This article originally appeared in the July 2001 issue of GammOnLine.
Thank you to Kit Woolsey for his kind permission to reproduce it here.

Dice Counting, an Alternative to Pip Counting

By Grant and Jackie Hoffman
If you are a mathematical genius and do Pip Counts of incredibly complex positions in your mind in less than five seconds, you are very, lucky because I can't. So I have devised a method for doing Pip Counts that is simple, fast and reliable, and that the majority of people can do.

Pip Counting is important (read essential), but unfortunately people find it too hard, so they just don't. When playing a long session of backgammon players either stop doing it or start making mistakes. Another problem is that it is not always obvious a Pip Count is called for when playing a particular move.

My breakthrough for Pip Counting came when I realised that in the majority of times, all you need to know is whether you are ahead of your opponent or behind and by how much. Kit Woolsey corroborates this in his article "Backgammon Mathematics".

The limiting factor of all the existing Pip Count methods I have seen is that you have to look at the board. Don't look at the board as a major source of information look at the dice. That's why I call my method Dice Counting.

Your opponent starts with the dice throw of 4:1. She is now five points ahead of you ( 4 + 1 = 5 ). That's not exactly going to stretch most people's mathematical abilities. You then throw 6:6. Your Opponent was 5 points ahead of you, but you have now just thrown 24 points ( 6 * 4 = 24 ) so you are now 19 points ahead of her. Every throw you adjust the difference by adding or subtracting the playable total of the dice thrown. I say playable total because if you throw 6:1 and all your 6's are blocked (or you have 2 checkers on the bar and only your opponent's 1 point is open) then you can only play the 1 so you only adjust the Dice Count by 1. A Dice Count of zero indicates you and your opponent are exactly equal.

If the game has no contact this is all you need to do. However, very few games have no contact so what do we do if a checker is hit? Firstly, we adjust the difference by the value of the dice thrown. Then we adjust for the value of the hit. There are two ways to do this :-

1. Subtract from 25. If a blot is hit, it is worth 25 points, which is 24 points plus the bar. We adjust the difference by 25 minus the value of the point that checker was on (from your opponent's point of view if it was her turn or your point of view if it was your turn). For example, your opponent starts her game with 4:1 and slots her 5 point. The Dice Count indicates that she is five points ahead of you. You then throw 4:3 ( 4 + 3 = 7 ), so now you are 2 points ahead of her. But because you hit her blot you also have to add 25 - 5 = 20 to the Dice Count. The 25 in this equation is the value of being off the board. The 5 is the point from her point of view her checker was on. Therefore you are now 22 points ahead of him / her.

2. Visual Inspection. If for example we hit our opponent's checker she slotted on her 5 point (with an opening of 2:1 say) then we are trying to adjust our total by the number of points she has lost. Her 5 point is our 20 point so we adjust the Dice Count by 20 points. For example, your opponent starts her game with 4:1 and slots her 5 point. The Dice Count indicates that she is five points ahead of you. You then throw 4:3 ( 4 + 3 = 7 ), so now you are 2 points ahead of her. But because you hit her blot you also have to add 20 (her 5 point = our 20 point) to the Dice Count. Therefore you are now 22 points ahead of her.

The major problem people see with this method is that you have to do the arithmetic on every throw. The arithmetic is easy, and having to do it on every throw is this method's strength. Knowing that Pip Count on every move is an advantage, not a problem because so many key decisions (e.g. should I build this prime, should I play a holding game and from which point, should I pay now or pay later) are dependent or partially dependent on the Pip Count. By always knowing, it you have an advantage over your opponent.

I only stop doing the Dice Count when both players are doing a bear off with no further contact possible. At that point I believe counting the number of rolls left is better.

It takes a little practice at first. If you lose the Dice Count total, start again next game and don't worry about it. It will suddenly click. It's like tying your shoelaces. The first time you did it you really had to concentrate but after a short time you can do it without much thought.

Editor's note:

I have tried the counting method suggested here. It does work, and it is feasible. Things can get a bit hectic when there is a lot of blot-hitting, but it is still fairly easy to keep track of what is going on if you know the points on the board instinctively and can add and subtract mentally without any effort. And it is nice to know all the time what the relative pip count is. Not only will you no longer have to stop off to take a pip count, but you will always know where you stand in the race which will be helpful for many play decisions.

I found two practical problems with the approach. First off all, unless you can keep the count instinctively it cuts into your rythem. If you like to play a fast game of backgammon, as I do, keeping the running count slows you up at times when there is a quick exchange of blot hits.

Secondly, keeping the count does require a mental effort. Backgammon requires a lot of thinking, and the extra strain of all the addition and subtraction may cause you to lose focus and fail to see an important concept which makes a big difference in your play. Unless you can accurately keep the count in the back of your mind without conscious effort, the cost of this mental strain is likely to be too great.

I would recommend to readers that they give this a try if only to get a feel for how keeping the running count works. Some may be able to do it without any other loss, and for them it will prove advantageous. For myself, I prefer to rely on my gut feel for most positions, and when I really need a pip count I just have to make to effort to get the count right.

Kit Woolsey

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