I like this problem because studying it led me to "see" this position, and others like it, differently. Such changes in vision, in my opinion, are one of the most important contributors to permanent increase in playing strength.
A little while ago I mentioned, as a general comment, that I sometimes ran into positions that I didn't know whether to classify as "blitz" or "containment." Stick found this a little odd. Though not the best example, the present position partially illustrates what I meant. This position definitely falls into the category of "containment" and *not* "blitz"; X is still miles behind in the race, and O's strong board prevents X from hitting loose with wild abandon. X has a clear advantage but O actually wins more gammons from this position than X does.
Nevertheless, OTB one can fall into the trap of adopting a blitz mentality. In a blitz, the rhythm is to hit, to make home-board points, and to bring more ammunition to the front lines as quickly as possible. This is the kind of mentality that leads one to see 12/9 as the natural 3. We want to make the 3pt, don't we?
Well, yes, all other things being equal, making the 3pt is valuable. But all other things are not equal. First of all, O's strong board means that if O hits with a 3, then we have a good chance of dancing. If that happens then we will deeply regret putting that blot on the 9pt for O to have a direct shot at. Second, 12/9 doesn't add all that much value, for two reasons: (a) we already have a whole lot of covering numbers, and (b) covering the 3pt doesn't solve all our problems, because we're still faced with a containment problem (an easier one, to be sure, but far from a slam dunk).
When we're containing, outfield coverage and priming can be as important as, if not more important than, hitting loose and making new home-board points. 16/13 contributes to those strategic goals with considerably less risk than 12/9. The rollout says that 12/9 is a whopper.
Containment is a tricky mixture of attack and defense. It's important to keep that in mind and not to assume that just because we're hitting with half of our roll then the other half of the roll has to be played aggressively. Safety does matter when the opponent's board is strong.
1. Rollout¹ 16/13 4/3* eq:+0.339
Player: 58.34% (G:9.46% B:0.28%)
Opponent: 41.66% (G:17.47% B:0.29%)
Confidence: ±0.010 (+0.329..+0.348) - [100.0%]
2. Rollout¹ 12/9 4/3* eq:+0.227 (-0.111)
Player: 54.97% (G:9.06% B:0.27%)
Opponent: 45.03% (G:19.55% B:0.37%)
Confidence: ±0.010 (+0.218..+0.237) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
eXtreme Gammon Version: 2.10
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Tim Chow