Nice thread, and what I like best is that it analyzes the process by which one must make their tactical decision here.
What's right for one player may be wrong for another and what's right against one opponent may be wrong against another.
All the good posts in this thread have identified the factors that need to be considered, and, here they are:
a) How strong is your opponent and what shots are you willing to chance leaving them?
b) How strong is your game? After three fouls, you'll trail 94-52. Can you overcome that or is your best chance to win a safety battle here and now while you still have 70?
c) How good are you at executing the opening break, the one required of you after a third foul? The less reliable you are at executing it, the the less you should be inclined to bet the ranch on your ability to execute it.
This thread, I would suggest, is not about whether it's ever advisable to take three fouls. I've attended fifteen different 14.1 world championship, so I've certainly seen it used successfully as a tactic on numerous occasions. It is, instead, about how to evaluate your next move and what factors must be considered in doing so. So much of 14.1 defense is about the decision making process, and this thread is a nice example of a position that is, quite simply, not the same for everybody.
Nice input from everybody here, and the result is a great instructional thread.