Digit Game Checker

Two players play a game with a string of digits. On each turn, a player removes either the first digit or the last digit from the current string. The game ends when all digits are removed. Each player sums up the digits they collected. The first player wins if their total is strictly greater than the second player's total; otherwise the second player wins. Both play optimally. Determine if the first player can win.

Examples
Input: "132"
Output: false
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Digit Game Checker

Two players play a game with a string of digits. On each turn, a player removes either the first digit or the last digit from the current string. The game ends when all digits are removed. Each player sums up the digits they collected. The first player wins if their total is strictly greater than the second player's total; otherwise the second player wins. Both play optimally. Determine if the first player can win.