How to quickly write down the scores, so it's clear to follow
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Lets run thought an example with players A and B, and lets say player B has won
the serve and decided to start from the right box.

The first scores would be written thus :-

 A  |  B
----+----
 0  |  
    |  1R
    |  
    |  
    |  
    |  

Note: player B's score is written on the line below player A's.

The way to read/interpret the score card is to read it from the bottom up.

So whichever players score is on the lower line - they are the one that is
serving.

So from the above, you can see that player B is the one serving, and they are
serving from the right (R), and the score is 1-0.

Now lets say player B wins the rally, the new entry is :-


 A  |  B
----+----
 0  |  
    |  1R
    |  2L
    |  
    |  
    |  

Again, reading from the bottom up, player B is serving, from the left (L), and
the score is 2-0.

Now lets say player A wins the rally and decided to start from the right box,
the new entry is :-

 A  |  B
----+----
 0  |  
    |  1R
    |  2L
 1R |  
    |  
    |  

Reading from the bottom up, now player A is serving, from the right (R), and
the score is 1-2.

So you go on like this, writing the new score of the player that won the last
rally on the line below the last entry.

This is a minimal amount of writing that is also very clear to read and follow,
even if you have to switch markers during a game.