import numpy as np
import matplotlib.pyplot as plt

# LMSR Cost function: C(q) = b * ln(sum(exp(q_i / b)))
# Here, we track two outcomes: Pacers and Thunder

def lmsr_cost(q1, q2, b):
    return b * np.log(np.exp(q1 / b) + np.exp(q2 / b))

# Marginal price of outcome 1 (Pacers)
def lmsr_price(q1, q2, b):
    return np.exp(q1 / b) / (np.exp(q1 / b) + np.exp(q2 / b))

# Simulate cost of buying shares
def simulate_lmsr_buy(initial_q1, initial_q2, b, buy_shares, outcome='q1'):
    # Determine which quantity we are increasing
    q1, q2 = initial_q1, initial_q2
    new_q1 = q1 + buy_shares if outcome == 'q1' else q1
    new_q2 = q2 + buy_shares if outcome == 'q2' else q2

    # Initial and final cost
    initial_cost = lmsr_cost(q1, q2, b)
    final_cost = lmsr_cost(new_q1, new_q2, b)

    # Total cost to buy `buy_shares` of the selected outcome
    cost = final_cost - initial_cost

    # Final probability (price)
    final_price = lmsr_price(new_q1, new_q2, b)

    return cost, final_price

# Parameters
b = 10000  # liquidity parameter (higher b = more stable market)
initial_q1 = 0
initial_q2 = 0
buy_shares = 50000

# Simulate buying 50K shares for Pacers (q1)
cost_pacers, final_price_pacers = simulate_lmsr_buy(initial_q1, initial_q2, b, buy_shares, 'q1')

# Now simulate how many shares of Thunder (q2) are needed to bring the price back to 0.50
# We'll iterate to find that point
def find_thunder_shares_to_balance(q1, initial_q2, b, target_price=0.5):
    for shares in range(1000, 100000, 100):
        q2 = initial_q2 + shares
        price = lmsr_price(q1, q2, b)
        if abs(price - target_price) < 0.001:
            cost = lmsr_cost(q1, q2, b) - lmsr_cost(q1, initial_q2, b)
            return shares, cost, price
    return None, None, None

thunder_shares, cost_thunder, final_price_thunder = find_thunder_shares_to_balance(buy_shares, 0, b)

(cost_pacers, final_price_pacers), (thunder_shares, cost_thunder, final_price_thunder)