Hole Me Him

1 0 2

2 1 0

3 -1 2

4 1 0

5 1 0

6 0 1

7 0 1

8 0 3

9 2 -1

10 3 1

11 1 0

12 0 1

13 2 -1

14 0 1

15 0 1

16 1 0

17 0 2

18 1 -1

Total 12 12

No ties at all seemed very unlikely. What is the probability of that? I tried to estimate it using a Monte Carlo approach with Excel. I got started by simulating just 10 rounds. Tied holes for the 10 simulated rounds were 4,5,2,5,3,8,5,8,2,6. The results indeed suggest that the probability of no ties is quite low. But how low?

I would be interested in a formulaic solution to this problem. For simplicity, assume that each player always has the same set of hole by hole scores, totaling 12 over par, but that the hole by hole pattern of the scores can vary.

Thanks,

Jonart