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Current distribution among tapes in superconducting cables has been studied as a function of variations in contact resistance, individual tape critical current, and index (n)-value of individual tapes. It has been shown that besides contact resistances, variations in other superconducting parameters affect current distribution. Variations in critical current and n-value become important at low contact resistances. The effects of collective variations in contact resistances, individual tape critical current, and n-value were studied using Monte Carlo simulations method. Using a validated mathematical model, 1000 cables were simulated with normally distributed random values of contact resistances, individual tape critical current, and n-value. Current distribution in the 1000 simulated cables demonstrated the need for selecting tapes with a narrow distribution in the superconducting parameters to minimize the risk of catastrophic damage to superconducting cables during their operation. It has been demonstrated that there is a potential danger of pushing some tapes closer to their critical current before the current in the cable reaches its design critical current.