Saving a gammon: the race to get one checker off

Your opponent has started bearing off while you still have all fifteen checkers on the board. You have been keeping checkers back for a hit, and moving them now can feel like giving up on the game.

That move may still be worth considering, because backgammon does not treat every loss in the same way. If the hit never comes, waiting can turn a single loss into a gammon or a backgammon. You need to compare what each plan leaves of your comeback with what it might cost if you lose.

Why one checker off changes the score

With the stake fixed at 1, an ordinary loss costs one point. A gammon costs two: your opponent has borne off all fifteen checkers before you have borne off any. If you also still have a checker on the bar or in the opponent’s home board when they finish, the loss is a backgammon and costs three.

Your first checker off rules out both the gammon and the backgammon. That remains true even if another checker gets hit later. You may still lose, but that loss will be worth the ordinary stake.

There is a condition that is easy to overlook: before bearing off that first checker, you must get all your remaining checkers into your own home board. Having fourteen there while the last one waits for a hit does not let you take one off. Your opponent can be racing to finish while you are still trying to reach the point where you can begin.

Leaving the opponent’s home board is a different milestone. If no checker is off yet, you can still lose a gammon; and a later hit could put you back at risk of a backgammon.

Compare three ways to play the same double

In the original position below, you play Ivory towards point 1 with a 4–4. Red has two checkers off and must bring the pair on 17 home before continuing to bear off. You still have all fifteen on the board, with anchors on 20 and 24. Those pairs can provide a chance to hit, but they also have a long way to travel before you can bear off.

We tried several positions before settling on this one. In some, the move that won most often also lost the fewest points, so there was no difficult choice to explain. Here, keeping a checker back really does buy extra chances to win, and you can see what those chances cost.

Try the three complete plays before opening the simulation results. Look at which checkers remain behind, what changes in your home board and how much work is left before your first checker can come off.

What would you play with this double?

Choose a play, then move the checkers one step at a time.

You play Ivory toward point 1. Red moves toward 24. Point numbers are from Ivory’s side.

Read the position

Ivory, point: number of checkers. 2: 2, 3: 2, 4: 3, 6: 2, 8: 1, 9: 1, 20: 2, 24: 2. Red: 17: 2, 19: 3, 21: 3, 22: 3, 23: 2. On the bar: Ivory 0, Red 0. Borne off: Ivory 0, Red 2.

Reveal the simulation results

GNU Backgammon estimates from 12,960 simulated games per play. The stake stays at 1, with no doubling; singles count 1, gammons 2 and backgammons 3.

1. Keep a checker on 20

One checker travels from 20 to 4. The other stays on 20, with the pair on 24 still behind it, leaving another possible chance to hit.

Win

16.2%

Single loss

47.3%

Gammon loss

33.3%

Backgammon loss

3.2%

Average points lost per game1.07

20 → 16 · 16 → 12 · 12 → 8 · 8 → 4

Position after this play

Ivory, point: number of checkers. 2: 2, 3: 2, 4: 4, 6: 2, 8: 1, 9: 1, 20: 1, 24: 2. Red: 17: 2, 19: 3, 21: 3, 22: 3, 23: 2. On the bar: Ivory 0, Red 0. Borne off: Ivory 0, Red 2.

2. Move both checkers from 20

Both checkers on 20 move to 12. The pair on 24 stays behind for a later hit, and the home board is unchanged.

Win

15.1%

Single loss

56.7%

Gammon loss

26.8%

Backgammon loss

1.4%

Average points lost per game1.00

Lowest average loss of these three

20 → 16 · 16 → 12 · 20 → 16 · 16 → 12

Position after this play

Ivory, point: number of checkers. 2: 2, 3: 2, 4: 3, 6: 2, 8: 1, 9: 1, 12: 2, 24: 2. Red: 17: 2, 19: 3, 21: 3, 22: 3, 23: 2. On the bar: Ivory 0, Red 0. Borne off: Ivory 0, Red 2.

3. Move the furthest pair forward

The pair on 24 moves to 16, outside Red’s home board. The pair on 20 stays in place, so you still have an anchor.

