I want to participate in the 2024 election prediction market.
There are 2 candidates: Kamala and Trump.
There are 2 markets: Election winner and Popular vote winner.
I want to be able to set the prices of Yes and No shares for each outcome and the joint probabilities of each pair of outcomes (i.e. Kamala winning the election but losing the popular vote, which is impossible and I want to set it to 0). They should be setable in the code, don't use input(). 
Write a Python program to find guaranteed opportunities given my custom odds.
Keep in mind, I can only buy shares since I don't have any right now.
Also, a common pitfall is giving a (0, 0, 0, 0) sulution with 0 profit, avoid that.
Also, sometimes the strategy could be just buying one share, when the probability of it is higher than the price, don't forget that, it's not always pairs.
Try to keep it simple, don't use tools that are unnecessary. Also, make comments less verbose or don't use them when they're not needed.

I got this solution and it doesn't see that just buying Trump popular vote shares is profitable, given the p of it is 0.6, when the price is 0.37:

from itertools import product

# Define share prices
# Election Winner Market
p_e_yes = 0.4   # Price for Kamala winning the election
p_e_no = 0.6    # Price for Trump winning the election

# Popular Vote Winner Market
p_p_yes = 0.63  # Price for Kamala winning the popular vote
p_p_no = 0.37   # Price for Trump winning the popular vote

# Define joint probabilities
# P(Kamala wins election and popular vote)
P_kk = 0.4

# P(Kamala wins election and Trump wins popular vote)
P_kt = 0.0  # Assume impossible

# P(Trump wins election and Kamala wins popular vote)
P_tk = 0.0  # Assume impossible

# P(Trump wins election and popular vote)
P_tt = 0.6

# Verify probabilities sum to 1
assert P_kk + P_kt + P_tk + P_tt == 1, "Joint probabilities must sum to 1."

# Define maximum shares to consider for each type to limit computation
MAX_SHARES = 10

# List to store arbitrage opportunities
arbitrage_opportunities = []

# Iterate through all possible combinations of shares to buy
for x_e_yes, x_e_no, x_p_yes, x_p_no in product(range(MAX_SHARES + 1), repeat=4):
    # Skip the trivial case where no shares are bought
    if x_e_yes == x_e_no == x_p_yes == x_p_no == 0:
        continue
    
    # Calculate total cost
    cost = (x_e_yes * p_e_yes) + (x_e_no * p_e_no) + (x_p_yes * p_p_yes) + (x_p_no * p_p_no)
    
    # Calculate payouts for each possible outcome
    payout_kk = x_e_yes + x_p_yes
    payout_kt = x_e_yes + x_p_no
    payout_tk = x_e_no + x_p_yes
    payout_tt = x_e_no + x_p_no
    
    # Check if payouts are at least the cost in all outcomes
    if (payout_kk >= cost and
        payout_kt >= cost and
        payout_tk >= cost and
        payout_tt >= cost):
        
        # Ensure that there's at least one outcome with a strict profit
        if (payout_kk > cost or
            payout_kt > cost or
            payout_tk > cost or
            payout_tt > cost):
            
            # Calculate net profit
            profit = min(payout_kk, payout_kt, payout_tk, payout_tt) - cost
            
            arbitrage_opportunities.append({
                'Election Yes': x_e_yes,
                'Election No': x_e_no,
                'Popular Yes': x_p_yes,
                'Popular No': x_p_no,
                'Cost': cost,
                'Minimum Payout': min(payout_kk, payout_kt, payout_tk, payout_tt),
                'Profit': profit
            })

# Display the arbitrage opportunities
if arbitrage_opportunities:
    print("Arbitrage Opportunities Found:")
    for opp in arbitrage_opportunities:
        print(f"Buy {opp['Election Yes']} Election Yes, {opp['Election No']} Election No, "
              f"{opp['Popular Yes']} Popular Yes, {opp['Popular No']} Popular No | "
              f"Cost: {opp['Cost']:.2f}, Min Payout: {opp['Minimum Payout']:.2f}, "
              f"Profit: {opp['Profit']:.2f}")
else:
    print("No arbitrage opportunities found with the given prices and probabilities.")