Question Author
Times up! (and I’m off out for a Ruby).
No, although I hadn’t discounted retiring in my question, ll_billym, it wasn’t the answer I was looking for.
The answer is 16. Player One comes to the table (with no score on the scoreboard for either player). He pots all fifteen reds off one stroke but goes in off (I had warned you!). So, no points for him, four to his opponent and all the reds are gone. The remaining 27 for the colours can then be split however you like so that one player reaches 16, and the other 15.