Win

8.6%

Single loss

58.1%

Gammon loss

33.2%

Backgammon loss

0.1%

Average points lost per game1.16

24 → 20 · 20 → 16 · 24 → 20 · 20 → 16

Position after this play

Ivory, point: number of checkers. 2: 2, 3: 2, 4: 3, 6: 2, 8: 1, 9: 1, 16: 2, 20: 2. Red: 17: 2, 19: 3, 21: 3, 22: 3, 23: 2. On the bar: Ivory 0, Red 0. Borne off: Ivory 0, Red 2.

The average includes wins as well as losses. Lower is better for Ivory. Percentages are rounded; gammon losses exclude backgammons.

How we calculated the average

A win adds 1 point here, because Red has already borne off checkers. A single loss subtracts 1, a gammon 2 and a backgammon 3. We weight each result by its estimated chance, then show the average net loss.

Among these three plays, moving both checkers from 20 to 12 gives the lowest average loss. It wins a little less often than leaving a checker on 20, but loses fewer gammons and backgammons. The extra comeback chance from keeping that checker back does not pay for the extra costly losses.

Moving the furthest pair, from 24 to 16, sharply reduces backgammon losses. Yet it also gives up more winning chances and leaves more gammon losses than moving the pair from 20. In this example, it costs more points on average than either of the other choices. Getting the last checkers out of Red’s home board is not the same as getting your first checker off.

All three plays use the full sixteen points on the dice and leave the same pip count. They differ in which chances to hit they retain and how the remaining dice will play. These are estimates for this position, not a rule to keep or abandon a particular anchor in every game.

What is an extra chance to win worth?

For a moment, keep the stake at 1 and set backgammons aside. Turning a single loss into a win improves your result from −1 to +1: a two-point difference. Turning a gammon loss into a single loss improves it from −2 to −1: a one-point difference.

Across 100 games, one extra ordinary win is therefore worth as much as saving two extra gammons, if nothing else changes. Giving up winning chances can be sensible, but the gammon savings need to justify it. Backgammons add another possible cost, so we include them in the comparison above.

Analysts use equity to compare the value of plays. In this fixed-stake example, it is the average number of points won or lost. The move that wins most often and the one that loses the fewest points on average need not be the same. Bill Robertie explains this balance in “Saving a Weak Back Game”; the principle is established backgammon strategy.

How do you judge this without guessing percentages?

It is hard to look at a board and distinguish a 4% winning chance from an 8% chance. During a game, start with questions you can answer more concretely:

• Where could a comeback come from? If you need a hit, ask where the opponent might leave a checker exposed and whether your home board could hold it afterwards. Keeping checkers back has less value if a hit is unlikely to lead to a win.
• What must happen before your first checker can come off? Follow the route of every checker outside your home board. A good total on the dice is not enough if several checkers each need a separate move to get home.
• How much time might Red leave you? Compare the work left for your first checker off with the work left for Red’s last. In a pure race, if only a large double could save the gammon, arrange your checkers so that the double would actually help.

Bob Floyd develops this comparison between the players’ remaining turns in “Advanced Gammon Avoidance”. It also explains why a pip count is useful without answering every endgame question: the distribution of the checkers determines how efficiently the next dice can be used.

Running is not always the best way to save a gammon. If you cannot get home in time, a hit may be your only way to delay the opponent. When reviewing with the coach in CUBE Backgammon, look for the reason behind the move: is it keeping a useful shot, bringing the last checkers home, or accepting fewer wins in exchange for cheaper losses?

Check whether the extra points matter

At 6–6 in a match to seven, a single loss already ends the match. Avoiding a gammon cannot save you; your remaining chance to win is what matters. At a score where losing one point keeps you in the match but losing two ends it, the same gammon risk can be much more expensive.

Our article on the same position at different match scores shows this change of priorities on another board. The cube changes how many points are at stake, while the game plan determines how you hope to win or limit the loss.

The next time a game looks lost, check whether you have borne off a checker yet. If you have not, your next move can still make a substantial difference to the score.