Well, If I am dispensing cookies, Dr. Bill gets it. And his explanation is spot on. For those of you who disagree with his choice you will have to back up your claim with a stronger case.
I will not add to the good Dr.'s analysis of his shot but I will address two of the other options which were provided. Please do not be offended because as I see it, it is all a matter of percentages.
First, The thought of playing the one ahead of the thirteen carries the risk of coming up dry or at least limiting the possibility of scoring heavily in this inning should the cue ball run directly into the ten ball which is on the bottom rail. This is a real possibility and therefore if a natural roll is used to shoot this shot, a draw stroke or a tempered shot with follow and inside English would have to be employed to avoid this from happening. All of this complicates a situation which is not necessary because of the option on the thirteen.
Second, and this shot has some merit but in my opinion is the weaker of the two best shots, is to play the thirteen and run the cue ball between the ten and fifteen. The problem with this option is two fold. The speed control on this shot is a concern. If solid position on the fifteen is not achieved there may not be a decent angle to get on the ten for the breakout and position on the one. And what happens should when shooting the thirteen the cue ball runs two rails into the fifteen either directly or to the high side? This shot has the potential of leaving the shooter with a one ball run followed up with a safety.
No, the Dr.'s choice is by far the best decision in this situation. His option is easy to execute, has much margin for error, and has back up possibilities with the ten ball or the one ball should things somehow not work quite as planned.
Below is the out come of having shot this shot as Bill described. Now the question is how do you run the seven remaining balls needed to win the game. A clue; the six ball is now dead in your hole but it is blocked by the one and the two will not pass the fourteen. Be specific.