The Race

Backgammon offers a great variety of strategies that can be applied in a number of situations. Still, many games end up in a race and there are a lot of players who enter a race at the earliest possibility. Only God knows what kind of kick they get out of it, one would think that a full-steam Blitz or priming game would offer a much more interesting game. Nevertheless, many games do end up in a race regardless whether you want to avoid it or not and since chances are that you’ll meet a lot of players on your favorite online backgammon site who just love an old-fashioned race, here it comes: how to play a Race.

In a traditional race the checkers have all cleared each other and the only goal both players have is to bring in all men to their own home boards for bearing them off. Before the doubling cube was invented a lot more games ended up in a (dull) race. There was no way to force your opponent to either gamble for more points or to resign and end the damned game that turned sour already at tossup.. The guy who invented the doubling cube should’ve got the Nobel prize for such a brilliant idea!

I guess you have already noticed that I don’t like races too much. You are rolling the dice, hoping for big numbers, waiting for the moment when you can double or sitting in cold sweat after a disastrous 2-1 roll. And to add to the misery, with today’s advanced computer processing capabilities I can sit here and write with full confidence that when your opponent offers the cube his pip count lead should not be more than 12,5% for a take because then you still have good mathematical odds for winning the game. At least that’s according to Lamford’s formula.

Elements of a race

Essentially a race is about two things:

• knowing when to double
• knowing when it is a pass or a take

In order for you to be able to determine those things you need to know:

• how to do a pip count (play online and you can forget about this)
• adjust the pip count for wastage

NOTE I - Keep in mind that there are several different formulas determining the correct moment for doubling, take, pass and crossovers, wastage and gaps. In this article we do offer a easy-to-understand overview for these main areas of a traditional non-contact race. If you are interested you can read more about cube handling in noncontact positions at Backgammon Galore.

NOTE II - It is important that you know the difference between the Race and Bear-off. In this article we deal with Race, i.e. the phase until the players have all their checkers on their home boards. In a later article we go through the elements of a Bear-off, which is the last stage of a game.

How to do a pip count?

Pip count is the most significant measure in backgammon to determine who is in the lead. Pip count means simply the number of total pips, or points, your checkers need to move before they are all born off. See the picture below how to do a pip count.

Picture 1. Pip count is
26+18+8+14+18+10+4+6 = 104

Wastage

There are four main things that cause wastage:

• Crossovers
• Gaps
• high stacks
• high stacks on low points

Crossovers

A backgammon board is made of four quadrants. Moving your checker from one quadrant to another is called a crossover. The most important crossover is the one when you move a checker over the bar to your home board, but moving a checker from your outer board to your own side of the board is also considered a crossover. Crossovers are shown in the illustrative picture below.

Picture 2. Calculate crossovers from one quadrant
to another. From quadrant 4 it takes 3 crossovers to

Crossovers are not very important elements in wastage and in early stages of a race with half or more of your checkers still outside your home board you can ignore them if you want to. They play a more important role in the final phases of a race.

Gaps

Say you have born in all checkers and you are ready for bearing them off. If you have a gap on your home board and you roll the number where the gap is, you will need to move checkers from above the gap to lower numbers. As a result you probably will be bearing off only one checker instead of too. Not a desirable situation in a tight race. That’s why before you get to bear off you need to try to fill gaps as much as possible when bearing in.

High stacks

High stacks mean lots of checkers on few points, which is bad distribution and results in gaps. Gaps bad. Avoid gaps. Avoid high stacks.

High stacks on low points

On first thought you might think that having your last 8 checkers on the 1 and 2-points is not too bad. Five checkers on the 1-point and three checkers on the 2-point will get your checkers off in four rolls. Pip count is also only 11. But imagine your opponent having the same pip count with one checker on the 2-point, one on the 4-point and one on the 5-point. That’s three checkers against your eight and a lot less rolls required to get those off the board.

Picture 3. Although both players’ pip count is 11,
White is in a much better position to play.

