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Pieces of the Backgammon Puzzle: Bearing Off vs the Ace Point

by Bart Brooks
25 April 2008

Bart Brooks

We would all like to be able to play like a world class master. Actually, you can and you do. Think about it. There are some small segments of the game that you play as well as any master. I like to look at backgammon as being able to be broken down into sections, let us say like the small pieces of a 1000 piece jigsaw puzzle. While you may not have the whole picture you can surely get a single piece just perfect. A master can do no better. Add all the pieces together and you have a masterpiece.`

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Subject: Re: Pieces of the Backgammon Puzzle: Bearing Off vs the Ace Point

From: Mr_Pedantic

Date: 25 Apr 2008 09:29 EST

Didn't Danny Kleinman write about this in his books? Are we paying subscriptions to GammonVillage to read what we have read before?

Subject: Re: Pieces of the Backgammon Puzzle: Bearing Off vs the Ace Point

From: Justin011234

Date: 26 Apr 2008 16:56 EST

Great NEW stuff, Bart. You are a real backgammon scientist in search of absolute truth, something your rollouts come closer to "bearing out" than anything Kleinman had available for such analysis. No disrespect whatsoever to Danny, but I don't recall these same conclusions having been noted at any point in his writings.

You provided some great rules of thumb that have perplexed me in the past... thanks.

Subject: Re: Pieces of the Backgammon Puzzle: Bearing Off vs the Ace Point

From: Perry

Date: 27 Apr 2008 10:37 EST

The position and rolls, rollout data, and your observations has sharpened my understanding of what is going on in these types of positions. Thanks for the work and I look forward to more of your contributions.

I do have 4 suggestions if you publish this kind of data again:

1. Give the answers to each roll immediately after the problem. Going back and forth to a table at the end is not nearly as convenient.

2. Highlight the DMP results where they differ from the money game results.

3. Use a 6 prime rather than a 5 prime for the defending side. The difference may be small but why not reduce the variable of a hit checker escaping to what ever extent possible?

4. Use 3 ply precise instead of 2. I don't know if it matters in contact bear-offs but it probably does in branches that develop after being hit, and the difference in cpu time using 7 truncated is quite small. In general 3 ply results yield higher level of play data and more reliable equities.

Subject: Re: Pieces of the Backgammon Puzzle: Bearing Off vs the Ace Point

From: Coolrey

Date: 30 Apr 2008 13:14 EST

Hi Bart,

I agree with Perry. Need the answers at the end of the problems. I only looked at the first problem then started scrolling to find the answer. It took awhile to get there, and then there appeared to be a typo on the very first answer! (moving 3 checkers 6/3 and one checker 5/3 w double twos can't be right).

I would tend to trust your results, and don't recommend you make them 3 ply. Time and effort are wasted and if an answer flip flops well, it was very close anyway. What you want is a rule of thumb like the 65 rule you came up with. I was surprised you didn't find more than that, though.

Ray

Subject: Re: Pieces of the Backgammon Puzzle: Bearing Off vs the Ace Point

From: kimba

Date: 19 May 2008 16:54 EST

I enjoyed & learned from the article, but:

In a whole bunch of positions the roll of 5-4 leaves a shot, but was ignored by the author.

Interesting to note that 2-2 & 6-2, played the exact same way, yield different equities!

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