Cash game, White owns the cube.
White to play 3-2
Problem 176 is an example of a type of position that arises fairly frequently, especially at the tail end of a mutual holding game. Black probably held White’s 5-point for a while, then left either to hit a shot or to create a spare on the midpoint. White scores a lucky hit, and now Black is stuck on the bar against a 5-point board.
For lack of a better term, I tend to call these ‘One Man on Bar’ positions, although it’s not really a great title, since there are many very different types of positions with a man caught on the bar. But this particular type of position occurs frequently, so it deserves a name.
Black’s moves from here on will generally be forced, so all the play belongs to White. Each turn he’ll need to decide how to arrange his outfield checkers for best effect, and at some point, if Black stays on the bar, White will have to start thinking about doubling. We’ll revisit the doubling situations in a future problem, but for now let’s just focus on where White’s checkers belong, and how he should play this tricky 3-2.
Rather than count the number of shots Black will have from the bar after various plays, let’s start by asking a simple question: What’s the most important point on the board right now for White? The answer, pretty clearly, is his 11-point, six pips away from the open point in White’s board. Here’s a quick summary of the reasons that make the 11-point so important:
(1) Owning the 11-point ensures that White will get a safe shot at Black after any entering number except 5-5.
(2) Owning the 11-point means that White will have at least two shots (3-3 and 6-6) to close his board every turn. That’s only a 5.5% chance, but over several turns it adds up to a significant probability that White can snuff out resistance without risk. If White later puts a checker on his 10-point, his chance of closing rises to 11% with only a 1-in-36 chance of being hit, which are great odds.
(3) White can keep the 11-point for a long time, while any point in Black’s outfield will need to be dismantled sooner.
White’s general goal is to bring checkers to his outfield, bearing on the 5-point, while leaving minimum shots. The 11-point is really the backbone of this effort, and you want to make it as soon as possible, because owning it makes all your subsequent play easier. That’s true even if making the 11-point leaves an extra indirect somewhere on the first turn.
Points in Black’s outfield like the 13-point and 14-point aren’t nearly so effective since they don’t bear on the 5-point and hence don’t provide a secure platform for applying pressure. Any roll which makes the 11-point is actually a great shot in this position. If a different home board point were open, you’d still want to make the outfield point six pips away. So if the 4-point were the open point in your board, the 10-point would be the key point to make.
Seeing the position this way makes the best play pretty easy: Make the 11-point with 13/11, after which 18/15 is forced.
