The following example shows the minimum acceptable chance of winning (and to justify a take), is actually 18.75%! Suppose a particular game has developed into a race and Black doubles. Furthermore, suppose White has some way of determining that he can reach the following position 25% of the time, and lose 75%.
It is fairly simple to prove that (in no-gammon positions) this is the minimum winning chance to justify a take (steaming is not a justifiable reason). There are certain one-way gammon positions in which a smaller winning percentage allows an acceptance of the cube. In fact, if every win were to lead to a backgammon for the person accepting the cube and all his losses were single games, then a 12.5% chance of winning would be the minimum. My God, is everything a take?!
No, of course not. The gammon chances on either side influence the drop/take decisions a great deal. However, there are many positions that appear to be very bad, which in fact are actually good takes.