Bill Robertie offers this analysis for problem play #2:

"Problem 2 shows a very basic type of middle game double. Structurally, White and Black's positions seem quite similar. Both sides have one man back. Black has one extra point made, but White's builders are well positioned, and he has no checkers out of play. White's rear checker is farther advanced, and therefore has more rolls to run home. With the positions so nearly balanced, wherein lies Black's doubling advantage?

Black's main advantage stems from the fact that he is on roll. In the language of nukespeak, this gives him a first strike capability. He can with the game on the next roll, given a sufficiently strong sequence. White's equity is retaliatory; he has to survive Black's next roll (or next two rolls, or next three rolls), then hang on to win later. White has no way to establish a winning advantage quickly. Black does.

If we divide Black's upcoming rolls into groups, we can see just how strong his initiative is.

Group A: Black points on White's blot (9 rolls - 53, 51, 31, 55, 33, 11). White is in serious danger whether he reenters or not. Black will have a 4-point board while White will not make an additional point.

Group B: Black hits the blot on the 15-point (4 rolls - 63, 54). White is forced into a 3-point game at best.

Group C: Black escapes his last checker (4 rolls - 65, 64). If White doesn't hot after 64, the game will be a race with Black leading by 25 pips less White's roll.

Group D: Black hits lose on the 3-point (12 rolls - 61, 52, 43, 41, 32, 21). White has 14 rolls to hit back, after which he has the edge. He misses with 22 rolls, after which Black has a more sizeable edge.

Group E: Big doubles (3 rolls - 66, 44, 22). Black makes a 5-prime and increases his racing lead.

Group F: Nullo rolls (4 rolls - 62, 42). Black plays 13/5 or makes the 2-point. He remains with a slight edge.

Black has no bad rolls, and a number of sequences that could lose his market: the perfect criteria for a strong initial double. White's position is sound enough so that he has a clear take. (His negative equity after accepting is about -0.6 points.) The lesson of this position is crucial to understanding early and middle game doubling: a slight structural advantage, combined with the roll and some clear threats, often produces a strong initial double.

Before leaving this position, it is worthwhile to make two further points. First, White would be better off if his rear checker were back on the 24-point rather than advanced to the 22-point. Black would have fewer attacking chances. I criticized the "European split" in the opening as giving the opponent too many chances. Even with one man back, the same principle applies. Second, Black's racing edge (125-140 plus the roll) is important even though contact is not yet broken. If there is no further hitting, or the same amount of hitting on both sides, Black retains an advantage in all potential racing variations."