Let’s look at how we should use it in straightforward racing games. Many of our games will end in a race, with no hitting possible and gammons out of the question, so it is important to know how to handle the cube, or we will give away large amounts of our precious equity.
To make our decisions in races, other than the roll races that we looked at last lesson, we need to have a method of comparing how we stand in the race.
In the roll races, even though the positions were even, the player on roll had a tremendous advantage, enough to cash in the very short versions and give a strong double in the others. Being on roll is an advantage in itself, but as the race gets longer, that advantage is diluted and we need to lead in the race in order to consider doubling.
We need to compare the pip counts. These are just the numbers of pips needed by either side to bring all their men home and bear them off. To be strictly accurate, it is the minimum number, because in the later stages of the race we will usually waste some pips in the bear off, but we can safely ignore that effect for the moment and talk about it later.
Let’s take a look at a simple medium length race.
Red is on roll and leads by 8 pips, 100 to 108. In online play, your client will display this number for you if asked and although it is clearly an artificial aid, it is accepted that all players are allowed to have the pipcount displayed for them. When you have to play in real life, this is of course not available and you will have to learn how to count the pips for both sides, in your head and then compare the two. This is one of the vital skills that you will need to master if you are going to be a good technical player, although there are people who find this very difficult yet still manage to play at the top level. They are few and far between, but they do exist. All one can say is that they would be even stronger if they could pipcount, because they have to guess in situations where one pip more or less can influence the cube decision.
Anyway, is this enough of an advantage to offer a double? We can’t know without comparing the two sides. One way of doing it is the percentage method, where we compare the size of the lead with the length of the race for the leader. Here, the lead is eight pips and the leader needs 100 pips. 8/100 is 8% and by an amazing coincidence, this is exactly what is needed to offer an initial double in a pip race. 9% is considered to be enough for a redouble and the trailer can take if the advantage doesn’t exceed 12%. The drawback to this method is that it is very easy to work out when the race is exactly 100 pips long, but of course considerably trickier when the numbers involved are more awkward. (Again, in online play, it is of course very easy to just use a calculator. Nobody will ever know, but it is cheating. Don’t do it. Take pride in playing fairly. Don’t offer the excuse that “everybody else is probably doing it”, as one wellknown champion did when caught using a computer program to assist him online. They aren’t, but even if they are, two wrongs don’t make a right.)
Fortunately, there is a method that will give an equally accurate result, developed by the American expert Walter Trice. You can find it in his superb book “Backgammon Boot Camp”, which I take great pleasure in recommending to you. The method works like this.
He divides races into two types, those that are more than 62 pips long and those that are 62 or fewer. Let’s look at the longer ones first. He has a formula that is quite simple to use and from it we can derive the trailer’s minimum take point. What you need to do is divide the leader’s pipcount by 10, add 2 and discard any odd fractions of a pip. The number that you get will be the maximum difference between the two sides at which the trailer can still take. This is technically known as the “point of last take”. Look at position two:
Red has a pip count of 76. 10% of this is 7.6 and then add 2 pips making it 9.6 and discard the odd 0.6, so that the answer is 9. For a race of this length, White can still take if she is 9 pips down, which in fact she is here. From the point of last take, we can derive the leader’s double and redouble points. Two pips less than this and he can redouble, three and he can offer an initial double. In this position, Red could redouble if White’s pip count was 83 and offer an initial double if she was on 82. I find this method easier to use than the 8, 9 & 12 % method.
It is worth noting here that many would be put off taking as White, because she still has six checkers to bring home, while Red has only three. This is usually unimportant and can be ignored. This position also nicely demonstrates the value of owning the cube, which we talked about last lesson. Cubeless, White wins about 21.7% of the time, but she still just has a take because of her potential redoubles later.
For races of 62 pips or fewer, Walter uses a different formula. You need to subtract 5 from the leader’s pipcount, divide by 7 and discard any odd fraction, to give you the trailer’s point of last take. Look at position three.
Red has a pipcount of 56. Subtract 5 to get 51 and divide by 7, which gives you 7.28. Round down to 7 and that is White’s point of last take. She can take with a pipcount of 63. Again, we can use this to get Red’s doubling points; Red could redouble if White’s count was 61 and offer a double from the middle if it was 60. How simple is that?
Of course these methods are a simplification, because they ignore other factors that may influence the result, such as the tendency to waste pips at the end of a race, due to gaps or stacks or an excess of checkers on the lower points. In each of these positions, I have constructed the board so that both players have a similar type of layout and are likely to have about the same amount of wastage. Generally speaking, wastage is not very important in longer races where there are several checkers still to come home, because intelligent play will fill in the gaps, avoid stacking a lot of checkers on one point (always bad) and avoid playing too many checkers deep into the board.
As the race gets shorter, the opportunities to smooth out the position are fewer and the flaws that do exist more important, so we will need to look at ways of finetuning the pipcounts to allow for wastage in the shorter races. For now, learn to use these formulae to control your cube decisions in races until they are second nature. Practice makes perfect, so by yourself or with a partner, set up your board in the position shown below, which is about as equal as you can get and start to play. Take turns to play the Red side, so that you get as much practice in taking (or passing) as in doubling. A reminder that the home boards are on the left in this diagram! It wouldn’t be possible for this position to arise in real life.