Here we are already a little more on the bear-off side of things than actual race and while the situation described above is quite an extreme one that doesn’t happen often, it hopefully delivers the message: when bearing in avoid stacking the checkers on a couple of points, even if they are low ones.

Adjusting pip count for wastage

Because of the above-mentioned elements you should not stare at the basic pip counts but allow for any possible wastage to determine the real race leader. While other formulas might work slightly better with low pip counts and others better with high pip counts, this gives you a good general rule.

For each player, start with the basic pip count and

• add 2 pips for each checker more than 1 on the one-point
• add 1 pip for each checker more than 1 on the two-point
• add 1 pip for each checker more than 3 on the three point
• add 1 pip for each empty space on points four, five, and six
• add 0.5 pips for each checker that has to make a crossover

Take a look at Picture 4 below. Black’s pip count is 62 but we add penalties:

• 1 pip for the second checker on his 2-point,
• 1 pip for the second checker on his 3-point and
• 2 x 0.5 pips, i.e. 1 pip for two crossoversTherefore Black’s adjusted pip count is 62 + 3 = 65.

White’s pip count is 52, but we add penalties:

• 2 x 2 pips, i.e. 4 pips for the two extra checkers on his 1-point,
• 1 pip for the extra checker on his 2-point,
• 2 x 1 pips, i.e. 2 pips for the extra checker on his 3-point,
• 1 pip for the empty 6-point
• 2 x 0.5 pips, i.e. 1 pip for two crossoversTherefore White’s pip-count is 52 + 9 = 61. In addition, because he is on the roll, his pip-count is increased by one-seventh (rounding down), i.e. 8 pips, giving him a final pip-count of 69. He now can determine to double or not.

When to double?

There are very simple formulas such as the one from Lamford stating that you should double when your pip count lead is 10% or more. Easy to remember, rather accurate and easy to calculate. However, there is an even easier one to remember and works just as well if not even better:

Increase your adjusted pip count by one-seventh (rounding down) and

• Double, if your pip count exceeds your opponent’s pip count by no more than 4.
• Redouble, if you pip count exceeds your opponent’s pip count by no more than 3. Redoubling means that you double when you already own the cube.

Note - increase your pip count by one-seventh only when you are on the roll!

In practice this means that if your adjusted pip count is e.g. 69 and your opponent’s 65 like in Picture 4 below and you are on the roll you should double. If you already own the cube, you shouldn’t double as the pip count difference is 4. See picture below.

Picture 4. White is on the roll, his adjusted
pip-count is no more than 4 higher than Black’s
- it’s a double.

When to take or pass?

In the same way you determine when to double you can just as easily see if you can take the cube or not:

• Take, if your opponent’s pip count exceeds yours by 2 or more. Otherwise, pass.

Other experts use similar calculations and work with percentages, but we feel that in the heat of the game it is easier to use these absolute values. Therefore, in Picture 4 the correct play would be for White to double and Black to take.

Summary

A backgammon race will require you to be able to judge accurately the situation and to know what to do with the cube in every moment. In a race it all comes down to probabilities and simple rules have been created to help players better judge those probabilities. It is important to keep in mind, though, that the rules are not waterproof but limit the statistical errors.

Perhaps that’s where the fascination for a race comes from. There’s no room for strategies, it requires quick thinking but at the same time involves a fair element of gambling.

Pip count and cube action summary

For each player, start with the basic pip count and

• add 2 pips for each checker more than 1 on the one-point
• add 1 pip for each checker more than 1 on the two-point
• add 1 pip for each checker more than 3 on the three point
• add 1 pip for each empty space on points four, five, and six
• add 0.5 pips for each checker that has to make a crossover

Increase your adjusted pip count by one-seventh (rounding down) and

• Double, if your pip count exceeds your opponent’s pip count by no more than 4.
• Redouble, if you pip count exceeds your opponent’s pip count by no more than 3. Redoubling means that you double when you already own the cube.
• Take, if your opponent’s pip count exceeds yours by 2 or more. Otherwise, pass.