In 501 Essential Backgammon Problems, Robertie writes (p. 354) that the optimal bear-off structure is a triangle with 5 pips on the 6 point, 5 pips on the 5 point, ..., and 1 pip on the 2 point.

However, in Backgammon Bootcamp, Trice (p. 135) writes that the optimal bearoff structure is 7 pips on the 6 point, 5 pips on the 5 point, and 3 pips on the 4 point. Kit Woolsey agrees.

Are these recommendations contradictory, or are they somehow intended to apply to different situations? And if they are indeed contradictory, who is right?

Of course you should prefer 543210 over 753000. 753000 leaves you with 79 pips to go, but 543210 leaves you with only 70 pips to go!

A better answer: You should aim for 753000 if possible; this is the 15-checker bearoff position with the least wastage. However, it is rare that you can achieve this exact position while bearing in.

The best answer: Actually, both positions are correct. 753000 is best* if your pip count is 79, and 543210 is best* if your pip count is 70. In bearing in, the dice determine what your pip count will be, and the position you should aim for depends on your pip count.

(* best among positions where all 15 checkers are still on the board)

Cheers,
Tom

Hi Tom,

Thanks for your answer. So to clarify: when I am bearing in, I should aim for 753, NOT the 'triangle' of 54321?

(I understand that the triangle may be the optimal distribution holding the pip count fixed at 70; however, what I really want to know is what distribution I should be aiming for when preparing to bear off!)

753 will waste slightly fewer pips on average than 54321, so yes, aim for that if you can.

If you already have checkers on your 1 and 2 points, you should aim for a slightly flatter structure with more checkers on your 5 and 4 points. The reason is if you have nothing on your 1 point and you hit a gap on your 5, it's not a such a big deal to play 6/1. It's just one checker down there and you'll probably roll a 1 at some point. But if you already have 2 checkers on your 1, and you have play 6/1 with a 5, that's pretty wasteful to put a 3rd checker there.

This stuff is all pretty minor. It's hard to make a big error if you know the basics.

Thanks!

So, just to try to apply this to real world...

If I'm in a pure racing game, aim for something closer to the 753 structure which basically means, make the most of my crossovers and don't waste too many pips making the crossovers to get to my inner board?

If I'm not in a pure racing game, I'm likely to already have made a couple points (or more) on my inner board and I should aim more for the triangle, which is probably the same concept of minimizing waste on my crossovers into my inner board?

Did I oversimplify that? Does that make sense? Both are right in different situations but are trying to convey the same concept of minimizing waste in crossovers?

Here's how I would explain it.

In the vast majority of games, by the time you reach a pure race you'll already have some points made in your inner board. In this case you're going to be aiming at something like "Woolsey's Wedge" (5-4-3-2-1).

In a few games, you'll break contact very early, before your inner board has started to be built. In this case you're shooting for "Trice's Tower" (7-5-3).

In my own experience, I've reached something like Woolsey's Wedge many many times, but only once or twice have I ever constructed Trice's Tower.

Thanks - that makes complete sense!

Thank you.