Trice’s tower

Having learned how to identify the optimal bearoff positions for 2 and 3 checkers, you might be interested in learning what to do with 4 checkers! Well, I don’t know that, but I do know the optimal position for 15 checkers!

It was actually formally calculated in the early 90s using early computer software. The solution is affectionately called Trice’s Tower, named after its discoverer, Walter Trice. It consists of 3 stacks of checkers: 7, 5, and 3 on the 6- 5- and 4- point, respectively:

This is the proven ideal structure with all 15 checkers in our homeboard. 7-5-3, 79 pips total. Memorize this, and when you’re bearing checkers in, aim for this configuration.

I’ll admit that this certainly feels a little bit counterintuitive — wouldn’t we rather have all of our checkers on the ace point? Then we take at least 2 checkers off every shake!

That’s a very reasonable assessment, but it ignores that, to get to the ace point in the first place, we need to roll and move the checkers there. Consider what to do if we roll a 5: it would be better to bear a checker off than to “prepare” it and place it on the ace point.

A different point of view is that any reasonable bear off sequence will, at some point, encounter a position with 79 pips. Any other position with 79 pips will have some wastage compared to this one, so we should strive for it.

Sometimes you already have checkers on the deeper points, and you can no longer build the tower. In those cases, another optimal position to pursue is Woolsey’s Wedge, named after Kit Woolsey:

It’s actually nearly as good as Trice’s tower, but for a 70 pip position.

Further reading:

• The original Chicago Point article by Paul Weaver, where Trice’s Tower was unveiled. Worth a read if only to admire Weaver’s writing. It also has different optimal positions for different numbers of checkers or pips.