Mental shift method

The mental shift method is a relative count method that is as old as time. It was described in Magriel’s classic Backgammon, and is very simple and intuitive. I don’t know that it’s worth using in every single position, but in some, it’s certainly by far the best tool for the job. Let’s study a position to see where it can used effectively.

This is a position we’ve previously discussed in doubling in racing positions: we have 88 pips remaining and Gary has 97, for a difference of only 9 pips. In that lesson, we stressed the importance of the race on the cube action, but we didn’t outline how you would obtain the pip count. The relative count can be computed nearly instantly in a position that has a lot of symmetry, like this one.

The figure below shows the mental shift method in action:

In order to make our checkers look like Gary’s, we just need to shift a handful of checkers:

• The 2 checkers on the 3-pt need to move back 6 pips each to get to the 9-pt.
• The checker on the 10-pt needs to advance 2 pips to get to the 8-pt.
• One of the checkers on the 6-pt needs to advance 1 pip to get to the 5-pt.

In summary, we need to add (−6×2)+2+1=−9 pips to our count to match our opponent’s. In other words, we are leading by 9 pips. A position like this one showcases how quick and easy the mental shift method can be, given some practice.

Colourless mental shifts

The mental shift method is also useful in other symmetric positions where contact hasn’t been broken yet. Consider the holding game position below:

This is the same position as we discussed in the 321 colourless pip count and the unit adjustments lessons, where we computed a relative count of −18 pips. It turns out that this position is much easier to compute using mental shifts. The trick here is to remember that in a relative count, we don’t need to care about the colours of the checkers. So what checkers do we need to move so that our side of the board is identical to our opponent’s side?

• The 2 checkers on the 3-pt need to move back 4 pips each to get to the 7-pt.
• One of the checkers on the 6-pt needs to move back 6 pips to get to the 12-pt.
• One of the checkers on the 8-pt needs to move back 4 pips to get to the 12-pt.

The count adds up to (−4 × 2) − 6 − 4 = −18, which agrees with our other counting methods in much fewer steps. Note that we completely ignore what color the checkers are, and just focus on matching the distribution on both sides of the board.

Hopefully these examples are enough to get you a sense of when this method should be used. Mental shifting is far from a universal tool, but it’s especially powerful in obtaining relative counts for certain close races, prime vs. prime positions, bare-off positions, and well-timed holding games.

Next lesson: Running pip count