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Backgammon + The Goldilocks Zone - Define - Rollout - Long

Posted By: Timothy Chow
Date: Sunday, 4 May 2014, at 6:41 p.m.

In Response To: Backgammon + The Goldilocks Zone - Define - Rollout - Long (Stick)

A quick search through the BG archives shows Chuck Bower using the term "Goldilocks" (though not "Goldilocks zone") for a 'tweener play that tries to compromise between two competing objectives. I don't think that anyone will contest priority for using "Goldilocks zone" for an ideal racing lead in a high-anchor holding game, but in my opinion, you may want to think twice before using such a useful word like "Goldilocks" for such a narrow concept. After reading your Gammon Village article where you talked about this, I kept an eye out in my own games for this principle, and found that it wasn't of as much practical use as I thought it might be, for the following reason. When you're shuffling checkers around freely constructing variants and reference positions, it is natural to play around with the holdee's race lead. However, I've found that it just isn't that common in practice for the holdee to get into such lopsided pip-count positions with a centered cube. The most likely scenarios in my experience have been:

1. The holdee creeps up on it without any big doublets. Typically this means the holdee missed a double along the way.

2. The holdee suddenly rolls big doublets. In that case, the resulting position doesn't usually look like your reference position. Both sides will have checker distributions that are more ragged, in a way that often favors the holdee and permits him to double.

3. The game starts off as a mutual holding game where the player with the big race lead clearly can't double, and then rolls small doublets to advance the rear anchor and turn it into a one-way holding game. This is the case most similar to your reference position, and doubling is often wrong. It's often fairly clear that doubling is wrong, though, because the midpoint usually won't have a spare on it.

Case 3 does arise in practice, but far less frequently than normal holding games do. For that reason your "Goldilocks zone" seems to me to be of limited practical value. In my experience, if I arrive at a holding-game position with a big race lead, then the circumstances will usually be such that doubling is the reasonable thing to do. There will be exceptions, but they are exceptions.

Regarding your other observations:

• I haven't seen your Keith Count exceptions specifically before, but when the race is that long I usually don't bother with the Keith Count. I just use Trice's rule of dividing the leader's pip count by 10, rounding up, and adding 1. It's only if it's a shorter race, or there's some funny distribution where I have to estimate wastage, that I use the Keith Count.

• Your 7-away match-equity trick is one that I first heard from you here and I have found it useful. A slight annoyance, though, is that Rockwell–Kazaross says that 3a7a is 24% rather than 23%.

• The 3-away/many-away rule is again one that I heard first explicitly articulated from you. A slight flaw is that when you first formulated the rule, you didn't have the crucial rider about gammons. However, I agree with you that since nobody seems to have challenged your priority after all this time, and this is the most well-known rule with your name attached to it, it seems that you're entitled to claim it.

• I still don't know what your DMP rule is. I haven't seen any formulation of it that both makes sense and seems original. One of the main lessons that the bots taught the BG community was that they hadn't been paying attention to gammons enough. So focusing on the play that wins most often is hardly a new concept.

• Your second-roll 66 rule is new to me. It sounds useful; I'll have to remember it.

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