You finish your move and count the checkers left on their own. Leaving one feels manageable; leaving two feels careless.

To understand the risk, you also need to look at which rolls can reach those checkers.

Start with one exposed checker

In our first position, the ivory checker on point 16 is alone. That makes it a blot: one red checker landing there would send it to the bar.

There are two red checkers on point 10, six spaces behind it. A six can hit. Several combinations can get there too, including 5–1, 4–2 and double three. Counting all the legal possibilities gives 17 hitting rolls out of 36, about 47.2%.

Now give Ivory a 5–1. Move the checker from 16 to 11, and one checker from 3 to 2. That is a legal play, and it leaves two exposed checkers.

Look at who can hit them. Red needs a one to go from 10 to 11. The red checkers on point 1 also need a one to hit the new blot on point 2. Ivory’s six-point prime, the consecutive closed points from 3 to 8, blocks the longer routes.

The same number does two jobs

Both threats now depend on a one. There are 11 rolls containing at least one one, so there are 11 hitting rolls in total. We count 1–6 once even though Red could use its one to hit either checker.

Ivory has created another exposed checker, yet the chance that Red can hit at least one has fallen from 17 out of 36 to 11 out of 36, about 30.6%.

This overlap is called duplication. You try to make the opponent need the same numbers for different useful jobs.

Count the rolls, then change the position

Choose an arrangement, then a roll. Play through one legal hitting reply when a hit is possible. The red checkers move toward point 24.

17 of 36 rolls can hit at least one checker (47.2%).

Ivory has a blot on 16.

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Ivory moves toward 1; Red toward 24. All point numbers are shown from Ivory’s side.

Read the position

Ivory, point: number of checkers. 3: 3, 4: 2, 5: 2, 6: 2, 7: 2, 8: 2, 16: 1. Red: 1: 2, 10: 2, 19: 3, 20: 3, 21: 3, 23: 2. On the bar: Ivory 0, Red 0. Borne off: Ivory 1, Red 0.

Change one detail

In the example, choose “Two, different distances”. We have moved the red pair back from point 10 to point 9. Keep everything else in place.

Now a two hits the checker on 11, while a one still hits the checker on 2. More rolls have a useful number: 20 out of 36 allow a hit.

The two ivory blots haven’t moved at all. The chance of being hit changed because the opposing checkers moved.

There is still a price

Try double one in the matching-distances position: Red can hit both checkers, so the smaller set of dangerous rolls still includes a particularly costly one.

That is why the count is a starting point for a decision. It doesn’t measure the damage of each hit, the strength of either home board or the chances of winning the game. We are comparing the possibility of at least one hit on the next turn, not declaring a best move.

Next time you have to leave a checker exposed, look past the number of blots. Count the numbers the opponent needs, and notice where those numbers overlap.

Duplication is an established backgammon principle. We used Kit Woolsey’s article on duplication as a reference for the idea. The positions, wording and interactive comparison here were created for CUBE Backgammon.

How we checked the example

Each position contains 15 checkers per side, including Ivory’s one checker already borne off. We checked all 36 ordered rolls against complete legal plays, including blocked intermediate points, four moves for doubles and the rules requiring the maximum number of dice to be used. A roll counts when at least one complete legal play contains a hit. Red may prefer another play in an actual game. We also count rolls that allow two hits, rather than treating every hit as equally costly.