Strategy › The 13-count
The 13-count: a faster way to count the race
Counting the race is the single most useful number in backgammon, and the slowest to work out over the board. The 13-count is a shortcut that trades a long sum for one multiplication. It was written up by Ash Dalvi, and once it clicks you will count positions in seconds that used to take a minute.
What the pip count tells you
Your pip count is the total distance, measured in points, that all fifteen of your checkers still have to travel to come home and bear off. At the start of the game both players sit on exactly 167. As checkers move, the numbers drift apart, and the gap between them is the race. The player with the lower count is in front; the size of the gap is what most cube decisions hinge on.
The trouble is that working the count out by adding every checker's distance is slow and easy to fumble, especially in the middle of a game with checkers scattered across all four quadrants. A point dropped here or a five added twice there, and a decision built on the number is wrong. Players have devised shortcuts for decades to make the arithmetic faster and safer.
Where the 13-count comes from
The 13-count is one such shortcut, published by Ashutosh "Ash" Dalvi on Backgammon Galore in 2011. He is candid about why it exists: by his own account he is not quick at mental arithmetic, so he looked for something easier. It is a personal method rather than a piece of received wisdom, and it is fair to treat it that way — a clever, well-documented tool from one player, not a rule handed down from the textbooks. It earns its place here because it works.
Its insight is simple. Both players open with five checkers on the 13-point, the midpoint, and checkers keep gathering there all game. Dalvi noticed that almost every count he did ended in a multiplication by 13 because of those midpoint checkers. So rather than fight that, he built the whole method around it: stop adding, start asking "how many 13s do I have?"
The core idea
You group your checkers into sets that are each worth thirteen pips, count the sets, multiply by 13 using a memorised thirteen-times table, then nudge the total with a few small corrections. The multiplication does the heavy lifting that a long column of addition used to.
In the outfield, four patterns cover almost everything:
- A single checker on your 13-point is one set of thirteen. Five of them, as in the opening, are five sets — sixty-five pips — read at a glance.
- Two checkers placed an equal distance either side of your bar point average to the 7 and total thirteen. The everyday case is a checker on the 8-point and one on the 6-point: eight plus six, less one, is thirteen.
- A checker sitting deep in the opponent's home board, or on the bar, is worth close to two sets of thirteen, with a small stated correction.
- Two checkers on "opposite" points can be paired off as two thirteens plus a single pip, another way to swallow awkward numbers into the same framework.
Tally the sets, multiply, correct. The second part of Dalvi's method extends the same thinking to the home board, either through a short list of memorised corrections — two on the 6-point is one set, correction minus one, and so on — or by learning to recognise common clumps that come to a clean thirteen with no correction at all.
A worked example: the opening position
Run the method on the starting layout and you should find thirteen sets of thirteen. Thirteen times thirteen is 169, and the corrections bring it down to 167 — the count every game begins on. That is the neatest possible check: if a method you are learning lands on the known opening figure, you are applying it correctly. From there, every checker you move changes the count by the size of the die, and you can keep a running total rather than recounting from scratch.
When to reach for it
A pip count earns its keep in two moments. The first is the decision to race or not: when you are clearly ahead in the count, you generally want to run for home and avoid contact; when you are behind, you hold an anchor and play for a hit. The second is the doubling cube, where the lead or deficit in the race is the main number feeding the decision. A rough rule for pure races is that a lead of roughly eight to ten per cent of the count is meaningful — and you cannot tell a 10 per cent lead from a 4 per cent one without counting.
It is worth saying that you do not always need an exact figure. Dalvi makes the point himself: often you only want to know who is ahead and roughly by how much, and an approximate count answers that in a second. He also recommends staying flexible — if a position lends itself to a different counting trick, use it, or combine methods. The 13-count is a tool, not a religion.
How it fits with the rest of your game
Counting is the quiet skill underneath the loud ones. It tells you when a bear-off is safe to start and when to play it cautiously, when a double is justified, and when an opponent's double should be passed. If you are still learning the moves, start with the rules and the board first; the count means more once the basic flow of a game is familiar. Either way, the fastest way to build the habit is to count a position or two every time you play a game, even when the decision is obvious.
Sources
Ash Dalvi's original write-up is published in two parts on Backgammon Galore, which remains the most complete source for the method.
References
Common questions
What is a pip count in backgammon?
It is the total number of points all fifteen of your checkers must still travel to reach home and bear off. Both players start level on 167. Whoever has the lower pip count is ahead in the race.
What is the 13-count?
A method for counting the race quickly, written up by Ash Dalvi in 2011. Instead of adding many separate numbers, you group your checkers into sets worth thirteen pips, multiply the number of sets by 13, and apply a few small corrections.
Why 13 and not some other number?
Because each player starts with five checkers on the 13-point, the midpoint, and checkers gather there throughout the game. Dalvi noticed that almost every count ends up multiplying something by 13, so he built the whole method around that fact.
Who is Ash Dalvi?
Ashutosh 'Ash' Dalvi is a club and online player who published the 13-count on Backgammon Galore in 2011. By his own account he devised it because he is not quick at mental arithmetic and wanted something easier to do over the board.
Is the 13-count an official or widely taught method?
No. It is one player's personal shortcut, well documented but niche. It sits alongside other counting systems such as Jack Kissane's cluster count rather than being a universally taught standard. It is taught here because it is genuinely useful, not because it is orthodoxy.
How do I count a checker on the 13-point?
A single checker on your 13-point is worth exactly one set of thirteen. Five checkers there, as in the opening, are five sets — sixty-five pips — counted almost at a glance.
How do two checkers either side of the bar point make a 13?
If two checkers sit an equal distance on each side of your 7-point, they average to the bar point and total thirteen between them. A checker on the 8-point and one on the 6-point is the classic example: 8 plus 6 minus 1 is 13.
Does the 13-count include checkers in the home board?
Yes. The second part of the method folds home-board checkers into the same framework, either through a short list of memorised corrections or by recognising common clumps that equal a set of thirteen exactly.
What does the opening position count to with this method?
Thirteen sets, which gives 169, corrected down to the true 167. Landing on the known starting figure is a useful check that you have applied the method correctly.
When is the pip count most useful?
In two situations: deciding whether to keep racing or switch to a holding game, and judging doubling-cube decisions, where the size of your lead or deficit is the main input.
Do I always need an exact count?
No. Often you only need to know who is ahead and roughly by how much. Dalvi himself notes that an approximate count is enough for many decisions, and that you can switch or combine methods when the position suits another approach better.
How big a lead matters in a race?
As a rough guide, a lead of around eight to ten per cent of the pip count is significant in a pure race, and that is the kind of margin a cube decision turns on. Counting accurately is what lets you tell a 10 per cent lead from a 4 per cent one.
Is the 13-count better than just adding the pips up?
It is faster for most people once learned, because multiplication by a memorised 13-times table replaces a long chain of addition. Whether it beats another shortcut for you depends on how your mind handles numbers.
Can I use the 13-count in a real tournament?
Yes. Any legitimate counting method is allowed; you are simply doing arithmetic in your head. The only thing that matters is that you arrive at the right number in reasonable time.
Where can I read Ash Dalvi's original explanation?
It is published in two parts on Backgammon Galore (bkgm.com), which remains the most complete primary source for the method and is linked at the foot of this page.