Every reference, human and computer, plays 3-1 the same way. It is the best opening roll in the game.
8/5 6/5Every source agrees
The position after 8/5 6/5. The 5-point is highlighted.
Why this play
The 5-point is the most valuable point on the board, and 3-1 makes it immediately with no checker left exposed. Nothing else in the opening does both.
It is the front door to your home board. Holding it means your opponent's two back checkers on their 24-point have to run past a made point on the way out, and it is one of the six points you will want when you eventually try to trap a checker behind a prime.
It also builds toward blocking. Combined with the 6-point and 8-point you already own, the 5-point gives you three of the six points you need for a full prime before your opponent has made anything.
The mistake to avoid
There is no serious alternative. If you find yourself playing 13/10 13/12 with a 3-1, you are giving away the largest edge the opening offers.
How settled is this? Every source agrees. There is no serious argument against it.
Knowing the play and making it under pressure are different skills
Play a rated game and the computer reviews every decision you made afterwards, including this one. The dice are sealed before you move and verifiable after, so what the review measures is you.