Since a play-off is not feasible, to determine a tournament winner for stroke play, then matching score-cards is the next-best USGA recommended method of settling a deadlock.
The winner will be determined on the basis of the best score for the last nine holes. If the tying players have the same score for the last nine holes, then the last six holes, then the last three holes, and finally the 18th hole will be used until the tie is broken.
Using this method, one-half, one-third, one-sixth, or one 18th of the Course Handicaps are deducted for Net computation. Fractions of one-half stroke or more count as a full stroke; any lesser fractions are disregarded.
Callaway ties are settled first by total gross score, then using the gross score for the last nine, last six, last three, and finally the 18th hole.
If the above process does not produce a winner, then the same process will be used on the basis of the best score for the first nine holes, then the last six holes of the front nine, then the last three holes of the front nine, and finally the 9th hole. This tie-breaking process applies to Gross, Net, and Callaway.
Settling ties is difficult and sometimes controversial, but these USGA guidelines help to decide the winner in an orderly and equitable fashion to ensure the competition was settled fairly using these time-proven methods.