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One Last Point

by Douglas Zare
1 November 2004

Douglas Zare

High-anchor holding games are common, so it is important to understand them. Let's consider one possible phase of a high-anchor holding game. Assume that the midpoint and all points higher than the 8 point have been cleared. The holding side is desperate to hit a shot from a single high anchor. Assume it has little racing equity, but a solid offense if a shot is hit. This is a common scenario, so understanding these positions can help us to make accurate plays game after game

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Subject: Re: One Last Point

From: DBrthrtn Member has a photo available

Date: 03 Nov 2004 20:34 EST

Very good stuff.

I often have questions about when to split in positions like 5S, 5T, and 4Z. Based on 5S and 5T, if you hold the golden anchor and your opponent has only the 8 point to clear, it looks like you should not split if your opponent has his ace through four points, but should if your opponent has only the ace and deuce points (and presumably only the ace). I'm assuming this is due to immediate bad shots in 5T that can be played in 5S, as well as double vs. single shot potential. How about if your opponent has the ace through three points? Maybe if he has lots of spares on the three you don't split, but if the three is stripped you do, or something like that?

Also, in 4Z, with two spares on the three, it looks like splitting is wrong. This makes me think that the previous guess about spares on the three indicating no split from the golden anchor may be correct. How about if the three is vacant, then is splitting more correct from the silver anchor than it is from the golden anchor? And similarly, if the three is stripped, then should one be more inclined to split from the silver anchor than one would be from the golden anchor?

Subject: Re: One Last Point

From: zare

Date: 04 Nov 2004 12:59 EST

Suppose Red has a stripped 8 point, and White has the golden anchor.

If Red has the lowest 4 points, White should not split.

If Red has the lowest 3 points, White should split with an ace.

If Red has the lowest 2 points, White should split with an ace or deuce.

If Red has just the ace point, White should split with anything. White prefers a blot to an anchor.

Spares don't seem to affet this decision much. If Red has a blot and three points behind the anchor, it can become right to split with a deuce.

Suppose Red has a stripped 8 points, and White has the silver anchor.

If Red has 3 points behind the anchor, White should not split.

If Red has the lower 2 points behind the anchor, White should split with any ace or deuce.

If Red has just the ace point, White should split with any ace, deuce, or trey, but prefers an anchor to a blot.

Suppose Red has a stipped 8 point and the lowest two points.

Splitting 20/19 gains 0.109 (cubeless).

Splitting 20/18 gains 0.008.

Splitting 21/20 gains 0.112.

Splitting 21/19 gains 0.045.

Splitting 21/18 costs 0.086.

I think these can be explained by looking at how Red's rolls play. When Red has more points, Red isn't able to stall very frequently. However, Red can pick-and-pass more frequently if White has split, and that possibility has to be weighed against improving some single shots to double shots. Also, if Red has more points and hits, it is harder for White to hit from the bar.

Douglas Zare

Subject: Re: One Last Point

From: DBrthrtn Member has a photo available

Date: 06 Nov 2004 00:16 EST

More good stuff - thanks. It seems odd to me that moving the anchor back makes it less correct to split. But, now that I've seen the answers, maybe I can rationalize it. :) I suppose that with the anchor further back Red will have more bad numbers anyway, so splitting becomes redundant for White. Also, the case where White prefers a blot to an anchor is very interesting. I don't think that I've seen that result anywhere else before.

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