Deep Anchors

From: DBrthrtn   

"For money play, a well-timed ace point game is worse than resigning a single game (even if backgammons didn't count, allowing you to stay until the bitter end)."

That statement seems to be based on cubeless equities (correct me if I'm wrong). In many cases the cube would be on the side with the ace point anchor. If you factor in cube vig for the side with the anchor, would this still be true?

Great article.

With the cube in play, ace point games are better for the anchored side than closeouts with the same cubeless equity because there are many opportunities to use the cube effectively in the frequent turnarounds. Well-timed ace point games can be slightly better than resigning a single game (on a 2-cube) if there is some awkwardness for the side bearing off. However, without that awkwardness, well- timed ace point games are often worse, 2.2+ passes if someone were to double from the center. They can be much worse if the anchored side has an imperfect offense.

Many poorly-timed ace point games are significantly better than resigning a single game on a 2-cube, making them better than well-timed ace point games. They generate some shots and usually run off the gammon when not hit. Of course, they still aren't takes. Some are 1.8 passes.

I don't agree with the "1/3 wins, 1/3 gammons, 1/3 losses" hypothesis. I'm glad you mentioned it. In a well-timed ace point game, you will almost always lose at least a gammon if you don't hit. While you are a big favorite to get a shot, you are not a favorite to hit. A well-timed ace point game with an ideal offense may win 25%, lose a single 20%, and get gammoned or backgammoned 55% of the time (including at least 8% backgammons). That's what goes into a cubeless equity of 1.1 to 1.2. 1/3-1/3-1/3 sounds like a blitz that is a small pass, worth .667 cubeless.

In many real situations, there are some chances to run off the gammon without hitting, but this also gives up a lot of the value of late hits. Of course, in real positions, hitting one checker is a long way from closing it out. When you have to roll 40 pips to complete a 6-prime, your opponent has many chances to hop the prime, or to advance to the edge so that you must break the prime to attack prematurely.

Taking is much more fun than passing, but if you are considering the paths the game may take, the possibility of a well-timed ace point game usually counts as a negative in money play.

Douglas Zare

The defender hits a lot because deep anchors produce a lot of shots, sometimes double shots, and sometimes repeated shots. That is why the defender can hit more than 11/36 of the time. When the defender does not have enough timing to stay back, or prefers to run off the gammon, this decreases the number of shots, and the shots may be less valuable. You can see some of this from the difference between the shots generated by ace point games when backgammons count or not.

The databases are built with the assumption that there is no chance to run off the gammon. Gammons do count, although their value can be adjusted. (In addition to money play, I have constructed databases for Crawford 3- away, Gammon-Go, DMP, and others.) A late hit will save the gammon, but probably will not win. Trice's contact bearoff database recognizes this, and the value of double hits, unlike the Sconyers backgame database, which treats all hits as equally valuable.

In real situations, your timing is rarely perfect, and your offense may have flaws when you hit a shot. In addition, after a hit, some structures are more likely than others to produce additional blots if you have a prime. I don't yet see a good way to incorporate these additional complications in the database. However, careful study of the database can help you to determine when shots are likely to occur, and you can try to weight the shots by how likely it is that you would be present and how good your offense will be at that time.

Douglas Zare