This problem should be changed to allow for alternative first moves. I agree that 7-3 is “best” but there are at least 4 winning first moves.
10-6 2. 1x10 15x6 3. 14-17 7-3 4. 8-12 28-24 5. 19x28 31-27 6. 16-19 27x18 7. 17-22 3-8 8.
19-24 6-2 9. 24-27 32x23 10. 22-26 13-9 11. 5x14 18x9 12. 26-31 *
13-9 2. 8-12 7-3 3. 14-17 31-27 4. 5x14 27x9 5. 1-5 9-6 *
7-2 2. 23-26 31x22 3. 14-17 22-18 *