-- Analyze event contracts for 10 minutes with an 80% payout rate
Rules:
Bet 5U each round
Win: Receive an 80% reward on the bet amount (i.e., win 4U), Total return = Principal 5 + Reward 4 = 9U
Loss: Lose the entire bet amount (-5U)
Strategy: Double the bet amount after each loss, and reset to the initial bet amount after a win
Simulation:
First round: Bet 5U (Result: Loss), Return -5
Second round: Bet 10U (Result: Loss), Return -15
Third round: Bet 20U (Result: Loss), Return -35
Fourth round: Bet 40U (Result: Loss), Return -75
Fifth round: Bet 80U (Result: Win), Return 80+80*80%-75 = 69
Let the initial bet be a, and the winning rate be p
Expected return per round: E = [p×0.8a]+[(1−p)×(−a)]=a(0.8p−1+p)=a(1.8p−1)
From the formula, it can be seen that when p<=55.6%, that is, 1.8p<=1, E<=0
Conclusion: Assuming the event contract is absolutely fair, i.e., p=50%, the expected return E=−0.1a (average loss of 10% per round)
Therefore: Long-term loss is inevitable
