Two checkers left

The first trick applies in situations where we’re down to the wire in a race against our opponent with only 2 checkers remaining on the board. The question is where to place them to maximize the chances of bearing off both in a single roll. This seems super inconsequential, but the wrong play is usually a blunder, so it’s worth getting right.

For example, consider the position below. Say we roll 61. The 6 is forced (6/off), so how do you play the ace: 2/1 or 4/3?

The “Right Way” to solve this position is to count how many rolls miss if we make the 4/3 play and compare that to how many rolls miss if we play 2/1… and sure, that’s a great skill to master, in general… but who has the time for that?

Thankfully, there’s a very simple trick for these positions. The optimal distance between the last 2 checkers turns out to be whatever is closest to 2.7 pips. If 3 pips is possible, go for that. If not, 2 pips is the next best choice. Then 4 pips, etc. For the position above, that prompts us to play 2/1 and have 3 pips between the 4-pt and the 1-pt.

The astute reader may wonder aloud, “Why 2.7?” It’s a fair question… It’s not like we can actually have 2.7 pips between 2 checkers anyway… besides that, 2.6 or 2.9 would work just as fine…. and actually, for a given roll, one could never find themselves debating between 2 or 3 pips anyway, so why not split the difference and say 2.5? All very good points. The answer is, I’m not quite sure why! This is one of those pieces of backgammon lore that gets passed down from player to player without being questioned too hard. I first learned about it in a lecture by none other than Mochy. As far as I can tell, this number was computed by Backgammon HOF inductee Danny Kleinman, and first put to print in Vision laughs at counting with Advice to the dicelorn (1980). If I ever get the chance to meet him, I’ll ask him.

Further reading:

• A lecture by Mochy on Non-contact positions, where he discusses the 2.7 pip trick (around 21:00).