Martingale Strategy Failure - Quant Trader Interview Question
Difficulty: Easy
Category: Conditional Expected Value
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Topics: probability, expected-value, risk-management
Problem Description
You are playing a game of chance with a 50% probability of winning each round. You start with a $1 bet. If you lose, you double your bet for the next round. You continue doubling until you win. What are the primary reasons this seemingly foolproof Martingale strategy ultimately fails in practice?
Example: Martingale Strategy
Round 1: Bet \$1, Lose
Round 2: Bet \$2, Lose
Round 3: Bet \$4, Lose
Round 4: Bet \$8, Win
Net Profit Calculation:
$$
\text{Net Profit} = -\$1 - \$2 - \$4 + \$8 = \$1
$$
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