Position 438

 How should White play 65 here:

Whatever you do, you must leave a blot and give black a shot, so you consider 13/2:

The advantage of this play is that you only leave one blot. But that is the only advantage. You will only be hit with 11 rolls here or 31% of the time.

The disadvantage of this play is that you might not be able to cover the blot you have created on your 2 point.

Consider 13/7 6/1*:

Now you have left 2 blots, and Black has more ways to hit you. Black will hit you with any 1 as well as 52, 42, 32, 22 and 43. That is 20 rolls or 56% of the time. That is 9 more rolls or 25% more hitting numbers than if you had just played 13/2. So why is this the correct play? First Black may roll 66 and stay on the bar. Also, Black may enter without hitting, in which case, their rear most checker is further forward in your home board, so now you can play your checkers safely behind their rear most checker.

Although you will be hit with 9 more rolls than 13/2, the follow-up is easier if you are missed, and that is why this is the correct move.