The difference between a random walk and a sub martingale is the expected price change in a random walk is zero, and the expected price change for a sub martingale is positive.
The random walk theory suggests that changes in stock prices have the same distribution and are independent of each other. The expected price change in a random walk is zero.
On the other hand, the martingale strategy involves doubling up on losing bets and reducing winning bets by half. Thus, the expected price change for a sub martingale is positive.
Hence, The answer was given and explained above.
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