In this series, we will look at actual cube or checker play mistakes.
Readers are invited to submit positions that they had trouble with or felt they didn’t understand. It is nice to understand backgammon theory, but getting the plays right at the table is what counts. We will try to explore what the player who erred was thinking or looking at, and what he should have been thinking about.
I receive a number of positions from a player who has been playing and studying the game for many years. I don’t want to give his name, because the point of this column is not to embarrass him. When he gets a position wrong he circulates it, and I think he is probably the most improved player on the U.S. circuit in the past ten years. I will focus on positions he sends me until we start to get positions from readers.
We will try to keep the same format for all problems:
1) State the match score, if any, and the considerations.
2) Review the key features of the position.
3) Explain what happened at the table.
4) We will do a Snowie 3-ply evaluation of the position and a rollout. We will not try to explain why the evaluations and rollouts might differ, but we will rely on the rollout results as being determinative.
5) Then we will try to understand what the players were thinking, and what caused the error.
Black on roll – what is the correct cube action?
1) The match score
The score is 3-3 to 7. The gammonless doubling windows are about the same as for money. If the cube goes to 2, gammons will figure much more prominently. Consider:
Score –2/-4: Match equity 66.4%
Score –4/-2: Match equity 33.6%
Score –0/-4: Match equity 100%
If the cube is turned, gammons will trade almost equally with wins.
2) Key Features
The race is almost even. Black has a solid 5-prime with one white checker back; White has a broken 5-prime with 2 black checkers back.
3) What happened at the table?
Black doubled and white passed.
4) How does the position roll out?
It is a close double and a trivial take. Black wins 63.6% with 17.6% gammons; White wins 38.4% with 11.3% gammons. Once the cube is turned, gammons become very powerful. If it weren’t for this factor and that Black wins about 6% more gammons than White, then doubling would be an error.
5) What were they thinking?
This is an interesting position. The most significant thing that white missed is that he has only one checker back, and black has a lot of work to do before white is fully primed. Look at how
black’s numbers play:
9 numbers dance. After dancing, black isn’t even the favorite anymore! Admittedly, white’s aces are duplicated, but he will hit with all aces except 61.
If Black enters but cannot come up to the 20pt, he is a slight favorite, the game being about even with White owning the cube. He will have the same problem white has, namely digging a checker out from behind a 5-prime.
In fact, white’s only crushing roll is 55, which enters and makes a full prime.
It is easy in backgammon to focus on the best, or the worst, coming sequences.
White focused on his bad sequences. He could indeed end up struggling for a while with the straggler. But he has time to play constructively for several rolls even if he can’t escape. Black has limited ammunition for an attack. He cannot slot the 2-point because of the strength of White’s board, and it will be difficult for him to extend the prime from the back.
White has a lot of ways to get back into the game. Black can dance or enter deep and have trouble escaping. White can step up to the 23-point before Black can attack effectively. White can hit Black as he is running for home. If Black cannot execute his main plan – trap White’s straggler – White will be the favorite.
In positions like this there are two things to ask – how likely is it that you can get into a favorable game plan, and how favorable are those plans? Here White has several viable plans, and all give him good winning chances. That’s what I think White missed.