One Extra Point

by Douglas Zare
4 March 2015

Douglas Zare

One of the most important features of a contact backgammon position is board strength. While the qualities of the boards matter, it is easy to classify positions by the numbers of home board points. How important is it to have a 2:1 board strength advantage, compared with a 3:2 advantage?

I was surprised to hear a guideline that a 2:1 board strength advantage is more valuable than a 3:2 advantage. My intuition was the opposite, since it is often harder to make a third inner board point than the second. The second inner board point only adds 3/36 ways to dance with one checker on the bar (in addition to 6-6), while the third inner board point adds 5/36 ways to dance (9/36 ways to dance minus the 4/36 without the third point). In this column, we will test the heuristic that a 2:1 advantage is more valuable than a 3:2 board strength advantage in a few situations in the opening.

1a. White to roll.

After an opening 3-1, Red has an EMG of about 0.230. Is Red's position better or worse than this if we give both players another point, say with a 5-3 each before Red's 3-1?

1b. White to roll.

It is debatable whether this counts as giving each side another point since Red lost the 8 point. If we give Red an extra home board point, this will mean Red has fewer spares some of the time, and that Red has lost a point elsewhere some of the time.

The value of this position with White on roll is 0.180 EMG to Red. So, in this case, the 3:2 home board advantage was worth less than a 2:1 home board advantage. What happens if we remake the 8 point, and give White 5 more pips, too?
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