The one opening roll where strong players and computers have never fully settled. Three plays are defensible: 24/18 13/9, 8/2 6/2 making the 2-point, and 24/14 running.
24/18 13/9Still contested
The position after 24/18 13/9. The 18-point and 9-point are highlighted.
Why this play
24/18 13/9 is the balanced choice: escape one back checker to the edge and add a builder. It leaves two blots but both in indirect range.
8/2 6/2 makes a point and leaves nothing exposed. The objection is that the 2-point is deep and nearly useless for blocking, so you have spent a good roll on a bad point.
24/14 runs a single checker fourteen pips. Safe from direct shots from the back, but it abandons the second back checker entirely.
The honest answer is that the margins between these are inside the noise of most rollouts. If someone tells you one of them is definitively correct, they are overstating the evidence.
The numbers
Shot counts below are enumerated over all 36 rolls of two dice, assuming the intermediate points are open.
A blot on your 9-point sits 15 pips from your opponent's back checkers, which is 1 rolls out of 36, or 2.8%.
The mistake to avoid
The error is playing it thoughtlessly. This is the roll worth pausing on, and the roll where your choice should depend on the match score more than on habit.
How settled is this? Still contested. Treat confident advice about this roll with suspicion, including ours.
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.
What is the best play for an opening 6-4 in backgammon?
24/18 13/9. The one opening roll where strong players and computers have never fully settled. Three plays are defensible: 24/18 13/9, 8/2 6/2 making the 2-point, and 24/14 running.
Why not play something else with 6-4?
The error is playing it thoughtlessly. This is the roll worth pausing on, and the roll where your choice should depend on the match score more than on habit.