Make yourself do the calculation every roll, until it becomes second nature. At first, you may find it helpful to have the formulae written out for easy referral and in fact in the beginning it doesn’t even matter if you use pencil and paper to work them out. The object is to instill in your brain the idea that this part of the game is just a routine that has to be gone through. The Intermediate and Advanced players, who botch these standard positions, do so because they won’t put in the effort. Put it in, it isn’t especially hard and it is essential.
So, to recap, for races longer than 62 pips, divide the leader’s pipcount by 10, add 2 pips, lop off the odd fraction and the resulting number added to the leader’s pipcount gives you the trailer’s point of last take. Two pips less than this is the leader’s redouble point and three less is his mark for an initial double. For 62 pips or less, subtract 5, divide by 7 and leave off any fraction, to get the trailer’s point of last take as before. The doubling points are derived from this in exactly the same way. It is more likely that with these shorter races, wastage may be a factor, but ignore that for now and we will look at that another day, when you have this procedure learned perfectly.
Now let’s have a look at our next chart of responses to the opening roll. This one covers all the possible replies to an opponent’s 64, played 8/2, 6/2. This play, once derided as a beginner play, is now very popular, so you need to know how to react to it. The old masters didn’t like it, because it plays two checkers very deep into the board and more or less commits you to a running or a blitzing game. However, rolling a very large number to start does make a running game advantageous, while making the 2pt does have a very subtle upside. It prevents your opponent from splitting to his 23pt with ones in the modern manner. In West London it is known as the Geoff point, in tribute to the visionary Geoff Oliver who championed this play long before the computers revealed its strength.
Here is the chart:
Responses to 64, played 8/2, 6/2 
Roll 
Money play 
DMP 
GammonGo 
GammonSave 
66 
24/18(2), 13/7(2) 
24/18(2), 13/7(2) 
24/18(2), 13/7(2) 
24/18(2), 13/7(2) 
65 
24/13 
24/13 
24/18, 13/8 
24/13 
64 
8/2, 6/2 
8/2, 6/2 
8/2, 6/2 
8/2, 6/2 
63 
24/15 
24/18, 13/10 
24/18, 13/10 
13/4 
62 
24/18, 13/11 
24/18, 13/11 
24/18, 13/11 
13/5 
61 
13/7, 8/7 
13/7, 8/7 
13/7, 8/7 
13/7, 8/7 
55 
13/3(2) 
13/3(2) 
13/3(2) 
13/3(2) 
54 
24/20, 13/8 
13/8, 13/9 
13/8, 13/9 
13/8, 13/9 
53 
8/3, 6/3 
8/3, 6/3 
8/3, 6/3 
8/3, 6/3 
52 
24/22, 13/8 
13/8, 13/11 
13/8, 13/11 
13/8, 13/11 
51 
13/8, 6/5 
13/8, 6/5 
13/8, 6/5 
13/8, 6/5 
44 
24/20(2), 13/9(2) 
24/20(2), 13/9(2) 
13/5(2) 
24/20(2), 13/9(2) 
43 
13/9, 13/10 
13/9, 13/10 
13/9, 13/10 
13/9, 13/10 
42 
8/4, 6/4 
8/4, 6/4 
8/4, 6/4 
8/4, 6/4 
41 
13/8 
13/9, 6/5 
13/9, 6/5 
13/8 
33 
24/21(2), 13/10(2) 
24/21(2), 6/3(2) 
8/5(2), 6/3(2) 
24/21(2), 13/10(2) 
32 
13/10, 13/11 
24/22, 13/10 
13/10, 13/11 
13/10, 13/11 
31 
8/5, 6/5 
8/5, 6/5 
8/5, 6/5 
8/5, 6/5 
22 
24/22(2), 6/4(2) 
13/11(2), 6/4(2) 
13/11(2), 6/4(2) 
24/22(2), 6/4(2) 
21 
13/11, 6/5 
13/11, 6/5 
13/11, 6/5 
13/10 
11 
8/7(2), 6/5(2) 
8/7(2), 6/5(2) 
8/7(2), 6/5(2) 
8/7(2), 6/5(2) 
Note: The moves suggested above are the #1 results of rollouts, however, sometimes other possible moves for a dice roll may have been listed as very close or as a reasonable alternate.
Last lesson for your homework, I asked you to make a chart showing the chances of entering two checkers from the bar into a home board with x points closed. This is much harder than for one checker, both to work out and to enter. How did you get on? It should look like this.

Rolls out of 36 that enter

Chances to enter 
1 
25/36 rolls enter both checkers 
69% 
2 
16/36 rolls enter both checkers 
44% 
3 
9/36 rolls enter both checkers 
25% 
4 
4/36 rolls enter both checkers 
11% 
5 
1/36 rolls rolls enter both checkers 
3% 
You can see from this how much harder life gets after a double hit. “Two on the bar is better by far” and aggressive players (in backgammon, aggressive = good) will take some risks to put two men on the roof.
Practise using the rule of 62 as I suggested for this lesson’s homework. Get it down pat and you will become an instant killer in your weekly chouette, as the rest of the team look to you for the correct cube action!
Next time we will look at some very common beginner mistakes, but until then, enjoy the game!
