running through this algorithm, and for each state take the max(Q(s,a)) for all possible actions, why would that not be equal to Q opt (s,a) ?

I have read up a bit on Q - learning and the update equation is different from MC epsilon soft. However, I can't seem to understand clearly how these 2 approaches are different.