Board strength

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by

Orad Reshef

The most important concept to improve your checker play immediately is that of board strength. Simply put, the relative state of your and your opponent’s homeboards determines the strength of your position and guides much of checker play. Let’s discuss why in greater detail.

First, how do you distinguish a strong board from a weak board? A board is strong if it has many pure points made. It is weak if it has few points made, or if it has blots inside of it. Here are examples of strong boards:

As we progress through the positions, the boards get stronger: they are stronger as the points made are purer and as the number of points increases. A pure inner board has its points made in sequence: the 5-pt, then the 4-pt, etc.

It should be evident to anyone who’s played a few games of backgammon why either of these qualities would be desirable: if more points are made, you have fewer entering numbers from the bar (or, conversely, more dancing numbers); if the points are continuous, you have fewer escaping numbers to jump the prime once you’ve entered. (Consider having a checker on the ace point in the last position — only 6s can leave the home board!)

Having more dancing numbers is obviously better for us, but it might not be easily appreciated how much stronger boards become with more points made. Below, we chart the number of dancing numbers as a function of the number of closed inner board points:

We see that every additional point made in our home board contributes a substantial number of dancing numbers, and the benefits quickly add up. For example, if we have a 3-point board, and Gary only has a 1-point board, any of his checkers that end up on the bar are 9 times more likely to stay there than any of ours. Viewed through this lens, we actually welcome contact and a blot-hitting contest; the outcome will largely favour us.

The increase in dancing numbers only makes up half the benefit of a strong board. The second, more subtle benefit is the loss of flexibility when coming off the bar. Consider the following position:

We hit one of Gary’s checkers, but unfortunately in doing so, we left him a direct shot on the 14-pt. A direct shot usually means at least 11 hitting numbers; however, though he would love to use a 2 to hit us, Gary could will likely need that 2 (or a 5) to enter from the bar. Our strong board has reduced his hitting numbers to just 3: 52, 25, and 221. Our board strength has indirectly protected the blot on the 14-pt from harm.

Another significant consideration in assessing board strength is the presence of blots in the homeboard. In the position above, Gary has a blot in his homeboard on the 24-pt. This blot will make him hesitate to hit us, even if he happens to roll one of those rare hitting numbers, since he will be forced to gift us 11 return shots from the bar. All things considered, if we were to assess our boards’ relative strengths, our board not only has more points made (4 vs 3), but his board has a blot in it, making it even weaker than a typical 3-point board. Eventually, noticing this disparity in relative board strengths becomes second nature, guiding nearly every checker play decision.

We are emphasizing this point early in our module on intermediate checker play to highlight the importance of making inner board points. In the early game, if a roll gifts us a safe play to build up our board strength, it is right more often than not. Even when our opponents have escaped their backcheckers, if there is contact left in the game, it is worth building up our inner board quickly to prepare for any ensuing battles.

Further reading:
  1. A quick trick to approximate the number of hitting numbers from the bar is the count the number of entering numbers (here 2: 2 and 5) and the number of direct hits (just 1: 2) and multiplying them by each other and doubling the result. In the position above, this adds up to 2 × 2 × 1 = 4. ↩︎

Next lesson: Just make the 5-point

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