Backgammon is essentially a race … being able to determine your relative position in this race is often essential

Magriel, "Bible of Backgammon", p.126

Why Count Pips?

An ability to swiftly count pips confers the master with a powerful advantage over the uninitiated in many common situations. The pip count is an essential factor in many cube decisions and can aid in determining the appropriate choice of strategy in mid-game holding positions

Magriel (Magriel, "Bible of Backgammon", p.132) provides a guideline for offering or accepting the cube in a racing situation: in a long race (about 100 pips) a player should be a minimum of 10 pips in the lead to offer a double, or a maximum of 13 pips behind to accept a double

Determining your position in this race is achieved by calculating the difference between the number of pips (units of distance or spaces on the board your men travel) that you need to get all your checkers home and off the board, and the number the opponent needs. The result is the pip count and is calculated through the technique known as pip counting

At the start of any game the arrangement of the checkers is such that each player will need to move 167 pips to complete their bear off. This number will decrease as the players move checkers around the board, or may increase when their checkers are hit and sent to the bar. At the start of the game each player has a pip count of 167, hence the difference between the sums is zero. Here is the starting position:

Games start with a pip count of 167 to 167

  2 × two checkers on the 24 point :  =  48
  5 × five checkers on the 13 point:  =  65
  3 × three checkers on the 8 point:  =  24
  5 × five checkers on the 6 point :  =  30
  ------------------------------------- ----
                                      = 167

In the following example at the closing stage of a game, Red has two checkers on the 6 point and White has one checker on the 6 point and two checkers on the 2 point. Red requires 12 pips to completely bear off (6 × 2 = 12), while White requires 10 pips (6 × 1) + (2 × 2) = 10. Therefore the pip count informs us that Red is 2 pips behind in the race

Red’s pip count is 12
White’s pip count is 10

The Quadrant Crossover Technique

In essence, it requires only four simple skills:

  • extensive familiarity with the multiplication tables for the number 6 (for example multiples of 6 up to the multiplier of 25)
  • the ability to visualize moving a checker six points
  • the ability to remember a single two or three-figure number while undertaking the previous tasks
  • The full technique can be quickly learnt by breaking down the process into easily mastered stages of gradually increasing difficulty. Furthermore, mastery of each stage is very useful in itself by giving the beginner progressively more detailed information of their race standing

    Stage One

    Initially, ignore all the checkers of both players that have made it home. Observe the number and position of the remaining checkers you have on the board. Count the number of crossovers required to bring each checker into the home board

    A crossover is the move of a checker of six spaces (or pips) from one quadrant of the board to the next quadrant

    It is important to note here that to simplify this tutorial, in the Example Position below, each opponent has cleared his checkers from his adversary’s home board. However, in other situations there will definitely be times that you will have to calculate the crossovers for checkers that have yet to escape their opponents’ home boards

    Example position, numbered from Red’s perspective

    In the example position above, White has managed to escape Red’s menacing prime. It is a racing position as there can be no further contact between the opponents’ checkers in this game. Red has two checkers on the seven point, four on the eight point and one checker on the nine point. Therefore, Red needs 7 crossovers to bring all her checkers into the home board

    Same example position, numbered from White’s perspective

    The view from White’s side of the board (shown above) shows that 8 crossovers are needed to bring all her checkers home. Two crossovers for the checker on her 14 point, two more crossovers for each of the checkers on White’s 13 point, plus one crossover for the checker on White’s 12 and another for the checker on White’s 7 point. Therefore we can deduce that Red is definitely leading the race by 1 crossover

    Since a crossover corresponds to a move of six pips we can deduce from this exercise that Red leads by one crossover or roughly 6 pips

    Stage Two

    Now that we understand what a crossover is and how to calculate how many we need for all of our checkers to reach our homeboard, we need to visualize and remember where they land to be able to arrive at the exact pipcount

    However, before going to that step in the tutorial, sometimes just knowing how many crossovers you are ahead or behind allows you to clearly see your advantage or disadvantage especially in doubling situations

    To facilitate an improvement in the accuracy of this estimation, we must mentally move the checkers to see where they land. For example, if we pretend we are playing as Red in the Example Position below, we must consider that the white checker on the 13 point (White’s 12) will land on White’s 6 point and White will have three checkers to bear off from the 6 point

    On the other hand, if we now visualize where Red’s checkers will land after Red does the crossovers and we compare, Red has only two checkers on the 6 point This means that Red is in the lead by about 12 pips six pips for the extra crossover and about six for the extra checker on the 6 point

    Example position, numbered from Red’s perspective

    Please note that these calculations are specific to this particular Example Position. In other scenarios, it will be plain to see that after the crossovers, the player with less checkers on his 6 and 5 points has the advantage

    Stage Three

    Beginners who have gained familiarity with the previous stages are now ready to calculate the exact pip count by including all the checkers on the board. Start with your own checkers. Calculate the number of crossovers and include the checkers on the 6 point. Multiply by six to get the subtotal then add the remaining checkers from the 5 point onwards to obtain a total count

    Don’t forget to include the checkers from the crossovers when calculating the number of checkers on each home board point! Remember your total, and then repeat the exercise for your opponent’s checkers. The difference between these two totals represents your exact standing in the race

    Calculation for Red:

    Example position, numbered from Red’s perspective

        Crossovers : 7  × 6          = 42    
        Six point  : 2  × 6          = 12
        Five point : 2  × 5          = 10
        Four point : 0  × 4          =  0
        Three point: 3' × 3          =  9
        Two point  : 6' × 2          = 12
        One point  : 2' × 1          =  2
                                     = 87
    Note: The asterisks indicate points where outer board checkers have landed from the crossovers and have been added to the checkers already there

    Calculation for White:

    Same example position, numbered from White’s perspective

        Crossovers : 2 × 6 + 3 × 12 = 48
        Six point  : 3  × 6         = 18
        Five point : 2  × 5         = 10
        Four point : 2  × 4         =  8
        Three point: 2  × 3         =  6
        Two point  : 2' × 2         =  4
        One point  : 4' × 1         =  4
                                    = 98
    Note: The asterisks indicate points where outer board checkers have landed from the crossovers and have been added to the checkers already there

    From this full pip count we have verified that Red leads White by 11 pips, (98 − 87 = 11)

    As previously mentioned, a player who can accurately calculate the pip count is in a position of power. In the example position, it is Red’s turn to roll the dice. What is the correct doubling strategy for both players? Using Magriel’s criteria (see above), this is a long race situation (approximately 100 pips) Therefore, this is a clear double for Red and an acceptable take for White.

    Tips on Training

    In real live situations the pip count process will need to be done quickly. In many tournaments clock rules may apply. In club or social settings you may feel that you are under pressure to count quickly even though your opponents are not casting withering glances at you. Frequent practice will enable you to rapidly and accurately calculate the pip count

    Remember that in some real world settings there may be added distractions from a cacophony of music and conversation. It would be useful to gain some experience by practicing under similar conditions. An effective method is to play some raucous music (Metallica are my favourite for training), at the same time turn up the volume on the TV. Voila an authentic caf /bar ambience